--- a/src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML Thu Aug 28 00:40:38 2014 +0200
@@ -359,7 +359,7 @@
Config.put Sledgehammer_Prover_ATP.atp_dest_dir dir
#> Config.put Sledgehammer_Prover_ATP.atp_problem_prefix
("prob_" ^ str0 (Position.line_of pos) ^ "__")
- #> Config.put SMT2_Config.debug_files
+ #> Config.put SMT_Config.debug_files
(dir ^ "/" ^ Name.desymbolize (SOME false) (ATP_Util.timestamp ()) ^ "_"
^ serial_string ())
| set_file_name NONE = I
@@ -541,9 +541,9 @@
ORELSE' sledge_tac 0.2 ATP_Proof.eN "poly_guards??"
ORELSE' sledge_tac 0.2 ATP_Proof.spassN "mono_native"
ORELSE' sledge_tac 0.2 ATP_Proof.z3_tptpN "poly_tags??"
- ORELSE' SMT2_Solver.smt2_tac ctxt thms
+ ORELSE' SMT_Solver.smt_tac ctxt thms
else if !meth = "smt" then
- SMT2_Solver.smt2_tac ctxt thms
+ SMT_Solver.smt_tac ctxt thms
else if full then
Metis_Tactic.metis_tac [ATP_Proof_Reconstruct.full_typesN]
ATP_Proof_Reconstruct.default_metis_lam_trans ctxt thms
--- a/src/HOL/Real.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Real.thy Thu Aug 28 00:40:38 2014 +0200
@@ -2180,10 +2180,10 @@
subsection {* Setup for SMT *}
-ML_file "Tools/SMT2/smt2_real.ML"
-ML_file "Tools/SMT2/z3_new_real.ML"
+ML_file "Tools/SMT/smt_real.ML"
+ML_file "Tools/SMT/z3_real.ML"
-lemma [z3_new_rule]:
+lemma [z3_rule]:
"0 + (x::real) = x"
"x + 0 = x"
"0 * x = 0"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/SMT.thy Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,379 @@
+(* Title: HOL/SMT.thy
+ Author: Sascha Boehme, TU Muenchen
+*)
+
+header {* Bindings to Satisfiability Modulo Theories (SMT) solvers based on SMT-LIB 2 *}
+
+theory SMT
+imports Divides
+keywords "smt_status" :: diag
+begin
+
+subsection {* Triggers for quantifier instantiation *}
+
+text {*
+Some SMT solvers support patterns as a quantifier instantiation
+heuristics. Patterns may either be positive terms (tagged by "pat")
+triggering quantifier instantiations -- when the solver finds a
+term matching a positive pattern, it instantiates the corresponding
+quantifier accordingly -- or negative terms (tagged by "nopat")
+inhibiting quantifier instantiations. A list of patterns
+of the same kind is called a multipattern, and all patterns in a
+multipattern are considered conjunctively for quantifier instantiation.
+A list of multipatterns is called a trigger, and their multipatterns
+act disjunctively during quantifier instantiation. Each multipattern
+should mention at least all quantified variables of the preceding
+quantifier block.
+*}
+
+typedecl 'a symb_list
+
+consts
+ Symb_Nil :: "'a symb_list"
+ Symb_Cons :: "'a \<Rightarrow> 'a symb_list \<Rightarrow> 'a symb_list"
+
+typedecl pattern
+
+consts
+ pat :: "'a \<Rightarrow> pattern"
+ nopat :: "'a \<Rightarrow> pattern"
+
+definition trigger :: "pattern symb_list symb_list \<Rightarrow> bool \<Rightarrow> bool" where
+ "trigger _ P = P"
+
+
+subsection {* Higher-order encoding *}
+
+text {*
+Application is made explicit for constants occurring with varying
+numbers of arguments. This is achieved by the introduction of the
+following constant.
+*}
+
+definition fun_app :: "'a \<Rightarrow> 'a" where "fun_app f = f"
+
+text {*
+Some solvers support a theory of arrays which can be used to encode
+higher-order functions. The following set of lemmas specifies the
+properties of such (extensional) arrays.
+*}
+
+lemmas array_rules = ext fun_upd_apply fun_upd_same fun_upd_other fun_upd_upd fun_app_def
+
+
+subsection {* Normalization *}
+
+lemma case_bool_if[abs_def]: "case_bool x y P = (if P then x else y)"
+ by simp
+
+lemmas Ex1_def_raw = Ex1_def[abs_def]
+lemmas Ball_def_raw = Ball_def[abs_def]
+lemmas Bex_def_raw = Bex_def[abs_def]
+lemmas abs_if_raw = abs_if[abs_def]
+lemmas min_def_raw = min_def[abs_def]
+lemmas max_def_raw = max_def[abs_def]
+
+
+subsection {* Integer division and modulo for Z3 *}
+
+text {*
+The following Z3-inspired definitions are overspecified for the case where @{text "l = 0"}. This
+Schönheitsfehler is corrected in the @{text div_as_z3div} and @{text mod_as_z3mod} theorems.
+*}
+
+definition z3div :: "int \<Rightarrow> int \<Rightarrow> int" where
+ "z3div k l = (if l \<ge> 0 then k div l else - (k div - l))"
+
+definition z3mod :: "int \<Rightarrow> int \<Rightarrow> int" where
+ "z3mod k l = k mod (if l \<ge> 0 then l else - l)"
+
+lemma div_as_z3div:
+ "\<forall>k l. k div l = (if l = 0 then 0 else if l > 0 then z3div k l else z3div (- k) (- l))"
+ by (simp add: z3div_def)
+
+lemma mod_as_z3mod:
+ "\<forall>k l. k mod l = (if l = 0 then k else if l > 0 then z3mod k l else - z3mod (- k) (- l))"
+ by (simp add: z3mod_def)
+
+
+subsection {* Setup *}
+
+ML_file "Tools/SMT/smt_util.ML"
+ML_file "Tools/SMT/smt_failure.ML"
+ML_file "Tools/SMT/smt_config.ML"
+ML_file "Tools/SMT/smt_builtin.ML"
+ML_file "Tools/SMT/smt_datatypes.ML"
+ML_file "Tools/SMT/smt_normalize.ML"
+ML_file "Tools/SMT/smt_translate.ML"
+ML_file "Tools/SMT/smtlib.ML"
+ML_file "Tools/SMT/smtlib_interface.ML"
+ML_file "Tools/SMT/smtlib_proof.ML"
+ML_file "Tools/SMT/smtlib_isar.ML"
+ML_file "Tools/SMT/z3_proof.ML"
+ML_file "Tools/SMT/z3_isar.ML"
+ML_file "Tools/SMT/smt_solver.ML"
+ML_file "Tools/SMT/z3_interface.ML"
+ML_file "Tools/SMT/z3_replay_util.ML"
+ML_file "Tools/SMT/z3_replay_literals.ML"
+ML_file "Tools/SMT/z3_replay_rules.ML"
+ML_file "Tools/SMT/z3_replay_methods.ML"
+ML_file "Tools/SMT/z3_replay.ML"
+ML_file "Tools/SMT/verit_proof.ML"
+ML_file "Tools/SMT/verit_isar.ML"
+ML_file "Tools/SMT/verit_proof_parse.ML"
+ML_file "Tools/SMT/smt_systems.ML"
+
+method_setup smt = {*
+ Scan.optional Attrib.thms [] >>
+ (fn thms => fn ctxt =>
+ METHOD (fn facts => HEADGOAL (SMT_Solver.smt_tac ctxt (thms @ facts))))
+*} "apply an SMT solver to the current goal (based on SMT-LIB 2)"
+
+
+subsection {* Configuration *}
+
+text {*
+The current configuration can be printed by the command
+@{text smt_status}, which shows the values of most options.
+*}
+
+
+subsection {* General configuration options *}
+
+text {*
+The option @{text smt_solver} can be used to change the target SMT
+solver. The possible values can be obtained from the @{text smt_status}
+command.
+
+Due to licensing restrictions, Z3 is not enabled by default. Z3 is free
+for non-commercial applications and can be enabled by setting Isabelle
+system option @{text z3_non_commercial} to @{text yes}.
+*}
+
+declare [[smt_solver = z3]]
+
+text {*
+Since SMT solvers are potentially nonterminating, there is a timeout
+(given in seconds) to restrict their runtime.
+*}
+
+declare [[smt_timeout = 20]]
+
+text {*
+SMT solvers apply randomized heuristics. In case a problem is not
+solvable by an SMT solver, changing the following option might help.
+*}
+
+declare [[smt_random_seed = 1]]
+
+text {*
+In general, the binding to SMT solvers runs as an oracle, i.e, the SMT
+solvers are fully trusted without additional checks. The following
+option can cause the SMT solver to run in proof-producing mode, giving
+a checkable certificate. This is currently only implemented for Z3.
+*}
+
+declare [[smt_oracle = false]]
+
+text {*
+Each SMT solver provides several commandline options to tweak its
+behaviour. They can be passed to the solver by setting the following
+options.
+*}
+
+declare [[cvc3_options = ""]]
+declare [[cvc4_options = ""]]
+declare [[veriT_options = ""]]
+declare [[z3_options = ""]]
+
+text {*
+The SMT method provides an inference mechanism to detect simple triggers
+in quantified formulas, which might increase the number of problems
+solvable by SMT solvers (note: triggers guide quantifier instantiations
+in the SMT solver). To turn it on, set the following option.
+*}
+
+declare [[smt_infer_triggers = false]]
+
+text {*
+Enable the following option to use built-in support for div/mod, datatypes,
+and records in Z3. Currently, this is implemented only in oracle mode.
+*}
+
+declare [[z3_extensions = false]]
+
+
+subsection {* Certificates *}
+
+text {*
+By setting the option @{text smt_certificates} to the name of a file,
+all following applications of an SMT solver a cached in that file.
+Any further application of the same SMT solver (using the very same
+configuration) re-uses the cached certificate instead of invoking the
+solver. An empty string disables caching certificates.
+
+The filename should be given as an explicit path. It is good
+practice to use the name of the current theory (with ending
+@{text ".certs"} instead of @{text ".thy"}) as the certificates file.
+Certificate files should be used at most once in a certain theory context,
+to avoid race conditions with other concurrent accesses.
+*}
+
+declare [[smt_certificates = ""]]
+
+text {*
+The option @{text smt_read_only_certificates} controls whether only
+stored certificates are should be used or invocation of an SMT solver
+is allowed. When set to @{text true}, no SMT solver will ever be
+invoked and only the existing certificates found in the configured
+cache are used; when set to @{text false} and there is no cached
+certificate for some proposition, then the configured SMT solver is
+invoked.
+*}
+
+declare [[smt_read_only_certificates = false]]
+
+
+subsection {* Tracing *}
+
+text {*
+The SMT method, when applied, traces important information. To
+make it entirely silent, set the following option to @{text false}.
+*}
+
+declare [[smt_verbose = true]]
+
+text {*
+For tracing the generated problem file given to the SMT solver as
+well as the returned result of the solver, the option
+@{text smt_trace} should be set to @{text true}.
+*}
+
+declare [[smt_trace = false]]
+
+
+subsection {* Schematic rules for Z3 proof reconstruction *}
+
+text {*
+Several prof rules of Z3 are not very well documented. There are two
+lemma groups which can turn failing Z3 proof reconstruction attempts
+into succeeding ones: the facts in @{text z3_rule} are tried prior to
+any implemented reconstruction procedure for all uncertain Z3 proof
+rules; the facts in @{text z3_simp} are only fed to invocations of
+the simplifier when reconstructing theory-specific proof steps.
+*}
+
+lemmas [z3_rule] =
+ refl eq_commute conj_commute disj_commute simp_thms nnf_simps
+ ring_distribs field_simps times_divide_eq_right times_divide_eq_left
+ if_True if_False not_not
+
+lemma [z3_rule]:
+ "(P \<and> Q) = (\<not> (\<not> P \<or> \<not> Q))"
+ "(P \<and> Q) = (\<not> (\<not> Q \<or> \<not> P))"
+ "(\<not> P \<and> Q) = (\<not> (P \<or> \<not> Q))"
+ "(\<not> P \<and> Q) = (\<not> (\<not> Q \<or> P))"
+ "(P \<and> \<not> Q) = (\<not> (\<not> P \<or> Q))"
+ "(P \<and> \<not> Q) = (\<not> (Q \<or> \<not> P))"
+ "(\<not> P \<and> \<not> Q) = (\<not> (P \<or> Q))"
+ "(\<not> P \<and> \<not> Q) = (\<not> (Q \<or> P))"
+ by auto
+
+lemma [z3_rule]:
+ "(P \<longrightarrow> Q) = (Q \<or> \<not> P)"
+ "(\<not> P \<longrightarrow> Q) = (P \<or> Q)"
+ "(\<not> P \<longrightarrow> Q) = (Q \<or> P)"
+ "(True \<longrightarrow> P) = P"
+ "(P \<longrightarrow> True) = True"
+ "(False \<longrightarrow> P) = True"
+ "(P \<longrightarrow> P) = True"
+ by auto
+
+lemma [z3_rule]:
+ "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not> P)))"
+ by auto
+
+lemma [z3_rule]:
+ "(\<not> True) = False"
+ "(\<not> False) = True"
+ "(x = x) = True"
+ "(P = True) = P"
+ "(True = P) = P"
+ "(P = False) = (\<not> P)"
+ "(False = P) = (\<not> P)"
+ "((\<not> P) = P) = False"
+ "(P = (\<not> P)) = False"
+ "((\<not> P) = (\<not> Q)) = (P = Q)"
+ "\<not> (P = (\<not> Q)) = (P = Q)"
+ "\<not> ((\<not> P) = Q) = (P = Q)"
+ "(P \<noteq> Q) = (Q = (\<not> P))"
+ "(P = Q) = ((\<not> P \<or> Q) \<and> (P \<or> \<not> Q))"
+ "(P \<noteq> Q) = ((\<not> P \<or> \<not> Q) \<and> (P \<or> Q))"
+ by auto
+
+lemma [z3_rule]:
+ "(if P then P else \<not> P) = True"
+ "(if \<not> P then \<not> P else P) = True"
+ "(if P then True else False) = P"
+ "(if P then False else True) = (\<not> P)"
+ "(if P then Q else True) = ((\<not> P) \<or> Q)"
+ "(if P then Q else True) = (Q \<or> (\<not> P))"
+ "(if P then Q else \<not> Q) = (P = Q)"
+ "(if P then Q else \<not> Q) = (Q = P)"
+ "(if P then \<not> Q else Q) = (P = (\<not> Q))"
+ "(if P then \<not> Q else Q) = ((\<not> Q) = P)"
+ "(if \<not> P then x else y) = (if P then y else x)"
+ "(if P then (if Q then x else y) else x) = (if P \<and> (\<not> Q) then y else x)"
+ "(if P then (if Q then x else y) else x) = (if (\<not> Q) \<and> P then y else x)"
+ "(if P then (if Q then x else y) else y) = (if P \<and> Q then x else y)"
+ "(if P then (if Q then x else y) else y) = (if Q \<and> P then x else y)"
+ "(if P then x else if P then y else z) = (if P then x else z)"
+ "(if P then x else if Q then x else y) = (if P \<or> Q then x else y)"
+ "(if P then x else if Q then x else y) = (if Q \<or> P then x else y)"
+ "(if P then x = y else x = z) = (x = (if P then y else z))"
+ "(if P then x = y else y = z) = (y = (if P then x else z))"
+ "(if P then x = y else z = y) = (y = (if P then x else z))"
+ by auto
+
+lemma [z3_rule]:
+ "0 + (x::int) = x"
+ "x + 0 = x"
+ "x + x = 2 * x"
+ "0 * x = 0"
+ "1 * x = x"
+ "x + y = y + x"
+ by (auto simp add: mult_2)
+
+lemma [z3_rule]: (* for def-axiom *)
+ "P = Q \<or> P \<or> Q"
+ "P = Q \<or> \<not> P \<or> \<not> Q"
+ "(\<not> P) = Q \<or> \<not> P \<or> Q"
+ "(\<not> P) = Q \<or> P \<or> \<not> Q"
+ "P = (\<not> Q) \<or> \<not> P \<or> Q"
+ "P = (\<not> Q) \<or> P \<or> \<not> Q"
+ "P \<noteq> Q \<or> P \<or> \<not> Q"
+ "P \<noteq> Q \<or> \<not> P \<or> Q"
+ "P \<noteq> (\<not> Q) \<or> P \<or> Q"
+ "(\<not> P) \<noteq> Q \<or> P \<or> Q"
+ "P \<or> Q \<or> P \<noteq> (\<not> Q)"
+ "P \<or> Q \<or> (\<not> P) \<noteq> Q"
+ "P \<or> \<not> Q \<or> P \<noteq> Q"
+ "\<not> P \<or> Q \<or> P \<noteq> Q"
+ "P \<or> y = (if P then x else y)"
+ "P \<or> (if P then x else y) = y"
+ "\<not> P \<or> x = (if P then x else y)"
+ "\<not> P \<or> (if P then x else y) = x"
+ "P \<or> R \<or> \<not> (if P then Q else R)"
+ "\<not> P \<or> Q \<or> \<not> (if P then Q else R)"
+ "\<not> (if P then Q else R) \<or> \<not> P \<or> Q"
+ "\<not> (if P then Q else R) \<or> P \<or> R"
+ "(if P then Q else R) \<or> \<not> P \<or> \<not> Q"
+ "(if P then Q else R) \<or> P \<or> \<not> R"
+ "(if P then \<not> Q else R) \<or> \<not> P \<or> Q"
+ "(if P then Q else \<not> R) \<or> P \<or> R"
+ by auto
+
+hide_type (open) symb_list pattern
+hide_const (open) Symb_Nil Symb_Cons trigger pat nopat fun_app z3div z3mod
+
+end
--- a/src/HOL/SMT2.thy Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,378 +0,0 @@
-(* Title: HOL/SMT2.thy
- Author: Sascha Boehme, TU Muenchen
-*)
-
-header {* Bindings to Satisfiability Modulo Theories (SMT) solvers based on SMT-LIB 2 *}
-
-theory SMT2
-imports Divides
-keywords "smt2_status" :: diag
-begin
-
-subsection {* Triggers for quantifier instantiation *}
-
-text {*
-Some SMT solvers support patterns as a quantifier instantiation
-heuristics. Patterns may either be positive terms (tagged by "pat")
-triggering quantifier instantiations -- when the solver finds a
-term matching a positive pattern, it instantiates the corresponding
-quantifier accordingly -- or negative terms (tagged by "nopat")
-inhibiting quantifier instantiations. A list of patterns
-of the same kind is called a multipattern, and all patterns in a
-multipattern are considered conjunctively for quantifier instantiation.
-A list of multipatterns is called a trigger, and their multipatterns
-act disjunctively during quantifier instantiation. Each multipattern
-should mention at least all quantified variables of the preceding
-quantifier block.
-*}
-
-typedecl 'a symb_list
-
-consts
- Symb_Nil :: "'a symb_list"
- Symb_Cons :: "'a \<Rightarrow> 'a symb_list \<Rightarrow> 'a symb_list"
-
-typedecl pattern
-
-consts
- pat :: "'a \<Rightarrow> pattern"
- nopat :: "'a \<Rightarrow> pattern"
-
-definition trigger :: "pattern symb_list symb_list \<Rightarrow> bool \<Rightarrow> bool" where
- "trigger _ P = P"
-
-
-subsection {* Higher-order encoding *}
-
-text {*
-Application is made explicit for constants occurring with varying
-numbers of arguments. This is achieved by the introduction of the
-following constant.
-*}
-
-definition fun_app :: "'a \<Rightarrow> 'a" where "fun_app f = f"
-
-text {*
-Some solvers support a theory of arrays which can be used to encode
-higher-order functions. The following set of lemmas specifies the
-properties of such (extensional) arrays.
-*}
-
-lemmas array_rules = ext fun_upd_apply fun_upd_same fun_upd_other fun_upd_upd fun_app_def
-
-
-subsection {* Normalization *}
-
-lemma case_bool_if[abs_def]: "case_bool x y P = (if P then x else y)"
- by simp
-
-lemmas Ex1_def_raw = Ex1_def[abs_def]
-lemmas Ball_def_raw = Ball_def[abs_def]
-lemmas Bex_def_raw = Bex_def[abs_def]
-lemmas abs_if_raw = abs_if[abs_def]
-lemmas min_def_raw = min_def[abs_def]
-lemmas max_def_raw = max_def[abs_def]
-
-
-subsection {* Integer division and modulo for Z3 *}
-
-text {*
-The following Z3-inspired definitions are overspecified for the case where @{text "l = 0"}. This
-Schönheitsfehler is corrected in the @{text div_as_z3div} and @{text mod_as_z3mod} theorems.
-*}
-
-definition z3div :: "int \<Rightarrow> int \<Rightarrow> int" where
- "z3div k l = (if l \<ge> 0 then k div l else - (k div - l))"
-
-definition z3mod :: "int \<Rightarrow> int \<Rightarrow> int" where
- "z3mod k l = k mod (if l \<ge> 0 then l else - l)"
-
-lemma div_as_z3div:
- "\<forall>k l. k div l = (if l = 0 then 0 else if l > 0 then z3div k l else z3div (- k) (- l))"
- by (simp add: z3div_def)
-
-lemma mod_as_z3mod:
- "\<forall>k l. k mod l = (if l = 0 then k else if l > 0 then z3mod k l else - z3mod (- k) (- l))"
- by (simp add: z3mod_def)
-
-
-subsection {* Setup *}
-
-ML_file "Tools/SMT2/smt2_util.ML"
-ML_file "Tools/SMT2/smt2_failure.ML"
-ML_file "Tools/SMT2/smt2_config.ML"
-ML_file "Tools/SMT2/smt2_builtin.ML"
-ML_file "Tools/SMT2/smt2_datatypes.ML"
-ML_file "Tools/SMT2/smt2_normalize.ML"
-ML_file "Tools/SMT2/smt2_translate.ML"
-ML_file "Tools/SMT2/smtlib2.ML"
-ML_file "Tools/SMT2/smtlib2_interface.ML"
-ML_file "Tools/SMT2/smtlib2_proof.ML"
-ML_file "Tools/SMT2/smtlib2_isar.ML"
-ML_file "Tools/SMT2/z3_new_proof.ML"
-ML_file "Tools/SMT2/z3_new_isar.ML"
-ML_file "Tools/SMT2/smt2_solver.ML"
-ML_file "Tools/SMT2/z3_new_interface.ML"
-ML_file "Tools/SMT2/z3_new_replay_util.ML"
-ML_file "Tools/SMT2/z3_new_replay_literals.ML"
-ML_file "Tools/SMT2/z3_new_replay_rules.ML"
-ML_file "Tools/SMT2/z3_new_replay_methods.ML"
-ML_file "Tools/SMT2/z3_new_replay.ML"
-ML_file "Tools/SMT2/verit_proof.ML"
-ML_file "Tools/SMT2/verit_isar.ML"
-ML_file "Tools/SMT2/verit_proof_parse.ML"
-ML_file "Tools/SMT2/smt2_systems.ML"
-
-method_setup smt2 = {*
- Scan.optional Attrib.thms [] >>
- (fn thms => fn ctxt =>
- METHOD (fn facts => HEADGOAL (SMT2_Solver.smt2_tac ctxt (thms @ facts))))
-*} "apply an SMT solver to the current goal (based on SMT-LIB 2)"
-
-
-subsection {* Configuration *}
-
-text {*
-The current configuration can be printed by the command
-@{text smt2_status}, which shows the values of most options.
-*}
-
-
-subsection {* General configuration options *}
-
-text {*
-The option @{text smt2_solver} can be used to change the target SMT
-solver. The possible values can be obtained from the @{text smt2_status}
-command.
-
-Due to licensing restrictions, Z3 is not enabled by default. Z3 is free
-for non-commercial applications and can be enabled by setting Isabelle
-system option @{text z3_non_commercial} to @{text yes}.
-*}
-
-declare [[smt2_solver = z3]]
-
-text {*
-Since SMT solvers are potentially nonterminating, there is a timeout
-(given in seconds) to restrict their runtime.
-*}
-
-declare [[smt2_timeout = 20]]
-
-text {*
-SMT solvers apply randomized heuristics. In case a problem is not
-solvable by an SMT solver, changing the following option might help.
-*}
-
-declare [[smt2_random_seed = 1]]
-
-text {*
-In general, the binding to SMT solvers runs as an oracle, i.e, the SMT
-solvers are fully trusted without additional checks. The following
-option can cause the SMT solver to run in proof-producing mode, giving
-a checkable certificate. This is currently only implemented for Z3.
-*}
-
-declare [[smt2_oracle = false]]
-
-text {*
-Each SMT solver provides several commandline options to tweak its
-behaviour. They can be passed to the solver by setting the following
-options.
-*}
-
-declare [[cvc3_new_options = ""]]
-declare [[cvc4_new_options = ""]]
-declare [[z3_new_options = ""]]
-
-text {*
-The SMT method provides an inference mechanism to detect simple triggers
-in quantified formulas, which might increase the number of problems
-solvable by SMT solvers (note: triggers guide quantifier instantiations
-in the SMT solver). To turn it on, set the following option.
-*}
-
-declare [[smt2_infer_triggers = false]]
-
-text {*
-Enable the following option to use built-in support for div/mod, datatypes,
-and records in Z3. Currently, this is implemented only in oracle mode.
-*}
-
-declare [[z3_new_extensions = false]]
-
-
-subsection {* Certificates *}
-
-text {*
-By setting the option @{text smt2_certificates} to the name of a file,
-all following applications of an SMT solver a cached in that file.
-Any further application of the same SMT solver (using the very same
-configuration) re-uses the cached certificate instead of invoking the
-solver. An empty string disables caching certificates.
-
-The filename should be given as an explicit path. It is good
-practice to use the name of the current theory (with ending
-@{text ".certs"} instead of @{text ".thy"}) as the certificates file.
-Certificate files should be used at most once in a certain theory context,
-to avoid race conditions with other concurrent accesses.
-*}
-
-declare [[smt2_certificates = ""]]
-
-text {*
-The option @{text smt2_read_only_certificates} controls whether only
-stored certificates are should be used or invocation of an SMT solver
-is allowed. When set to @{text true}, no SMT solver will ever be
-invoked and only the existing certificates found in the configured
-cache are used; when set to @{text false} and there is no cached
-certificate for some proposition, then the configured SMT solver is
-invoked.
-*}
-
-declare [[smt2_read_only_certificates = false]]
-
-
-subsection {* Tracing *}
-
-text {*
-The SMT method, when applied, traces important information. To
-make it entirely silent, set the following option to @{text false}.
-*}
-
-declare [[smt2_verbose = true]]
-
-text {*
-For tracing the generated problem file given to the SMT solver as
-well as the returned result of the solver, the option
-@{text smt2_trace} should be set to @{text true}.
-*}
-
-declare [[smt2_trace = false]]
-
-
-subsection {* Schematic rules for Z3 proof reconstruction *}
-
-text {*
-Several prof rules of Z3 are not very well documented. There are two
-lemma groups which can turn failing Z3 proof reconstruction attempts
-into succeeding ones: the facts in @{text z3_rule} are tried prior to
-any implemented reconstruction procedure for all uncertain Z3 proof
-rules; the facts in @{text z3_simp} are only fed to invocations of
-the simplifier when reconstructing theory-specific proof steps.
-*}
-
-lemmas [z3_new_rule] =
- refl eq_commute conj_commute disj_commute simp_thms nnf_simps
- ring_distribs field_simps times_divide_eq_right times_divide_eq_left
- if_True if_False not_not
-
-lemma [z3_new_rule]:
- "(P \<and> Q) = (\<not> (\<not> P \<or> \<not> Q))"
- "(P \<and> Q) = (\<not> (\<not> Q \<or> \<not> P))"
- "(\<not> P \<and> Q) = (\<not> (P \<or> \<not> Q))"
- "(\<not> P \<and> Q) = (\<not> (\<not> Q \<or> P))"
- "(P \<and> \<not> Q) = (\<not> (\<not> P \<or> Q))"
- "(P \<and> \<not> Q) = (\<not> (Q \<or> \<not> P))"
- "(\<not> P \<and> \<not> Q) = (\<not> (P \<or> Q))"
- "(\<not> P \<and> \<not> Q) = (\<not> (Q \<or> P))"
- by auto
-
-lemma [z3_new_rule]:
- "(P \<longrightarrow> Q) = (Q \<or> \<not> P)"
- "(\<not> P \<longrightarrow> Q) = (P \<or> Q)"
- "(\<not> P \<longrightarrow> Q) = (Q \<or> P)"
- "(True \<longrightarrow> P) = P"
- "(P \<longrightarrow> True) = True"
- "(False \<longrightarrow> P) = True"
- "(P \<longrightarrow> P) = True"
- by auto
-
-lemma [z3_new_rule]:
- "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not> P)))"
- by auto
-
-lemma [z3_new_rule]:
- "(\<not> True) = False"
- "(\<not> False) = True"
- "(x = x) = True"
- "(P = True) = P"
- "(True = P) = P"
- "(P = False) = (\<not> P)"
- "(False = P) = (\<not> P)"
- "((\<not> P) = P) = False"
- "(P = (\<not> P)) = False"
- "((\<not> P) = (\<not> Q)) = (P = Q)"
- "\<not> (P = (\<not> Q)) = (P = Q)"
- "\<not> ((\<not> P) = Q) = (P = Q)"
- "(P \<noteq> Q) = (Q = (\<not> P))"
- "(P = Q) = ((\<not> P \<or> Q) \<and> (P \<or> \<not> Q))"
- "(P \<noteq> Q) = ((\<not> P \<or> \<not> Q) \<and> (P \<or> Q))"
- by auto
-
-lemma [z3_new_rule]:
- "(if P then P else \<not> P) = True"
- "(if \<not> P then \<not> P else P) = True"
- "(if P then True else False) = P"
- "(if P then False else True) = (\<not> P)"
- "(if P then Q else True) = ((\<not> P) \<or> Q)"
- "(if P then Q else True) = (Q \<or> (\<not> P))"
- "(if P then Q else \<not> Q) = (P = Q)"
- "(if P then Q else \<not> Q) = (Q = P)"
- "(if P then \<not> Q else Q) = (P = (\<not> Q))"
- "(if P then \<not> Q else Q) = ((\<not> Q) = P)"
- "(if \<not> P then x else y) = (if P then y else x)"
- "(if P then (if Q then x else y) else x) = (if P \<and> (\<not> Q) then y else x)"
- "(if P then (if Q then x else y) else x) = (if (\<not> Q) \<and> P then y else x)"
- "(if P then (if Q then x else y) else y) = (if P \<and> Q then x else y)"
- "(if P then (if Q then x else y) else y) = (if Q \<and> P then x else y)"
- "(if P then x else if P then y else z) = (if P then x else z)"
- "(if P then x else if Q then x else y) = (if P \<or> Q then x else y)"
- "(if P then x else if Q then x else y) = (if Q \<or> P then x else y)"
- "(if P then x = y else x = z) = (x = (if P then y else z))"
- "(if P then x = y else y = z) = (y = (if P then x else z))"
- "(if P then x = y else z = y) = (y = (if P then x else z))"
- by auto
-
-lemma [z3_new_rule]:
- "0 + (x::int) = x"
- "x + 0 = x"
- "x + x = 2 * x"
- "0 * x = 0"
- "1 * x = x"
- "x + y = y + x"
- by (auto simp add: mult_2)
-
-lemma [z3_new_rule]: (* for def-axiom *)
- "P = Q \<or> P \<or> Q"
- "P = Q \<or> \<not> P \<or> \<not> Q"
- "(\<not> P) = Q \<or> \<not> P \<or> Q"
- "(\<not> P) = Q \<or> P \<or> \<not> Q"
- "P = (\<not> Q) \<or> \<not> P \<or> Q"
- "P = (\<not> Q) \<or> P \<or> \<not> Q"
- "P \<noteq> Q \<or> P \<or> \<not> Q"
- "P \<noteq> Q \<or> \<not> P \<or> Q"
- "P \<noteq> (\<not> Q) \<or> P \<or> Q"
- "(\<not> P) \<noteq> Q \<or> P \<or> Q"
- "P \<or> Q \<or> P \<noteq> (\<not> Q)"
- "P \<or> Q \<or> (\<not> P) \<noteq> Q"
- "P \<or> \<not> Q \<or> P \<noteq> Q"
- "\<not> P \<or> Q \<or> P \<noteq> Q"
- "P \<or> y = (if P then x else y)"
- "P \<or> (if P then x else y) = y"
- "\<not> P \<or> x = (if P then x else y)"
- "\<not> P \<or> (if P then x else y) = x"
- "P \<or> R \<or> \<not> (if P then Q else R)"
- "\<not> P \<or> Q \<or> \<not> (if P then Q else R)"
- "\<not> (if P then Q else R) \<or> \<not> P \<or> Q"
- "\<not> (if P then Q else R) \<or> P \<or> R"
- "(if P then Q else R) \<or> \<not> P \<or> \<not> Q"
- "(if P then Q else R) \<or> P \<or> \<not> R"
- "(if P then \<not> Q else R) \<or> \<not> P \<or> Q"
- "(if P then Q else \<not> R) \<or> P \<or> R"
- by auto
-
-hide_type (open) symb_list pattern
-hide_const (open) Symb_Nil Symb_Cons trigger pat nopat fun_app z3div z3mod
-
-end
--- a/src/HOL/SMT_Examples/Boogie.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/SMT_Examples/Boogie.thy Thu Aug 28 00:40:38 2014 +0200
@@ -51,22 +51,22 @@
section {* Verification condition proofs *}
-declare [[smt2_oracle = false]]
-declare [[smt2_read_only_certificates = true]]
+declare [[smt_oracle = false]]
+declare [[smt_read_only_certificates = true]]
-declare [[smt2_certificates = "Boogie_Max.certs2"]]
+declare [[smt_certificates = "Boogie_Max.certs2"]]
boogie_file Boogie_Max
-declare [[smt2_certificates = "Boogie_Dijkstra.certs2"]]
+declare [[smt_certificates = "Boogie_Dijkstra.certs2"]]
boogie_file Boogie_Dijkstra
-declare [[z3_new_extensions = true]]
-declare [[smt2_certificates = "VCC_Max.certs2"]]
+declare [[z3_extensions = true]]
+declare [[smt_certificates = "VCC_Max.certs2"]]
boogie_file VCC_Max
--- a/src/HOL/SMT_Examples/SMT_Examples.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples.thy Thu Aug 28 00:40:38 2014 +0200
@@ -8,19 +8,19 @@
imports Complex_Main
begin
-declare [[smt2_certificates = "SMT_Examples.certs2"]]
-declare [[smt2_read_only_certificates = true]]
+declare [[smt_certificates = "SMT_Examples.certs2"]]
+declare [[smt_read_only_certificates = true]]
section {* Propositional and first-order logic *}
-lemma "True" by smt2
-lemma "p \<or> \<not>p" by smt2
-lemma "(p \<and> True) = p" by smt2
-lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt2
-lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)" by smt2
-lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt2
-lemma "P = P = P = P = P = P = P = P = P = P" by smt2
+lemma "True" by smt
+lemma "p \<or> \<not>p" by smt
+lemma "(p \<and> True) = p" by smt
+lemma "(p \<or> q) \<and> \<not>p \<Longrightarrow> q" by smt
+lemma "(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)" by smt
+lemma "(p1 \<and> p2) \<or> p3 \<longrightarrow> (p1 \<longrightarrow> (p3 \<and> p2) \<or> (p1 \<and> p3)) \<or> p1" by smt
+lemma "P = P = P = P = P = P = P = P = P = P" by smt
lemma
assumes "a \<or> b \<or> c \<or> d"
@@ -30,12 +30,12 @@
and "\<not> (d \<or> False) \<or> c"
and "\<not> (c \<or> (\<not> p \<and> (p \<or> (q \<and> \<not> q))))"
shows False
- using assms by smt2
+ using assms by smt
axiomatization symm_f :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" where
symm_f: "symm_f x y = symm_f y x"
-lemma "a = a \<and> symm_f a b = symm_f b a" by (smt2 symm_f)
+lemma "a = a \<and> symm_f a b = symm_f b a" by (smt symm_f)
(*
Taken from ~~/src/HOL/ex/SAT_Examples.thy.
@@ -227,55 +227,55 @@
and "~x29 \<or> ~x58"
and "~x28 \<or> ~x58"
shows False
- using assms by smt2
+ using assms by smt
lemma "\<forall>x::int. P x \<longrightarrow> (\<forall>y::int. P x \<or> P y)"
- by smt2
+ by smt
lemma
assumes "(\<forall>x y. P x y = x)"
shows "(\<exists>y. P x y) = P x c"
- using assms by smt2
+ using assms by smt
lemma
assumes "(\<forall>x y. P x y = x)"
and "(\<forall>x. \<exists>y. P x y) = (\<forall>x. P x c)"
shows "(EX y. P x y) = P x c"
- using assms by smt2
+ using assms by smt
lemma
assumes "if P x then \<not>(\<exists>y. P y) else (\<forall>y. \<not>P y)"
shows "P x \<longrightarrow> P y"
- using assms by smt2
+ using assms by smt
section {* Arithmetic *}
subsection {* Linear arithmetic over integers and reals *}
-lemma "(3::int) = 3" by smt2
-lemma "(3::real) = 3" by smt2
-lemma "(3 :: int) + 1 = 4" by smt2
-lemma "x + (y + z) = y + (z + (x::int))" by smt2
-lemma "max (3::int) 8 > 5" by smt2
-lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt2
-lemma "P ((2::int) < 3) = P True" by smt2
-lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt2
+lemma "(3::int) = 3" by smt
+lemma "(3::real) = 3" by smt
+lemma "(3 :: int) + 1 = 4" by smt
+lemma "x + (y + z) = y + (z + (x::int))" by smt
+lemma "max (3::int) 8 > 5" by smt
+lemma "abs (x :: real) + abs y \<ge> abs (x + y)" by smt
+lemma "P ((2::int) < 3) = P True" by smt
+lemma "x + 3 \<ge> 4 \<or> x < (1::int)" by smt
lemma
assumes "x \<ge> (3::int)" and "y = x + 4"
shows "y - x > 0"
- using assms by smt2
+ using assms by smt
-lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt2
+lemma "let x = (2 :: int) in x + x \<noteq> 5" by smt
lemma
fixes x :: real
assumes "3 * x + 7 * a < 4" and "3 < 2 * x"
shows "a < 0"
- using assms by smt2
+ using assms by smt
-lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt2
+lemma "(0 \<le> y + -1 * x \<or> \<not> 0 \<le> x \<or> 0 \<le> (x::int)) = (\<not> False)" by smt
lemma "
(n < m \<and> m < n') \<or> (n < m \<and> m = n') \<or> (n < n' \<and> n' < m) \<or>
@@ -285,7 +285,7 @@
(m < n \<and> n < n') \<or> (m < n \<and> n' = n) \<or> (m < n' \<and> n' < n) \<or>
(m = n \<and> n < n') \<or> (m = n' \<and> n' < n) \<or>
(n' = m \<and> m = (n::int))"
- by smt2
+ by smt
text{*
The following example was taken from HOL/ex/PresburgerEx.thy, where it says:
@@ -307,79 +307,79 @@
x6 = abs x5 - x4; x7 = abs x6 - x5; x8 = abs x7 - x6;
x9 = abs x8 - x7; x10 = abs x9 - x8; x11 = abs x10 - x9 \<rbrakk>
\<Longrightarrow> x1 = x10 \<and> x2 = (x11::int)"
- by smt2
+ by smt
-lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt2
+lemma "let P = 2 * x + 1 > x + (x::real) in P \<or> False \<or> P" by smt
lemma "x + (let y = x mod 2 in 2 * y + 1) \<ge> x + (1::int)"
- using [[z3_new_extensions]] by smt2
+ using [[z3_extensions]] by smt
lemma "x + (let y = x mod 2 in y + y) < x + (3::int)"
- using [[z3_new_extensions]] by smt2
+ using [[z3_extensions]] by smt
lemma
assumes "x \<noteq> (0::real)"
shows "x + x \<noteq> (let P = (abs x > 1) in if P \<or> \<not> P then 4 else 2) * x"
- using assms [[z3_new_extensions]] by smt2
+ using assms [[z3_extensions]] by smt
lemma
assumes "(n + m) mod 2 = 0" and "n mod 4 = 3"
shows "n mod 2 = 1 \<and> m mod 2 = (1::int)"
- using assms [[z3_new_extensions]] by smt2
+ using assms [[z3_extensions]] by smt
subsection {* Linear arithmetic with quantifiers *}
-lemma "~ (\<exists>x::int. False)" by smt2
-lemma "~ (\<exists>x::real. False)" by smt2
+lemma "~ (\<exists>x::int. False)" by smt
+lemma "~ (\<exists>x::real. False)" by smt
-lemma "\<exists>x::int. 0 < x" by smt2
+lemma "\<exists>x::int. 0 < x" by smt
lemma "\<exists>x::real. 0 < x"
- using [[smt2_oracle=true]] (* no Z3 proof *)
- by smt2
+ using [[smt_oracle=true]] (* no Z3 proof *)
+ by smt
-lemma "\<forall>x::int. \<exists>y. y > x" by smt2
+lemma "\<forall>x::int. \<exists>y. y > x" by smt
-lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt2
-lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt2
-lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt2
-lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt2
-lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt2
-lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt2
-lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt2
-lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt2
-lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt2
-lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt2
-lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt2
-lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt2
+lemma "\<forall>x y::int. (x = 0 \<and> y = 1) \<longrightarrow> x \<noteq> y" by smt
+lemma "\<exists>x::int. \<forall>y. x < y \<longrightarrow> y < 0 \<or> y >= 0" by smt
+lemma "\<forall>x y::int. x < y \<longrightarrow> (2 * x + 1) < (2 * y)" by smt
+lemma "\<forall>x y::int. (2 * x + 1) \<noteq> (2 * y)" by smt
+lemma "\<forall>x y::int. x + y > 2 \<or> x + y = 2 \<or> x + y < 2" by smt
+lemma "\<forall>x::int. if x > 0 then x + 1 > 0 else 1 > x" by smt
+lemma "if (ALL x::int. x < 0 \<or> x > 0) then False else True" by smt
+lemma "(if (ALL x::int. x < 0 \<or> x > 0) then -1 else 3) > (0::int)" by smt
+lemma "~ (\<exists>x y z::int. 4 * x + -6 * y = (1::int))" by smt
+lemma "\<exists>x::int. \<forall>x y. 0 < x \<and> 0 < y \<longrightarrow> (0::int) < x + y" by smt
+lemma "\<exists>u::int. \<forall>(x::int) y::real. 0 < x \<and> 0 < y \<longrightarrow> -1 < x" by smt
+lemma "\<exists>x::int. (\<forall>y. y \<ge> x \<longrightarrow> y > 0) \<longrightarrow> x > 0" by smt
lemma "\<forall>x::int.
- SMT2.trigger (SMT2.Symb_Cons (SMT2.Symb_Cons (SMT2.pat x) SMT2.Symb_Nil) SMT2.Symb_Nil)
- (x < a \<longrightarrow> 2 * x < 2 * a)" by smt2
-lemma "\<forall>(a::int) b::int. 0 < b \<or> b < 1" by smt2
+ SMT.trigger (SMT.Symb_Cons (SMT.Symb_Cons (SMT.pat x) SMT.Symb_Nil) SMT.Symb_Nil)
+ (x < a \<longrightarrow> 2 * x < 2 * a)" by smt
+lemma "\<forall>(a::int) b::int. 0 < b \<or> b < 1" by smt
subsection {* Non-linear arithmetic over integers and reals *}
lemma "a > (0::int) \<Longrightarrow> a*b > 0 \<Longrightarrow> b > 0"
- using [[smt2_oracle, z3_new_extensions]]
- by smt2
+ using [[smt_oracle, z3_extensions]]
+ by smt
lemma "(a::int) * (x + 1 + y) = a * x + a * (y + 1)"
- using [[z3_new_extensions]]
- by smt2
+ using [[z3_extensions]]
+ by smt
lemma "((x::real) * (1 + y) - x * (1 - y)) = (2 * x * y)"
- using [[z3_new_extensions]]
- by smt2
+ using [[z3_extensions]]
+ by smt
lemma
"(U::int) + (1 + p) * (b + e) + p * d =
U + (2 * (1 + p) * (b + e) + (1 + p) * d + d * p) - (1 + p) * (b + d + e)"
- using [[z3_new_extensions]] by smt2
+ using [[z3_extensions]] by smt
-lemma [z3_new_rule]:
+lemma [z3_rule]:
fixes x :: "int"
assumes "x * y \<le> 0" and "\<not> y \<le> 0" and "\<not> x \<le> 0"
shows False
@@ -389,40 +389,40 @@
section {* Pairs *}
lemma "fst (x, y) = a \<Longrightarrow> x = a"
- using fst_conv by smt2
+ using fst_conv by smt
lemma "p1 = (x, y) \<and> p2 = (y, x) \<Longrightarrow> fst p1 = snd p2"
- using fst_conv snd_conv by smt2
+ using fst_conv snd_conv by smt
section {* Higher-order problems and recursion *}
lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> (f (i1 := v1, i2 := v2)) i = f i"
- using fun_upd_same fun_upd_apply by smt2
+ using fun_upd_same fun_upd_apply by smt
lemma "(f g (x::'a::type) = (g x \<and> True)) \<or> (f g x = True) \<or> (g x = True)"
- by smt2
+ by smt
lemma "id x = x \<and> id True = True"
- by (smt2 id_def)
+ by (smt id_def)
lemma "i \<noteq> i1 \<and> i \<noteq> i2 \<Longrightarrow> ((f (i1 := v1)) (i2 := v2)) i = f i"
- using fun_upd_same fun_upd_apply by smt2
+ using fun_upd_same fun_upd_apply by smt
lemma
"f (\<exists>x. g x) \<Longrightarrow> True"
"f (\<forall>x. g x) \<Longrightarrow> True"
- by smt2+
+ by smt+
-lemma True using let_rsp by smt2
-lemma "le = op \<le> \<Longrightarrow> le (3::int) 42" by smt2
-lemma "map (\<lambda>i::int. i + 1) [0, 1] = [1, 2]" by (smt2 list.map)
-lemma "(ALL x. P x) \<or> ~ All P" by smt2
+lemma True using let_rsp by smt
+lemma "le = op \<le> \<Longrightarrow> le (3::int) 42" by smt
+lemma "map (\<lambda>i::int. i + 1) [0, 1] = [1, 2]" by (smt list.map)
+lemma "(ALL x. P x) \<or> ~ All P" by smt
fun dec_10 :: "int \<Rightarrow> int" where
"dec_10 n = (if n < 10 then n else dec_10 (n - 10))"
-lemma "dec_10 (4 * dec_10 4) = 6" by (smt2 dec_10.simps)
+lemma "dec_10 (4 * dec_10 4) = 6" by (smt dec_10.simps)
axiomatization
eval_dioph :: "int list \<Rightarrow> int list \<Rightarrow> int"
@@ -437,9 +437,9 @@
"(eval_dioph ks xs = l) =
(eval_dioph ks (map (\<lambda>x. x mod 2) xs) mod 2 = l mod 2 \<and>
eval_dioph ks (map (\<lambda>x. x div 2) xs) = (l - eval_dioph ks (map (\<lambda>x. x mod 2) xs)) div 2)"
- using [[smt2_oracle = true]] (*FIXME*)
- using [[z3_new_extensions]]
- by (smt2 eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
+ using [[smt_oracle = true]] (*FIXME*)
+ using [[z3_extensions]]
+ by (smt eval_dioph_mod[where n=2] eval_dioph_div_mult[where n=2])
context complete_lattice
@@ -449,7 +449,7 @@
assumes "Sup {a | i::bool. True} \<le> Sup {b | i::bool. True}"
and "Sup {b | i::bool. True} \<le> Sup {a | i::bool. True}"
shows "Sup {a | i::bool. True} \<le> Sup {a | i::bool. True}"
- using assms by (smt2 order_trans)
+ using assms by (smt order_trans)
end
@@ -460,7 +460,7 @@
lemma poly_Pred: "Pred x \<and> (Pred [x] \<or> \<not> Pred [x])" by (simp add: Pred_def)
-lemma "Pred (1::int)" by (smt2 poly_Pred)
+lemma "Pred (1::int)" by (smt poly_Pred)
axiomatization g :: "'a \<Rightarrow> nat"
axiomatization where
@@ -468,6 +468,6 @@
g2: "g None = g []" and
g3: "g xs = length xs"
-lemma "g (Some (3::int)) = g (Some True)" by (smt2 g1 g2 g3 list.size)
+lemma "g (Some (3::int)) = g (Some True)" by (smt g1 g2 g3 list.size)
end
--- a/src/HOL/SMT_Examples/SMT_Tests.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/SMT_Examples/SMT_Tests.thy Thu Aug 28 00:40:38 2014 +0200
@@ -8,7 +8,7 @@
imports Complex_Main
begin
-smt2_status
+smt_status
text {* Most examples are taken from various Isabelle theories and from HOL4. *}
@@ -23,7 +23,7 @@
"True \<or> False"
"False \<longrightarrow> True"
"\<not> (False \<longleftrightarrow> True)"
- by smt2+
+ by smt+
lemma
"P \<or> \<not> P"
@@ -62,7 +62,7 @@
"\<not> (P \<longleftrightarrow> \<not> P)"
"(P \<longrightarrow> Q) \<longleftrightarrow> (\<not> Q \<longrightarrow> \<not> P)"
"P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P"
- by smt2+
+ by smt+
lemma
"(if P then Q1 else Q2) \<longleftrightarrow> ((P \<longrightarrow> Q1) \<and> (\<not> P \<longrightarrow> Q2))"
@@ -71,14 +71,14 @@
"(if P1 \<and> P2 then Q1 else Q2) \<longleftrightarrow> (if P1 then if P2 then Q1 else Q2 else Q2)"
"(P1 \<longrightarrow> (if P2 then Q1 else Q2)) \<longleftrightarrow>
(if P1 \<longrightarrow> P2 then P1 \<longrightarrow> Q1 else P1 \<longrightarrow> Q2)"
- by smt2+
+ by smt+
lemma
"case P of True \<Rightarrow> P | False \<Rightarrow> \<not> P"
"case P of False \<Rightarrow> \<not> P | True \<Rightarrow> P"
"case \<not> P of True \<Rightarrow> \<not> P | False \<Rightarrow> P"
"case P of True \<Rightarrow> (Q \<longrightarrow> P) | False \<Rightarrow> (P \<longrightarrow> Q)"
- by smt2+
+ by smt+
section {* First-order logic with equality *}
@@ -91,7 +91,7 @@
"x = y \<longrightarrow> g x y = g y x"
"f (f x) = x \<and> f (f (f (f (f x)))) = x \<longrightarrow> f x = x"
"((if a then b else c) = d) = ((a \<longrightarrow> (b = d)) \<and> (\<not> a \<longrightarrow> (c = d)))"
- by smt2+
+ by smt+
lemma
"\<forall>x. x = x"
@@ -104,11 +104,11 @@
"(\<forall>x. P x \<longrightarrow> P (f x)) \<and> P d \<longrightarrow> P (f(f(f(d))))"
"(\<forall>x y. s x y = s y x) \<longrightarrow> a = a \<and> s a b = s b a"
"(\<forall>s. q s \<longrightarrow> r s) \<and> \<not> r s \<and> (\<forall>s. \<not> r s \<and> \<not> q s \<longrightarrow> p t \<or> q t) \<longrightarrow> p t \<or> r t"
- by smt2+
+ by smt+
lemma
"(\<forall>x. P x) \<and> R \<longleftrightarrow> (\<forall>x. P x \<and> R)"
- by smt2
+ by smt
lemma
"\<exists>x. x = x"
@@ -117,7 +117,7 @@
"(\<exists>x. P x) \<and> R \<longleftrightarrow> (\<exists>x. P x \<and> R)"
"(\<exists>x y z. S x z) \<longleftrightarrow> (\<exists>x z. S x z)"
"\<not> ((\<exists>x. \<not> P x) \<and> ((\<exists>x. P x) \<or> (\<exists>x. P x \<and> Q x)) \<and> \<not> (\<exists>x. P x))"
- by smt2+
+ by smt+
lemma
"\<exists>x y. x = y"
@@ -126,7 +126,7 @@
"\<exists>x. P x \<longrightarrow> P a \<and> P b"
"\<exists>x. (\<exists>y. P y) \<longrightarrow> P x"
"(\<exists>x. Q \<longrightarrow> P x) \<longleftrightarrow> (Q \<longrightarrow> (\<exists>x. P x))"
- by smt2+
+ by smt+
lemma
"(\<not> (\<exists>x. P x)) \<longleftrightarrow> (\<forall>x. \<not> P x)"
@@ -134,7 +134,7 @@
"(\<forall>x y. R x y = x) \<longrightarrow> (\<exists>y. R x y) = R x c"
"(if P x then \<not> (\<exists>y. P y) else (\<forall>y. \<not> P y)) \<longrightarrow> P x \<longrightarrow> P y"
"(\<forall>x y. R x y = x) \<and> (\<forall>x. \<exists>y. R x y) = (\<forall>x. R x c) \<longrightarrow> (\<exists>y. R x y) = R x c"
- by smt2+
+ by smt+
lemma
"\<forall>x. \<exists>y. f x y = f x (g x)"
@@ -145,7 +145,7 @@
"(\<exists>x. \<forall>y. P x \<longleftrightarrow> P y) \<longrightarrow> ((\<exists>x. P x) \<longleftrightarrow> (\<forall>y. P y))"
"\<exists>z. P z \<longrightarrow> (\<forall>x. P x)"
"(\<exists>y. \<forall>x. R x y) \<longrightarrow> (\<forall>x. \<exists>y. R x y)"
- by smt2+
+ by smt+
lemma
"(\<exists>!x. P x) \<longrightarrow> (\<exists>x. P x)"
@@ -153,12 +153,12 @@
"P a \<longrightarrow> (\<forall>x. P x \<longrightarrow> x = a) \<longrightarrow> (\<exists>!x. P x)"
"(\<exists>x. P x) \<and> (\<forall>x y. P x \<and> P y \<longrightarrow> x = y) \<longrightarrow> (\<exists>!x. P x)"
"(\<exists>!x. P x) \<and> (\<forall>x. P x \<and> (\<forall>y. P y \<longrightarrow> y = x) \<longrightarrow> R) \<longrightarrow> R"
- by smt2+
+ by smt+
lemma
"(\<forall>x\<in>M. P x) \<and> c \<in> M \<longrightarrow> P c"
"(\<exists>x\<in>M. P x) \<or> \<not> (P c \<and> c \<in> M)"
- by smt2+
+ by smt+
lemma
"let P = True in P"
@@ -169,33 +169,33 @@
"(let x = y1; z = y2 in R x z) \<longleftrightarrow> (let z = y2; x = y1 in R x z)"
"(let x = y1; z = y2 in R x z) \<longleftrightarrow> (let z = y1; x = y2 in R z x)"
"let P = (\<forall>x. Q x) in if P then P else \<not> P"
- by smt2+
+ by smt+
lemma
"a \<noteq> b \<and> a \<noteq> c \<and> b \<noteq> c \<and> (\<forall>x y. f x = f y \<longrightarrow> y = x) \<longrightarrow> f a \<noteq> f b"
- by smt2
+ by smt
lemma
"(\<forall>x y z. f x y = f x z \<longrightarrow> y = z) \<and> b \<noteq> c \<longrightarrow> f a b \<noteq> f a c"
"(\<forall>x y z. f x y = f z y \<longrightarrow> x = z) \<and> a \<noteq> d \<longrightarrow> f a b \<noteq> f d b"
- by smt2+
+ by smt+
section {* Guidance for quantifier heuristics: patterns *}
lemma
assumes "\<forall>x.
- SMT2.trigger (SMT2.Symb_Cons (SMT2.Symb_Cons (SMT2.pat (f x)) SMT2.Symb_Nil) SMT2.Symb_Nil)
+ SMT.trigger (SMT.Symb_Cons (SMT.Symb_Cons (SMT.pat (f x)) SMT.Symb_Nil) SMT.Symb_Nil)
(f x = x)"
shows "f 1 = 1"
- using assms using [[smt2_trace]] by smt2
+ using assms using [[smt_trace]] by smt
lemma
assumes "\<forall>x y.
- SMT2.trigger (SMT2.Symb_Cons (SMT2.Symb_Cons (SMT2.pat (f x))
- (SMT2.Symb_Cons (SMT2.pat (g y)) SMT2.Symb_Nil)) SMT2.Symb_Nil) (f x = g y)"
+ SMT.trigger (SMT.Symb_Cons (SMT.Symb_Cons (SMT.pat (f x))
+ (SMT.Symb_Cons (SMT.pat (g y)) SMT.Symb_Nil)) SMT.Symb_Nil) (f x = g y)"
shows "f a = g b"
- using assms by smt2
+ using assms by smt
section {* Meta-logical connectives *}
@@ -219,7 +219,7 @@
"(\<And>x y. h x y \<and> h y x) \<Longrightarrow> \<forall>x. h x x"
"(p \<or> q) \<and> \<not> p \<Longrightarrow> q"
"(a \<and> b) \<or> (c \<and> d) \<Longrightarrow> (a \<and> b) \<or> (c \<and> d)"
- by smt2+
+ by smt+
section {* Integers *}
@@ -234,7 +234,7 @@
"-123 + 345 < (567::int)"
"(123456789::int) < 2345678901"
"(-123456789::int) < 2345678901"
- by smt2+
+ by smt+
lemma
"(x::int) + 0 = x"
@@ -242,7 +242,7 @@
"x + y = y + x"
"x + (y + z) = (x + y) + z"
"(x + y = 0) = (x = -y)"
- by smt2+
+ by smt+
lemma
"(-1::int) = - 1"
@@ -250,7 +250,7 @@
"-(x::int) < 0 \<longleftrightarrow> x > 0"
"x > 0 \<longrightarrow> -x < 0"
"x < 0 \<longrightarrow> -x > 0"
- by smt2+
+ by smt+
lemma
"(x::int) - 0 = x"
@@ -259,7 +259,7 @@
"x - y = -(y - x)"
"x - y = -y + x"
"x - y - z = x - (y + z)"
- by smt2+
+ by smt+
lemma
"(x::int) * 0 = 0"
@@ -269,7 +269,7 @@
"x * -1 = -x"
"-1 * x = -x"
"3 * x = x * 3"
- by smt2+
+ by smt+
lemma
"(0::int) div 0 = 0"
@@ -296,8 +296,8 @@
"(-1::int) div -3 = 0"
"(-3::int) div -3 = 1"
"(-5::int) div -3 = 1"
- using [[z3_new_extensions]]
- by smt2+
+ using [[z3_extensions]]
+ by smt+
lemma
"(0::int) mod 0 = 0"
@@ -326,14 +326,14 @@
"(-5::int) mod -3 = -2"
"x mod 3 < 3"
"(x mod 3 = x) \<longrightarrow> (x < 3)"
- using [[z3_new_extensions]]
- by smt2+
+ using [[z3_extensions]]
+ by smt+
lemma
"(x::int) = x div 1 * 1 + x mod 1"
"x = x div 3 * 3 + x mod 3"
- using [[z3_new_extensions]]
- by smt2+
+ using [[z3_extensions]]
+ by smt+
lemma
"abs (x::int) \<ge> 0"
@@ -341,7 +341,7 @@
"(x \<ge> 0) = (abs x = x)"
"(x \<le> 0) = (abs x = -x)"
"abs (abs x) = abs x"
- by smt2+
+ by smt+
lemma
"min (x::int) y \<le> x"
@@ -350,7 +350,7 @@
"min x y = min y x"
"x \<ge> 0 \<longrightarrow> min x 0 = 0"
"min x y \<le> abs (x + y)"
- by smt2+
+ by smt+
lemma
"max (x::int) y \<ge> x"
@@ -359,7 +359,7 @@
"max x y = max y x"
"x \<ge> 0 \<longrightarrow> max x 0 = x"
"max x y \<ge> - abs x - abs y"
- by smt2+
+ by smt+
lemma
"0 < (x::int) \<and> x \<le> 1 \<longrightarrow> x = 1"
@@ -374,7 +374,7 @@
"x \<le> y \<longrightarrow> y < z \<longrightarrow> x \<le> z"
"x < y \<longrightarrow> y < z \<longrightarrow> x < z"
"x < y \<and> y < z \<longrightarrow> \<not> (z < x)"
- by smt2+
+ by smt+
section {* Reals *}
@@ -390,7 +390,7 @@
"-123 + 345 < (567::real)"
"(123456789::real) < 2345678901"
"(-123456789::real) < 2345678901"
- by smt2+
+ by smt+
lemma
"(x::real) + 0 = x"
@@ -398,7 +398,7 @@
"x + y = y + x"
"x + (y + z) = (x + y) + z"
"(x + y = 0) = (x = -y)"
- by smt2+
+ by smt+
lemma
"(-1::real) = - 1"
@@ -406,7 +406,7 @@
"-(x::real) < 0 \<longleftrightarrow> x > 0"
"x > 0 \<longrightarrow> -x < 0"
"x < 0 \<longrightarrow> -x > 0"
- by smt2+
+ by smt+
lemma
"(x::real) - 0 = x"
@@ -415,7 +415,7 @@
"x - y = -(y - x)"
"x - y = -y + x"
"x - y - z = x - (y + z)"
- by smt2+
+ by smt+
lemma
"(x::real) * 0 = 0"
@@ -425,7 +425,7 @@
"x * -1 = -x"
"-1 * x = -x"
"3 * x = x * 3"
- by smt2+
+ by smt+
lemma
"(1/2 :: real) < 1"
@@ -436,16 +436,16 @@
"(x::real) / 1 = x"
"x > 0 \<longrightarrow> x / 3 < x"
"x < 0 \<longrightarrow> x / 3 > x"
- using [[z3_new_extensions]]
- by smt2+
+ using [[z3_extensions]]
+ by smt+
lemma
"(3::real) * (x / 3) = x"
"(x * 3) / 3 = x"
"x > 0 \<longrightarrow> 2 * x / 3 < x"
"x < 0 \<longrightarrow> 2 * x / 3 > x"
- using [[z3_new_extensions]]
- by smt2+
+ using [[z3_extensions]]
+ by smt+
lemma
"abs (x::real) \<ge> 0"
@@ -453,7 +453,7 @@
"(x \<ge> 0) = (abs x = x)"
"(x \<le> 0) = (abs x = -x)"
"abs (abs x) = abs x"
- by smt2+
+ by smt+
lemma
"min (x::real) y \<le> x"
@@ -462,7 +462,7 @@
"min x y = min y x"
"x \<ge> 0 \<longrightarrow> min x 0 = 0"
"min x y \<le> abs (x + y)"
- by smt2+
+ by smt+
lemma
"max (x::real) y \<ge> x"
@@ -471,7 +471,7 @@
"max x y = max y x"
"x \<ge> 0 \<longrightarrow> max x 0 = x"
"max x y \<ge> - abs x - abs y"
- by smt2+
+ by smt+
lemma
"x \<le> (x::real)"
@@ -484,7 +484,7 @@
"x \<le> y \<longrightarrow> y < z \<longrightarrow> x \<le> z"
"x < y \<longrightarrow> y < z \<longrightarrow> x < z"
"x < y \<and> y < z \<longrightarrow> \<not> (z < x)"
- by smt2+
+ by smt+
section {* Datatypes, Records, and Typedefs *}
@@ -507,7 +507,7 @@
"(fst (x, y) = snd (x, y)) = (x = y)"
"(fst p = snd p) = (p = (snd p, fst p))"
using fst_conv snd_conv pair_collapse
- by smt2+
+ by smt+
lemma
"[x] \<noteq> Nil"
@@ -520,13 +520,13 @@
"hd (tl [x, y, z]) = y"
"tl (tl [x, y, z]) = [z]"
using list.sel(1,3) list.simps
- by smt2+
+ by smt+
lemma
"fst (hd [(a, b)]) = a"
"snd (hd [(a, b)]) = b"
using fst_conv snd_conv pair_collapse list.sel(1,3) list.simps
- by smt2+
+ by smt+
subsubsection {* Records *}
@@ -544,7 +544,7 @@
"cx p1 \<noteq> cx p2 \<longrightarrow> p1 \<noteq> p2"
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps
- by smt2+
+ by smt+
lemma
"cx \<lparr> cx = 3, cy = 4 \<rparr> = 3"
@@ -555,7 +555,7 @@
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr> = p"
using point.simps
- by smt2+
+ by smt+
lemma
"cy (p \<lparr> cx := a \<rparr>) = cy p"
@@ -571,7 +571,7 @@
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
"black p1 \<noteq> black p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps bw_point.simps
- by smt2+
+ by smt+
lemma
"cx \<lparr> cx = 3, cy = 4, black = b \<rparr> = 3"
@@ -587,7 +587,7 @@
"p = \<lparr> cx = 3, cy = 4, black = True \<rparr> \<longrightarrow>
p \<lparr> black := True \<rparr> \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
using point.simps bw_point.simps
- sorry (* smt2 FIXME: bad Z3 4.3.x proof *)
+ sorry (* smt FIXME: bad Z3 4.3.x proof *)
lemma
"\<lparr> cx = 3, cy = 4, black = b \<rparr> \<lparr> black := w \<rparr> = \<lparr> cx = 3, cy = 4, black = w \<rparr>"
@@ -611,7 +611,7 @@
"n0 \<noteq> n1"
"plus' n1 n1 = n2"
"plus' n0 n2 = n2"
- by (smt2 n0_def n1_def n2_def plus'_def Abs_int'_inverse Rep_int'_inverse UNIV_I)+
+ by (smt n0_def n1_def n2_def plus'_def Abs_int'_inverse Rep_int'_inverse UNIV_I)+
subsection {* With support by the SMT solver (but without proofs) *}
@@ -632,8 +632,8 @@
"(fst (x, y) = snd (x, y)) = (x = y)"
"(fst p = snd p) = (p = (snd p, fst p))"
using fst_conv snd_conv pair_collapse
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"[x] \<noteq> Nil"
@@ -646,15 +646,15 @@
"hd (tl [x, y, z]) = y"
"tl (tl [x, y, z]) = [z]"
using list.sel(1,3)
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"fst (hd [(a, b)]) = a"
"snd (hd [(a, b)]) = b"
using fst_conv snd_conv pair_collapse list.sel(1,3)
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
subsubsection {* Records *}
@@ -665,8 +665,8 @@
"cx p1 \<noteq> cx p2 \<longrightarrow> p1 \<noteq> p2"
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"cx \<lparr> cx = 3, cy = 4 \<rparr> = 3"
@@ -677,16 +677,16 @@
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
"p = \<lparr> cx = 3, cy = 4 \<rparr> \<longrightarrow> p \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr> = p"
using point.simps
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"cy (p \<lparr> cx := a \<rparr>) = cy p"
"cx (p \<lparr> cy := a \<rparr>) = cx p"
"p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr>"
using point.simps
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"p1 = p2 \<longrightarrow> cx p1 = cx p2"
@@ -696,8 +696,8 @@
"cy p1 \<noteq> cy p2 \<longrightarrow> p1 \<noteq> p2"
"black p1 \<noteq> black p2 \<longrightarrow> p1 \<noteq> p2"
using point.simps bw_point.simps
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"cx \<lparr> cx = 3, cy = 4, black = b \<rparr> = 3"
@@ -713,8 +713,8 @@
"p = \<lparr> cx = 3, cy = 4, black = True \<rparr> \<longrightarrow>
p \<lparr> black := True \<rparr> \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> = p"
using point.simps bw_point.simps
- using [[smt2_oracle, z3_new_extensions]]
- by smt2+
+ using [[smt_oracle, z3_extensions]]
+ by smt+
lemma
"\<lparr> cx = 3, cy = 4, black = b \<rparr> \<lparr> black := w \<rparr> = \<lparr> cx = 3, cy = 4, black = w \<rparr>"
@@ -726,8 +726,8 @@
"p \<lparr> cx := 3 \<rparr> \<lparr> cy := 4 \<rparr> \<lparr> black := True \<rparr> =
p \<lparr> black := True \<rparr> \<lparr> cy := 4 \<rparr> \<lparr> cx := 3 \<rparr>"
using point.simps bw_point.simps
- using [[smt2_oracle, z3_new_extensions]]
- by smt2
+ using [[smt_oracle, z3_extensions]]
+ by smt
subsubsection {* Type definitions *}
@@ -736,8 +736,8 @@
"n0 \<noteq> n1"
"plus' n1 n1 = n2"
"plus' n0 n2 = n2"
- using [[smt2_oracle, z3_new_extensions]]
- by (smt2 n0_def n1_def n2_def plus'_def)+
+ using [[smt_oracle, z3_extensions]]
+ by (smt n0_def n1_def n2_def plus'_def)+
section {* Function updates *}
@@ -751,14 +751,14 @@
"i1 = i2 \<longrightarrow> (f (i1 := v1, i2 := v2)) i1 = v2"
"i1 \<noteq> i2 \<and>i1 \<noteq> i3 \<and> i2 \<noteq> i3 \<longrightarrow> (f (i1 := v1, i2 := v2)) i3 = f i3"
using fun_upd_same fun_upd_apply
- by smt2+
+ by smt+
section {* Sets *}
lemma Empty: "x \<notin> {}" by simp
-lemmas smt2_sets = Empty UNIV_I Un_iff Int_iff
+lemmas smt_sets = Empty UNIV_I Un_iff Int_iff
lemma
"x \<notin> {}"
@@ -776,6 +776,6 @@
"x \<in> P \<inter> P \<longleftrightarrow> x \<in> P"
"x \<in> P \<inter> (Q \<inter> R) \<longleftrightarrow> x \<in> (P \<inter> Q) \<inter> R"
"{x. x \<in> P} = {y. y \<in> P}"
- by (smt2 smt2_sets)+
+ by (smt smt_sets)+
end
--- a/src/HOL/SMT_Examples/SMT_Word_Examples.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/SMT_Examples/SMT_Word_Examples.thy Thu Aug 28 00:40:38 2014 +0200
@@ -8,10 +8,10 @@
imports "~~/src/HOL/Word/Word"
begin
-declare [[smt2_oracle = true]]
-declare [[z3_new_extensions = true]]
-declare [[smt2_certificates = "SMT_Word_Examples.certs2"]]
-declare [[smt2_read_only_certificates = true]]
+declare [[smt_oracle = true]]
+declare [[z3_extensions = true]]
+declare [[smt_certificates = "SMT_Word_Examples.certs2"]]
+declare [[smt_read_only_certificates = true]]
text {*
Currently, there is no proof reconstruction for words.
@@ -21,36 +21,36 @@
section {* Bitvector numbers *}
-lemma "(27 :: 4 word) = -5" by smt2
-lemma "(27 :: 4 word) = 11" by smt2
-lemma "23 < (27::8 word)" by smt2
-lemma "27 + 11 = (6::5 word)" by smt2
-lemma "7 * 3 = (21::8 word)" by smt2
-lemma "11 - 27 = (-16::8 word)" by smt2
-lemma "- -11 = (11::5 word)" by smt2
-lemma "-40 + 1 = (-39::7 word)" by smt2
-lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by smt2
-lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4" by smt2
+lemma "(27 :: 4 word) = -5" by smt
+lemma "(27 :: 4 word) = 11" by smt
+lemma "23 < (27::8 word)" by smt
+lemma "27 + 11 = (6::5 word)" by smt
+lemma "7 * 3 = (21::8 word)" by smt
+lemma "11 - 27 = (-16::8 word)" by smt
+lemma "- -11 = (11::5 word)" by smt
+lemma "-40 + 1 = (-39::7 word)" by smt
+lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by smt
+lemma "x = (5 :: 4 word) \<Longrightarrow> 4 * x = 4" by smt
section {* Bit-level logic *}
-lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by smt2
-lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by smt2
-lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)" by smt2
-lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by smt2
-lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)" by smt2
-lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)" by smt2
-lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt2
-lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt2
-lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt2
-lemma "0b10011 << 2 = (0b1001100::8 word)" by smt2
-lemma "0b11001 >> 2 = (0b110::8 word)" by smt2
-lemma "0b10011 >>> 2 = (0b100::8 word)" by smt2
-lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt2
-lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt2
-lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt2
-lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt2
+lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by smt
+lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by smt
+lemma "0xF0 XOR 0xFF = (0x0F :: 8 word)" by smt
+lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by smt
+lemma "word_cat (27::4 word) (27::8 word) = (2843::12 word)" by smt
+lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)" by smt
+lemma "slice 1 (0b10110 :: 4 word) = (0b11 :: 2 word)" by smt
+lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by smt
+lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by smt
+lemma "0b10011 << 2 = (0b1001100::8 word)" by smt
+lemma "0b11001 >> 2 = (0b110::8 word)" by smt
+lemma "0b10011 >>> 2 = (0b100::8 word)" by smt
+lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by smt
+lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by smt
+lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" by smt
+lemma "w < 256 \<Longrightarrow> (w :: 16 word) AND 0x00FF = w" by smt
section {* Combined integer-bitvector properties *}
@@ -62,8 +62,8 @@
and "bv2int 3 = 3"
and "\<forall>x::2 word. bv2int x > 0"
shows "\<forall>i::int. i < 0 \<longrightarrow> (\<forall>x::2 word. bv2int x > i)"
- using assms by smt2
+ using assms by smt
-lemma "P (0 \<le> (a :: 4 word)) = P True" by smt2
+lemma "P (0 \<le> (a :: 4 word)) = P True" by smt
end
--- a/src/HOL/SMT_Examples/boogie.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/SMT_Examples/boogie.ML Thu Aug 28 00:40:38 2014 +0200
@@ -92,18 +92,18 @@
fun mk_quant q (Free (x, T)) t = q T $ absfree (x, T) t
| mk_quant _ t _ = raise TERM ("bad variable", [t])
-val patternT = @{typ "SMT2.pattern"}
+val patternT = @{typ "SMT.pattern"}
fun mk_pat t =
- Const (@{const_name "SMT2.pat"}, Term.fastype_of t --> patternT) $ t
+ Const (@{const_name "SMT.pat"}, Term.fastype_of t --> patternT) $ t
fun mk_pattern [] = raise TERM ("mk_pattern", [])
- | mk_pattern ts = SMT2_Util.mk_symb_list patternT (map mk_pat ts)
+ | mk_pattern ts = SMT_Util.mk_symb_list patternT (map mk_pat ts)
fun mk_trigger [] t = t
| mk_trigger pss t =
- @{term "SMT2.trigger"} $
- SMT2_Util.mk_symb_list @{typ "SMT2.pattern SMT2.symb_list"} (map mk_pattern pss) $ t
+ @{term "SMT.trigger"} $
+ SMT_Util.mk_symb_list @{typ "SMT.pattern SMT.symb_list"} (map mk_pattern pss) $ t
(* parser *)
@@ -247,7 +247,7 @@
[@{thm fun_upd_same}, @{thm fun_upd_apply}]
fun boogie_tac ctxt axioms =
- ALLGOALS (SMT2_Solver.smt2_tac ctxt (boogie_rules @ axioms))
+ ALLGOALS (SMT_Solver.smt_tac ctxt (boogie_rules @ axioms))
fun boogie_prove thy lines =
let
--- a/src/HOL/Sledgehammer.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Sledgehammer.thy Thu Aug 28 00:40:38 2014 +0200
@@ -7,7 +7,7 @@
header {* Sledgehammer: Isabelle--ATP Linkup *}
theory Sledgehammer
-imports Presburger SMT2
+imports Presburger SMT
keywords "sledgehammer" :: diag and "sledgehammer_params" :: thy_decl
begin
@@ -26,7 +26,7 @@
ML_file "Tools/Sledgehammer/sledgehammer_isar.ML"
ML_file "Tools/Sledgehammer/sledgehammer_prover.ML"
ML_file "Tools/Sledgehammer/sledgehammer_prover_atp.ML"
-ML_file "Tools/Sledgehammer/sledgehammer_prover_smt2.ML"
+ML_file "Tools/Sledgehammer/sledgehammer_prover_smt.ML"
ML_file "Tools/Sledgehammer/sledgehammer_prover_minimize.ML"
ML_file "Tools/Sledgehammer/sledgehammer_mepo.ML"
ML_file "Tools/Sledgehammer/sledgehammer_mash.ML"
--- a/src/HOL/TPTP/mash_eval.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/TPTP/mash_eval.ML Thu Aug 28 00:40:38 2014 +0200
@@ -104,7 +104,7 @@
in
Config.put atp_dest_dir dir
#> Config.put atp_problem_prefix (prob_prefix ^ "__")
- #> Config.put SMT2_Config.debug_files (dir ^ "/" ^ prob_prefix)
+ #> Config.put SMT_Config.debug_files (dir ^ "/" ^ prob_prefix)
end
| set_file_name _ NONE = I
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_builtin.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,222 @@
+(* Title: HOL/Tools/SMT/smt_builtin.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Tables of types and terms directly supported by SMT solvers.
+*)
+
+signature SMT_BUILTIN =
+sig
+ (*for experiments*)
+ val filter_builtins: (typ -> bool) -> Proof.context -> Proof.context
+
+ (*built-in types*)
+ val add_builtin_typ: SMT_Util.class ->
+ typ * (typ -> string option) * (typ -> int -> string option) -> Context.generic ->
+ Context.generic
+ val add_builtin_typ_ext: typ * (typ -> bool) -> Context.generic ->
+ Context.generic
+ val dest_builtin_typ: Proof.context -> typ -> string option
+ val is_builtin_typ_ext: Proof.context -> typ -> bool
+
+ (*built-in numbers*)
+ val dest_builtin_num: Proof.context -> term -> (string * typ) option
+ val is_builtin_num: Proof.context -> term -> bool
+ val is_builtin_num_ext: Proof.context -> term -> bool
+
+ (*built-in functions*)
+ type 'a bfun = Proof.context -> typ -> term list -> 'a
+ type bfunr = string * int * term list * (term list -> term)
+ val add_builtin_fun: SMT_Util.class -> (string * typ) * bfunr option bfun -> Context.generic ->
+ Context.generic
+ val add_builtin_fun': SMT_Util.class -> term * string -> Context.generic -> Context.generic
+ val add_builtin_fun_ext: (string * typ) * term list bfun -> Context.generic -> Context.generic
+ val add_builtin_fun_ext': string * typ -> Context.generic -> Context.generic
+ val add_builtin_fun_ext'': string -> Context.generic -> Context.generic
+ val dest_builtin_fun: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin_eq: Proof.context -> term -> term -> bfunr option
+ val dest_builtin_pred: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin_conn: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin: Proof.context -> string * typ -> term list -> bfunr option
+ val dest_builtin_ext: Proof.context -> string * typ -> term list -> term list option
+ val is_builtin_fun: Proof.context -> string * typ -> term list -> bool
+ val is_builtin_fun_ext: Proof.context -> string * typ -> term list -> bool
+end;
+
+structure SMT_Builtin: SMT_BUILTIN =
+struct
+
+
+(* built-in tables *)
+
+datatype ('a, 'b) kind = Ext of 'a | Int of 'b
+
+type ('a, 'b) ttab = ((typ * ('a, 'b) kind) Ord_List.T) SMT_Util.dict
+
+fun typ_ord ((T, _), (U, _)) =
+ let
+ fun tord (TVar _, Type _) = GREATER
+ | tord (Type _, TVar _) = LESS
+ | tord (Type (n, Ts), Type (m, Us)) =
+ if n = m then list_ord tord (Ts, Us)
+ else Term_Ord.typ_ord (T, U)
+ | tord TU = Term_Ord.typ_ord TU
+ in tord (T, U) end
+
+fun insert_ttab cs T f =
+ SMT_Util.dict_map_default (cs, [])
+ (Ord_List.insert typ_ord (perhaps (try Logic.varifyT_global) T, f))
+
+fun merge_ttab ttabp = SMT_Util.dict_merge (Ord_List.merge typ_ord) ttabp
+
+fun lookup_ttab ctxt ttab T =
+ let fun match (U, _) = Sign.typ_instance (Proof_Context.theory_of ctxt) (T, U)
+ in
+ get_first (find_first match) (SMT_Util.dict_lookup ttab (SMT_Config.solver_class_of ctxt))
+ end
+
+type ('a, 'b) btab = ('a, 'b) ttab Symtab.table
+
+fun insert_btab cs n T f =
+ Symtab.map_default (n, []) (insert_ttab cs T f)
+
+fun merge_btab btabp = Symtab.join (K merge_ttab) btabp
+
+fun lookup_btab ctxt btab (n, T) =
+ (case Symtab.lookup btab n of
+ NONE => NONE
+ | SOME ttab => lookup_ttab ctxt ttab T)
+
+type 'a bfun = Proof.context -> typ -> term list -> 'a
+
+type bfunr = string * int * term list * (term list -> term)
+
+structure Builtins = Generic_Data
+(
+ type T =
+ (typ -> bool, (typ -> string option) * (typ -> int -> string option)) ttab *
+ (term list bfun, bfunr option bfun) btab
+ val empty = ([], Symtab.empty)
+ val extend = I
+ fun merge ((t1, b1), (t2, b2)) = (merge_ttab (t1, t2), merge_btab (b1, b2))
+)
+
+fun filter_ttab keep_T = map (apsnd (filter (keep_T o fst)))
+
+fun filter_builtins keep_T =
+ Context.proof_map (Builtins.map (fn (ttab, btab) =>
+ (filter_ttab keep_T ttab, Symtab.map (K (filter_ttab keep_T)) btab)))
+
+
+(* built-in types *)
+
+fun add_builtin_typ cs (T, f, g) =
+ Builtins.map (apfst (insert_ttab cs T (Int (f, g))))
+
+fun add_builtin_typ_ext (T, f) = Builtins.map (apfst (insert_ttab SMT_Util.basicC T (Ext f)))
+
+fun lookup_builtin_typ ctxt =
+ lookup_ttab ctxt (fst (Builtins.get (Context.Proof ctxt)))
+
+fun dest_builtin_typ ctxt T =
+ (case lookup_builtin_typ ctxt T of
+ SOME (_, Int (f, _)) => f T
+ | _ => NONE)
+
+fun is_builtin_typ_ext ctxt T =
+ (case lookup_builtin_typ ctxt T of
+ SOME (_, Int (f, _)) => is_some (f T)
+ | SOME (_, Ext f) => f T
+ | NONE => false)
+
+
+(* built-in numbers *)
+
+fun dest_builtin_num ctxt t =
+ (case try HOLogic.dest_number t of
+ NONE => NONE
+ | SOME (T, i) =>
+ if i < 0 then NONE else
+ (case lookup_builtin_typ ctxt T of
+ SOME (_, Int (_, g)) => g T i |> Option.map (rpair T)
+ | _ => NONE))
+
+val is_builtin_num = is_some oo dest_builtin_num
+
+fun is_builtin_num_ext ctxt t =
+ (case try HOLogic.dest_number t of
+ NONE => false
+ | SOME (T, _) => is_builtin_typ_ext ctxt T)
+
+
+(* built-in functions *)
+
+fun add_builtin_fun cs ((n, T), f) =
+ Builtins.map (apsnd (insert_btab cs n T (Int f)))
+
+fun add_builtin_fun' cs (t, n) =
+ let
+ val c as (m, T) = Term.dest_Const t
+ fun app U ts = Term.list_comb (Const (m, U), ts)
+ fun bfun _ U ts = SOME (n, length (Term.binder_types T), ts, app U)
+ in add_builtin_fun cs (c, bfun) end
+
+fun add_builtin_fun_ext ((n, T), f) =
+ Builtins.map (apsnd (insert_btab SMT_Util.basicC n T (Ext f)))
+
+fun add_builtin_fun_ext' c = add_builtin_fun_ext (c, fn _ => fn _ => I)
+
+fun add_builtin_fun_ext'' n context =
+ let val thy = Context.theory_of context
+ in add_builtin_fun_ext' (n, Sign.the_const_type thy n) context end
+
+fun lookup_builtin_fun ctxt =
+ lookup_btab ctxt (snd (Builtins.get (Context.Proof ctxt)))
+
+fun dest_builtin_fun ctxt (c as (_, T)) ts =
+ (case lookup_builtin_fun ctxt c of
+ SOME (_, Int f) => f ctxt T ts
+ | _ => NONE)
+
+fun dest_builtin_eq ctxt t u =
+ let
+ val aT = TFree (Name.aT, @{sort type})
+ val c = (@{const_name HOL.eq}, aT --> aT --> @{typ bool})
+ fun mk ts = Term.list_comb (HOLogic.eq_const (Term.fastype_of (hd ts)), ts)
+ in
+ dest_builtin_fun ctxt c []
+ |> Option.map (fn (n, i, _, _) => (n, i, [t, u], mk))
+ end
+
+fun special_builtin_fun pred ctxt (c as (_, T)) ts =
+ if pred (Term.body_type T, Term.binder_types T) then
+ dest_builtin_fun ctxt c ts
+ else NONE
+
+fun dest_builtin_pred ctxt = special_builtin_fun (equal @{typ bool} o fst) ctxt
+
+fun dest_builtin_conn ctxt =
+ special_builtin_fun (forall (equal @{typ bool}) o (op ::)) ctxt
+
+fun dest_builtin ctxt c ts =
+ let val t = Term.list_comb (Const c, ts)
+ in
+ (case dest_builtin_num ctxt t of
+ SOME (n, _) => SOME (n, 0, [], K t)
+ | NONE => dest_builtin_fun ctxt c ts)
+ end
+
+fun dest_builtin_fun_ext ctxt (c as (_, T)) ts =
+ (case lookup_builtin_fun ctxt c of
+ SOME (_, Int f) => f ctxt T ts |> Option.map (fn (_, _, us, _) => us)
+ | SOME (_, Ext f) => SOME (f ctxt T ts)
+ | NONE => NONE)
+
+fun dest_builtin_ext ctxt c ts =
+ if is_builtin_num_ext ctxt (Term.list_comb (Const c, ts)) then SOME []
+ else dest_builtin_fun_ext ctxt c ts
+
+fun is_builtin_fun ctxt c ts = is_some (dest_builtin_fun ctxt c ts)
+
+fun is_builtin_fun_ext ctxt c ts = is_some (dest_builtin_fun_ext ctxt c ts)
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_config.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,249 @@
+(* Title: HOL/Tools/SMT/smt_config.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Configuration options and diagnostic tools for SMT.
+*)
+
+signature SMT_CONFIG =
+sig
+ (*solver*)
+ type solver_info = {
+ name: string,
+ class: Proof.context -> SMT_Util.class,
+ avail: unit -> bool,
+ options: Proof.context -> string list }
+ val add_solver: solver_info -> Context.generic -> Context.generic
+ val set_solver_options: string * string -> Context.generic -> Context.generic
+ val is_available: Proof.context -> string -> bool
+ val available_solvers_of: Proof.context -> string list
+ val select_solver: string -> Context.generic -> Context.generic
+ val solver_of: Proof.context -> string
+ val solver_class_of: Proof.context -> SMT_Util.class
+ val solver_options_of: Proof.context -> string list
+
+ (*options*)
+ val oracle: bool Config.T
+ val timeout: real Config.T
+ val random_seed: int Config.T
+ val read_only_certificates: bool Config.T
+ val verbose: bool Config.T
+ val trace: bool Config.T
+ val monomorph_limit: int Config.T
+ val monomorph_instances: int Config.T
+ val infer_triggers: bool Config.T
+ val debug_files: string Config.T
+ val sat_solver: string Config.T
+
+ (*tools*)
+ val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b
+
+ (*diagnostics*)
+ val trace_msg: Proof.context -> ('a -> string) -> 'a -> unit
+ val verbose_msg: Proof.context -> ('a -> string) -> 'a -> unit
+
+ (*certificates*)
+ val select_certificates: string -> Context.generic -> Context.generic
+ val certificates_of: Proof.context -> Cache_IO.cache option
+
+ (*setup*)
+ val print_setup: Proof.context -> unit
+end;
+
+structure SMT_Config: SMT_CONFIG =
+struct
+
+(* solver *)
+
+type solver_info = {
+ name: string,
+ class: Proof.context -> SMT_Util.class,
+ avail: unit -> bool,
+ options: Proof.context -> string list}
+
+(* FIXME just one data slot (record) per program unit *)
+structure Solvers = Generic_Data
+(
+ type T = (solver_info * string list) Symtab.table * string option
+ val empty = (Symtab.empty, NONE)
+ val extend = I
+ fun merge ((ss1, s1), (ss2, s2)) =
+ (Symtab.merge (K true) (ss1, ss2), merge_options (s1, s2))
+)
+
+fun set_solver_options (name, options) =
+ let val opts = String.tokens (Symbol.is_ascii_blank o str) options
+ in Solvers.map (apfst (Symtab.map_entry name (apsnd (K opts)))) end
+
+fun add_solver (info as {name, ...} : solver_info) context =
+ if Symtab.defined (fst (Solvers.get context)) name then
+ error ("Solver already registered: " ^ quote name)
+ else
+ context
+ |> Solvers.map (apfst (Symtab.update (name, (info, []))))
+ |> Context.map_theory (Attrib.setup (Binding.name (name ^ "_options"))
+ (Scan.lift (@{keyword "="} |-- Args.name) >>
+ (Thm.declaration_attribute o K o set_solver_options o pair name))
+ ("Additional command line options for SMT solver " ^ quote name))
+
+fun all_solvers_of ctxt = Symtab.keys (fst (Solvers.get (Context.Proof ctxt)))
+
+fun solver_name_of ctxt = snd (Solvers.get (Context.Proof ctxt))
+
+fun is_available ctxt name =
+ (case Symtab.lookup (fst (Solvers.get (Context.Proof ctxt))) name of
+ SOME ({avail, ...}, _) => avail ()
+ | NONE => false)
+
+fun available_solvers_of ctxt =
+ filter (is_available ctxt) (all_solvers_of ctxt)
+
+fun warn_solver (Context.Proof ctxt) name =
+ if Context_Position.is_visible ctxt then
+ warning ("The SMT solver " ^ quote name ^ " is not installed")
+ else ()
+ | warn_solver _ _ = ()
+
+fun select_solver name context =
+ let
+ val ctxt = Context.proof_of context
+ val upd = Solvers.map (apsnd (K (SOME name)))
+ in
+ if not (member (op =) (all_solvers_of ctxt) name) then
+ error ("Trying to select unknown solver: " ^ quote name)
+ else if not (is_available ctxt name) then
+ (warn_solver context name; upd context)
+ else upd context
+ end
+
+fun no_solver_err () = error "No SMT solver selected"
+
+fun solver_of ctxt =
+ (case solver_name_of ctxt of
+ SOME name => name
+ | NONE => no_solver_err ())
+
+fun solver_info_of default select ctxt =
+ (case Solvers.get (Context.Proof ctxt) of
+ (solvers, SOME name) => select (Symtab.lookup solvers name)
+ | (_, NONE) => default ())
+
+fun solver_class_of ctxt =
+ let fun class_of ({class, ...}: solver_info, _) = class ctxt
+ in solver_info_of no_solver_err (class_of o the) ctxt end
+
+fun solver_options_of ctxt =
+ let
+ fun all_options NONE = []
+ | all_options (SOME ({options, ...} : solver_info, opts)) =
+ opts @ options ctxt
+ in solver_info_of (K []) all_options ctxt end
+
+val setup_solver =
+ Attrib.setup @{binding smt_solver}
+ (Scan.lift (@{keyword "="} |-- Args.name) >>
+ (Thm.declaration_attribute o K o select_solver))
+ "SMT solver configuration"
+
+
+(* options *)
+
+val oracle = Attrib.setup_config_bool @{binding smt_oracle} (K true)
+val timeout = Attrib.setup_config_real @{binding smt_timeout} (K 30.0)
+val random_seed = Attrib.setup_config_int @{binding smt_random_seed} (K 1)
+val read_only_certificates = Attrib.setup_config_bool @{binding smt_read_only_certificates} (K false)
+val verbose = Attrib.setup_config_bool @{binding smt_verbose} (K true)
+val trace = Attrib.setup_config_bool @{binding smt_trace} (K false)
+val monomorph_limit = Attrib.setup_config_int @{binding smt_monomorph_limit} (K 10)
+val monomorph_instances = Attrib.setup_config_int @{binding smt_monomorph_instances} (K 500)
+val infer_triggers = Attrib.setup_config_bool @{binding smt_infer_triggers} (K false)
+val debug_files = Attrib.setup_config_string @{binding smt_debug_files} (K "")
+val sat_solver = Attrib.setup_config_string @{binding smt_sat_solver} (K "cdclite")
+
+
+(* diagnostics *)
+
+fun cond_trace flag f x = if flag then tracing ("SMT: " ^ f x) else ()
+
+fun verbose_msg ctxt = cond_trace (Config.get ctxt verbose)
+
+fun trace_msg ctxt = cond_trace (Config.get ctxt trace)
+
+
+(* tools *)
+
+fun with_timeout ctxt f x =
+ TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) f x
+ handle TimeLimit.TimeOut => raise SMT_Failure.SMT SMT_Failure.Time_Out
+
+
+(* certificates *)
+
+(* FIXME just one data slot (record) per program unit *)
+structure Certificates = Generic_Data
+(
+ type T = Cache_IO.cache option
+ val empty = NONE
+ val extend = I
+ fun merge (s, _) = s (* FIXME merge options!? *)
+)
+
+val get_certificates_path =
+ Option.map (Cache_IO.cache_path_of) o Certificates.get o Context.Proof
+
+fun select_certificates name context = context |> Certificates.put (
+ if name = "" then NONE
+ else
+ Path.explode name
+ |> Path.append (Resources.master_directory (Context.theory_of context))
+ |> SOME o Cache_IO.unsynchronized_init)
+
+val certificates_of = Certificates.get o Context.Proof
+
+val setup_certificates =
+ Attrib.setup @{binding smt_certificates}
+ (Scan.lift (@{keyword "="} |-- Args.name) >>
+ (Thm.declaration_attribute o K o select_certificates))
+ "SMT certificates configuration"
+
+
+(* setup *)
+
+val _ = Theory.setup (
+ setup_solver #>
+ setup_certificates)
+
+fun print_setup ctxt =
+ let
+ fun string_of_bool b = if b then "true" else "false"
+
+ val names = available_solvers_of ctxt
+ val ns = if null names then ["(none)"] else sort_strings names
+ val n = the_default "(none)" (solver_name_of ctxt)
+ val opts = solver_options_of ctxt
+
+ val t = string_of_real (Config.get ctxt timeout)
+
+ val certs_filename =
+ (case get_certificates_path ctxt of
+ SOME path => Path.print path
+ | NONE => "(disabled)")
+ in
+ Pretty.writeln (Pretty.big_list "SMT setup:" [
+ Pretty.str ("Current SMT solver: " ^ n),
+ Pretty.str ("Current SMT solver options: " ^ space_implode " " opts),
+ Pretty.str_list "Available SMT solvers: " "" ns,
+ Pretty.str ("Current timeout: " ^ t ^ " seconds"),
+ Pretty.str ("With proofs: " ^
+ string_of_bool (not (Config.get ctxt oracle))),
+ Pretty.str ("Certificates cache: " ^ certs_filename),
+ Pretty.str ("Fixed certificates: " ^
+ string_of_bool (Config.get ctxt read_only_certificates))])
+ end
+
+val _ =
+ Outer_Syntax.improper_command @{command_spec "smt_status"}
+ "show the available SMT solvers, the currently selected SMT solver, \
+ \and the values of SMT configuration options"
+ (Scan.succeed (Toplevel.keep (print_setup o Toplevel.context_of)))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_datatypes.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,93 @@
+(* Title: HOL/Tools/SMT/smt_datatypes.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Collector functions for common type declarations and their representation
+as algebraic datatypes.
+*)
+
+signature SMT_DATATYPES =
+sig
+ val add_decls: typ ->
+ (typ * (term * term list) list) list list * Proof.context ->
+ (typ * (term * term list) list) list list * Proof.context
+end;
+
+structure SMT_Datatypes: SMT_DATATYPES =
+struct
+
+fun mk_selectors T Ts =
+ Variable.variant_fixes (replicate (length Ts) "select")
+ #>> map2 (fn U => fn n => Free (n, T --> U)) Ts
+
+
+(* free constructor type declarations *)
+
+fun get_ctr_sugar_decl ({ctrs, ...} : Ctr_Sugar.ctr_sugar) T Ts ctxt =
+ let
+ fun mk_constr ctr0 =
+ let val ctr = Ctr_Sugar.mk_ctr Ts ctr0 in
+ mk_selectors T (binder_types (fastype_of ctr)) #>> pair ctr
+ end
+ in
+ fold_map mk_constr ctrs ctxt
+ |>> (pair T #> single)
+ end
+
+
+(* typedef declarations *)
+
+fun get_typedef_decl (({Abs_name, Rep_name, abs_type, rep_type, ...}, {Abs_inverse, ...})
+ : Typedef.info) T Ts =
+ if can (curry (op RS) @{thm UNIV_I}) Abs_inverse then
+ let
+ val env = snd (Term.dest_Type abs_type) ~~ Ts
+ val instT = Term.map_atyps (perhaps (AList.lookup (op =) env))
+
+ val constr = Const (Abs_name, instT (rep_type --> abs_type))
+ val select = Const (Rep_name, instT (abs_type --> rep_type))
+ in [(T, [(constr, [select])])] end
+ else
+ []
+
+
+(* collection of declarations *)
+
+fun declared declss T = exists (exists (equal T o fst)) declss
+fun declared' dss T = exists (exists (equal T o fst) o snd) dss
+
+fun get_decls T n Ts ctxt =
+ (case Ctr_Sugar.ctr_sugar_of ctxt n of
+ SOME ctr_sugar => get_ctr_sugar_decl ctr_sugar T Ts ctxt
+ | NONE =>
+ (case Typedef.get_info ctxt n of
+ [] => ([], ctxt)
+ | info :: _ => (get_typedef_decl info T Ts, ctxt)))
+
+fun add_decls T (declss, ctxt) =
+ let
+ fun depends Ts ds = exists (member (op =) (map fst ds)) Ts
+
+ fun add (TFree _) = I
+ | add (TVar _) = I
+ | add (T as Type (@{type_name fun}, _)) =
+ fold add (Term.body_type T :: Term.binder_types T)
+ | add @{typ bool} = I
+ | add (T as Type (n, Ts)) = (fn (dss, ctxt1) =>
+ if declared declss T orelse declared' dss T then (dss, ctxt1)
+ else if SMT_Builtin.is_builtin_typ_ext ctxt1 T then (dss, ctxt1)
+ else
+ (case get_decls T n Ts ctxt1 of
+ ([], _) => (dss, ctxt1)
+ | (ds, ctxt2) =>
+ let
+ val constrTs = maps (map (snd o Term.dest_Const o fst) o snd) ds
+ val Us = fold (union (op =) o Term.binder_types) constrTs []
+
+ fun ins [] = [(Us, ds)]
+ | ins ((Uds as (Us', _)) :: Udss) =
+ if depends Us' ds then (Us, ds) :: Uds :: Udss
+ else Uds :: ins Udss
+ in fold add Us (ins dss, ctxt2) end))
+ in add T ([], ctxt) |>> append declss o map snd end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_failure.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,40 @@
+(* Title: HOL/Tools/SMT/smt_failure.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Failures and exception of SMT.
+*)
+
+signature SMT_FAILURE =
+sig
+ datatype failure =
+ Counterexample of bool |
+ Time_Out |
+ Out_Of_Memory |
+ Abnormal_Termination of int |
+ Other_Failure of string
+ val string_of_failure: failure -> string
+ exception SMT of failure
+end;
+
+structure SMT_Failure: SMT_FAILURE =
+struct
+
+datatype failure =
+ Counterexample of bool |
+ Time_Out |
+ Out_Of_Memory |
+ Abnormal_Termination of int |
+ Other_Failure of string
+
+fun string_of_failure (Counterexample genuine) =
+ if genuine then "Counterexample found (possibly spurious)"
+ else "Potential counterexample found"
+ | string_of_failure Time_Out = "Timed out"
+ | string_of_failure Out_Of_Memory = "Ran out of memory"
+ | string_of_failure (Abnormal_Termination err) =
+ "Solver terminated abnormally with error code " ^ string_of_int err
+ | string_of_failure (Other_Failure msg) = msg
+
+exception SMT of failure
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_normalize.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,441 @@
+(* Title: HOL/Tools/SMT/smt_normalize.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Normalization steps on theorems required by SMT solvers.
+*)
+
+signature SMT_NORMALIZE =
+sig
+ val drop_fact_warning: Proof.context -> thm -> unit
+ val atomize_conv: Proof.context -> conv
+
+ val special_quant_table: (string * thm) list
+ val case_bool_entry: string * thm
+ val abs_min_max_table: (string * thm) list
+
+ type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
+ val add_extra_norm: SMT_Util.class * extra_norm -> Context.generic -> Context.generic
+ val normalize: Proof.context -> thm list -> (int * thm) list
+end;
+
+structure SMT_Normalize: SMT_NORMALIZE =
+struct
+
+fun drop_fact_warning ctxt =
+ SMT_Config.verbose_msg ctxt (prefix "Warning: dropping assumption: " o
+ Display.string_of_thm ctxt)
+
+
+(* general theorem normalizations *)
+
+(** instantiate elimination rules **)
+
+local
+ val (cpfalse, cfalse) = `SMT_Util.mk_cprop (Thm.cterm_of @{theory} @{const False})
+
+ fun inst f ct thm =
+ let val cv = f (Drule.strip_imp_concl (Thm.cprop_of thm))
+ in Thm.instantiate ([], [(cv, ct)]) thm end
+in
+
+fun instantiate_elim thm =
+ (case Thm.concl_of thm of
+ @{const Trueprop} $ Var (_, @{typ bool}) => inst Thm.dest_arg cfalse thm
+ | Var _ => inst I cpfalse thm
+ | _ => thm)
+
+end
+
+
+(** normalize definitions **)
+
+fun norm_def thm =
+ (case Thm.prop_of thm of
+ @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>
+ norm_def (thm RS @{thm fun_cong})
+ | Const (@{const_name Pure.eq}, _) $ _ $ Abs _ => norm_def (thm RS @{thm meta_eq_to_obj_eq})
+ | _ => thm)
+
+
+(** atomization **)
+
+fun atomize_conv ctxt ct =
+ (case Thm.term_of ct of
+ @{const Pure.imp} $ _ $ _ =>
+ Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_imp}
+ | Const (@{const_name Pure.eq}, _) $ _ $ _ =>
+ Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_eq}
+ | Const (@{const_name Pure.all}, _) $ Abs _ =>
+ Conv.binder_conv (atomize_conv o snd) ctxt then_conv Conv.rewr_conv @{thm atomize_all}
+ | _ => Conv.all_conv) ct
+
+val setup_atomize =
+ fold SMT_Builtin.add_builtin_fun_ext'' [@{const_name Pure.imp}, @{const_name Pure.eq},
+ @{const_name Pure.all}, @{const_name Trueprop}]
+
+
+(** unfold special quantifiers **)
+
+val special_quant_table = [
+ (@{const_name Ex1}, @{thm Ex1_def_raw}),
+ (@{const_name Ball}, @{thm Ball_def_raw}),
+ (@{const_name Bex}, @{thm Bex_def_raw})]
+
+local
+ fun special_quant (Const (n, _)) = AList.lookup (op =) special_quant_table n
+ | special_quant _ = NONE
+
+ fun special_quant_conv _ ct =
+ (case special_quant (Thm.term_of ct) of
+ SOME thm => Conv.rewr_conv thm
+ | NONE => Conv.all_conv) ct
+in
+
+fun unfold_special_quants_conv ctxt =
+ SMT_Util.if_exists_conv (is_some o special_quant) (Conv.top_conv special_quant_conv ctxt)
+
+val setup_unfolded_quants = fold (SMT_Builtin.add_builtin_fun_ext'' o fst) special_quant_table
+
+end
+
+
+(** trigger inference **)
+
+local
+ (*** check trigger syntax ***)
+
+ fun dest_trigger (Const (@{const_name pat}, _) $ _) = SOME true
+ | dest_trigger (Const (@{const_name nopat}, _) $ _) = SOME false
+ | dest_trigger _ = NONE
+
+ fun eq_list [] = false
+ | eq_list (b :: bs) = forall (equal b) bs
+
+ fun proper_trigger t =
+ t
+ |> these o try SMT_Util.dest_symb_list
+ |> map (map_filter dest_trigger o these o try SMT_Util.dest_symb_list)
+ |> (fn [] => false | bss => forall eq_list bss)
+
+ fun proper_quant inside f t =
+ (case t of
+ Const (@{const_name All}, _) $ Abs (_, _, u) => proper_quant true f u
+ | Const (@{const_name Ex}, _) $ Abs (_, _, u) => proper_quant true f u
+ | @{const trigger} $ p $ u =>
+ (if inside then f p else false) andalso proper_quant false f u
+ | Abs (_, _, u) => proper_quant false f u
+ | u1 $ u2 => proper_quant false f u1 andalso proper_quant false f u2
+ | _ => true)
+
+ fun check_trigger_error ctxt t =
+ error ("SMT triggers must only occur under quantifier and multipatterns " ^
+ "must have the same kind: " ^ Syntax.string_of_term ctxt t)
+
+ fun check_trigger_conv ctxt ct =
+ if proper_quant false proper_trigger (SMT_Util.term_of ct) then Conv.all_conv ct
+ else check_trigger_error ctxt (Thm.term_of ct)
+
+
+ (*** infer simple triggers ***)
+
+ fun dest_cond_eq ct =
+ (case Thm.term_of ct of
+ Const (@{const_name HOL.eq}, _) $ _ $ _ => Thm.dest_binop ct
+ | @{const HOL.implies} $ _ $ _ => dest_cond_eq (Thm.dest_arg ct)
+ | _ => raise CTERM ("no equation", [ct]))
+
+ fun get_constrs thy (Type (n, _)) = these (Datatype_Data.get_constrs thy n)
+ | get_constrs _ _ = []
+
+ fun is_constr thy (n, T) =
+ let fun match (m, U) = m = n andalso Sign.typ_instance thy (T, U)
+ in can (the o find_first match o get_constrs thy o Term.body_type) T end
+
+ fun is_constr_pat thy t =
+ (case Term.strip_comb t of
+ (Free _, []) => true
+ | (Const c, ts) => is_constr thy c andalso forall (is_constr_pat thy) ts
+ | _ => false)
+
+ fun is_simp_lhs ctxt t =
+ (case Term.strip_comb t of
+ (Const c, ts as _ :: _) =>
+ not (SMT_Builtin.is_builtin_fun_ext ctxt c ts) andalso
+ forall (is_constr_pat (Proof_Context.theory_of ctxt)) ts
+ | _ => false)
+
+ fun has_all_vars vs t =
+ subset (op aconv) (vs, map Free (Term.add_frees t []))
+
+ fun minimal_pats vs ct =
+ if has_all_vars vs (Thm.term_of ct) then
+ (case Thm.term_of ct of
+ _ $ _ =>
+ (case pairself (minimal_pats vs) (Thm.dest_comb ct) of
+ ([], []) => [[ct]]
+ | (ctss, ctss') => union (eq_set (op aconvc)) ctss ctss')
+ | _ => [])
+ else []
+
+ fun proper_mpat _ _ _ [] = false
+ | proper_mpat thy gen u cts =
+ let
+ val tps = (op ~~) (`gen (map Thm.term_of cts))
+ fun some_match u = tps |> exists (fn (t', t) =>
+ Pattern.matches thy (t', u) andalso not (t aconv u))
+ in not (Term.exists_subterm some_match u) end
+
+ val pat = SMT_Util.mk_const_pat @{theory} @{const_name pat} SMT_Util.destT1
+ fun mk_pat ct = Thm.apply (SMT_Util.instT' ct pat) ct
+
+ fun mk_clist T =
+ pairself (Thm.cterm_of @{theory}) (SMT_Util.symb_cons_const T, SMT_Util.symb_nil_const T)
+ fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil
+ val mk_pat_list = mk_list (mk_clist @{typ pattern})
+ val mk_mpat_list = mk_list (mk_clist @{typ "pattern symb_list"})
+ fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss
+
+ val trigger_eq = mk_meta_eq @{lemma "p = trigger t p" by (simp add: trigger_def)}
+
+ fun insert_trigger_conv [] ct = Conv.all_conv ct
+ | insert_trigger_conv ctss ct =
+ let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct
+ in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end
+
+ fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct =
+ let
+ val (lhs, rhs) = dest_cond_eq ct
+
+ val vs = map Thm.term_of cvs
+ val thy = Proof_Context.theory_of ctxt
+
+ fun get_mpats ct =
+ if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct
+ else []
+ val gen = Variable.export_terms ctxt outer_ctxt
+ val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs))
+
+ in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end
+
+ fun has_trigger (@{const trigger} $ _ $ _) = true
+ | has_trigger _ = false
+
+ fun try_trigger_conv cv ct =
+ if SMT_Util.under_quant has_trigger (SMT_Util.term_of ct) then Conv.all_conv ct
+ else Conv.try_conv cv ct
+
+ fun infer_trigger_conv ctxt =
+ if Config.get ctxt SMT_Config.infer_triggers then
+ try_trigger_conv (SMT_Util.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt)
+ else Conv.all_conv
+in
+
+fun trigger_conv ctxt =
+ SMT_Util.prop_conv (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt)
+
+val setup_trigger =
+ fold SMT_Builtin.add_builtin_fun_ext''
+ [@{const_name pat}, @{const_name nopat}, @{const_name trigger}]
+
+end
+
+
+(** combined general normalizations **)
+
+fun gen_normalize1_conv ctxt =
+ atomize_conv ctxt then_conv
+ unfold_special_quants_conv ctxt then_conv
+ Thm.beta_conversion true then_conv
+ trigger_conv ctxt
+
+fun gen_normalize1 ctxt =
+ instantiate_elim #>
+ norm_def #>
+ Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion) #>
+ Drule.forall_intr_vars #>
+ Conv.fconv_rule (gen_normalize1_conv ctxt) #>
+ (* Z3 4.3.1 silently normalizes "P --> Q --> R" to "P & Q --> R" *)
+ Raw_Simplifier.rewrite_rule ctxt @{thms HOL.imp_conjL[symmetric, THEN eq_reflection]}
+
+fun gen_norm1_safe ctxt (i, thm) =
+ (case try (gen_normalize1 ctxt) thm of
+ SOME thm' => SOME (i, thm')
+ | NONE => (drop_fact_warning ctxt thm; NONE))
+
+fun gen_normalize ctxt iwthms = map_filter (gen_norm1_safe ctxt) iwthms
+
+
+(* unfolding of definitions and theory-specific rewritings *)
+
+fun expand_head_conv cv ct =
+ (case Thm.term_of ct of
+ _ $ _ =>
+ Conv.fun_conv (expand_head_conv cv) then_conv
+ Conv.try_conv (Thm.beta_conversion false)
+ | _ => cv) ct
+
+
+(** rewrite bool case expressions as if expressions **)
+
+val case_bool_entry = (@{const_name "bool.case_bool"}, @{thm case_bool_if})
+
+local
+ fun is_case_bool (Const (@{const_name "bool.case_bool"}, _)) = true
+ | is_case_bool _ = false
+
+ fun unfold_conv _ =
+ SMT_Util.if_true_conv (is_case_bool o Term.head_of)
+ (expand_head_conv (Conv.rewr_conv @{thm case_bool_if}))
+in
+
+fun rewrite_case_bool_conv ctxt =
+ SMT_Util.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt)
+
+val setup_case_bool = SMT_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"}
+
+end
+
+
+(** unfold abs, min and max **)
+
+val abs_min_max_table = [
+ (@{const_name min}, @{thm min_def_raw}),
+ (@{const_name max}, @{thm max_def_raw}),
+ (@{const_name abs}, @{thm abs_if_raw})]
+
+local
+ fun abs_min_max ctxt (Const (n, Type (@{type_name fun}, [T, _]))) =
+ (case AList.lookup (op =) abs_min_max_table n of
+ NONE => NONE
+ | SOME thm => if SMT_Builtin.is_builtin_typ_ext ctxt T then SOME thm else NONE)
+ | abs_min_max _ _ = NONE
+
+ fun unfold_amm_conv ctxt ct =
+ (case abs_min_max ctxt (Term.head_of (Thm.term_of ct)) of
+ SOME thm => expand_head_conv (Conv.rewr_conv thm)
+ | NONE => Conv.all_conv) ct
+in
+
+fun unfold_abs_min_max_conv ctxt =
+ SMT_Util.if_exists_conv (is_some o abs_min_max ctxt) (Conv.top_conv unfold_amm_conv ctxt)
+
+val setup_abs_min_max = fold (SMT_Builtin.add_builtin_fun_ext'' o fst) abs_min_max_table
+
+end
+
+
+(** normalize numerals **)
+
+local
+ (*
+ rewrite Numeral1 into 1
+ rewrite - 0 into 0
+ *)
+
+ fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) =
+ true
+ | is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) =
+ true
+ | is_irregular_number _ = false
+
+ fun is_strange_number ctxt t = is_irregular_number t andalso SMT_Builtin.is_builtin_num ctxt t
+
+ val proper_num_ss =
+ simpset_of (put_simpset HOL_ss @{context} addsimps @{thms Num.numeral_One minus_zero})
+
+ fun norm_num_conv ctxt =
+ SMT_Util.if_conv (is_strange_number ctxt) (Simplifier.rewrite (put_simpset proper_num_ss ctxt))
+ Conv.no_conv
+in
+
+fun normalize_numerals_conv ctxt =
+ SMT_Util.if_exists_conv (is_strange_number ctxt) (Conv.top_sweep_conv norm_num_conv ctxt)
+
+end
+
+
+(** combined unfoldings and rewritings **)
+
+fun unfold_conv ctxt =
+ rewrite_case_bool_conv ctxt then_conv
+ unfold_abs_min_max_conv ctxt then_conv
+ Thm.beta_conversion true
+
+fun unfold_polymorph ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt)))
+fun unfold_monomorph ctxt = map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt)))
+
+
+(* overall normalization *)
+
+fun burrow_ids f ithms =
+ let
+ val (is, thms) = split_list ithms
+ val (thms', extra_thms) = f thms
+ in (is ~~ thms') @ map (pair ~1) extra_thms end
+
+type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
+
+structure Extra_Norms = Generic_Data
+(
+ type T = extra_norm SMT_Util.dict
+ val empty = []
+ val extend = I
+ fun merge data = SMT_Util.dict_merge fst data
+)
+
+fun add_extra_norm (cs, norm) = Extra_Norms.map (SMT_Util.dict_update (cs, norm))
+
+fun apply_extra_norms ctxt ithms =
+ let
+ val cs = SMT_Config.solver_class_of ctxt
+ val es = SMT_Util.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs
+ in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end
+
+local
+ val ignored = member (op =) [@{const_name All}, @{const_name Ex},
+ @{const_name Let}, @{const_name If}, @{const_name HOL.eq}]
+
+ val schematic_consts_of =
+ let
+ fun collect (@{const trigger} $ p $ t) = collect_trigger p #> collect t
+ | collect (t $ u) = collect t #> collect u
+ | collect (Abs (_, _, t)) = collect t
+ | collect (t as Const (n, _)) =
+ if not (ignored n) then Monomorph.add_schematic_consts_of t else I
+ | collect _ = I
+ and collect_trigger t =
+ let val dest = these o try SMT_Util.dest_symb_list
+ in fold (fold collect_pat o dest) (dest t) end
+ and collect_pat (Const (@{const_name pat}, _) $ t) = collect t
+ | collect_pat (Const (@{const_name nopat}, _) $ t) = collect t
+ | collect_pat _ = I
+ in (fn t => collect t Symtab.empty) end
+in
+
+fun monomorph ctxt xthms =
+ let val (xs, thms) = split_list xthms
+ in
+ map (pair 1) thms
+ |> Monomorph.monomorph schematic_consts_of ctxt
+ |> maps (uncurry (map o pair)) o map2 pair xs o map (map snd)
+ end
+
+end
+
+fun normalize ctxt wthms =
+ wthms
+ |> map_index I
+ |> gen_normalize ctxt
+ |> unfold_polymorph ctxt
+ |> monomorph ctxt
+ |> unfold_monomorph ctxt
+ |> apply_extra_norms ctxt
+
+val _ = Theory.setup (Context.theory_map (
+ setup_atomize #>
+ setup_unfolded_quants #>
+ setup_trigger #>
+ setup_case_bool #>
+ setup_abs_min_max))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_real.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,113 @@
+(* Title: HOL/Tools/SMT/smt_real.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT setup for reals.
+*)
+
+structure SMT_Real: sig end =
+struct
+
+
+(* SMT-LIB logic *)
+
+fun smtlib_logic ts =
+ if exists (Term.exists_type (Term.exists_subtype (equal @{typ real}))) ts
+ then SOME "AUFLIRA"
+ else NONE
+
+
+(* SMT-LIB and Z3 built-ins *)
+
+local
+ fun real_num _ i = SOME (string_of_int i ^ ".0")
+
+ fun is_linear [t] = SMT_Util.is_number t
+ | is_linear [t, u] = SMT_Util.is_number t orelse SMT_Util.is_number u
+ | is_linear _ = false
+
+ fun mk_times ts = Term.list_comb (@{const times (real)}, ts)
+
+ fun times _ _ ts = if is_linear ts then SOME ("*", 2, ts, mk_times) else NONE
+in
+
+val setup_builtins =
+ SMT_Builtin.add_builtin_typ SMTLIB_Interface.smtlibC
+ (@{typ real}, K (SOME "Real"), real_num) #>
+ fold (SMT_Builtin.add_builtin_fun' SMTLIB_Interface.smtlibC) [
+ (@{const less (real)}, "<"),
+ (@{const less_eq (real)}, "<="),
+ (@{const uminus (real)}, "-"),
+ (@{const plus (real)}, "+"),
+ (@{const minus (real)}, "-") ] #>
+ SMT_Builtin.add_builtin_fun SMTLIB_Interface.smtlibC
+ (Term.dest_Const @{const times (real)}, times) #>
+ SMT_Builtin.add_builtin_fun' Z3_Interface.smtlib_z3C
+ (@{const times (real)}, "*") #>
+ SMT_Builtin.add_builtin_fun' Z3_Interface.smtlib_z3C
+ (@{const divide (real)}, "/")
+
+end
+
+
+(* Z3 constructors *)
+
+local
+ fun z3_mk_builtin_typ (Z3_Interface.Sym ("Real", _)) = SOME @{typ real}
+ | z3_mk_builtin_typ (Z3_Interface.Sym ("real", _)) = SOME @{typ real}
+ (*FIXME: delete*)
+ | z3_mk_builtin_typ _ = NONE
+
+ fun z3_mk_builtin_num _ i T =
+ if T = @{typ real} then SOME (Numeral.mk_cnumber @{ctyp real} i)
+ else NONE
+
+ fun mk_nary _ cu [] = cu
+ | mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
+
+ val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (real)})
+ val add = Thm.cterm_of @{theory} @{const plus (real)}
+ val real0 = Numeral.mk_cnumber @{ctyp real} 0
+ val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (real)})
+ val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (real)})
+ val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const divide (real)})
+ val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (real)})
+ val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (real)})
+
+ fun z3_mk_builtin_fun (Z3_Interface.Sym ("-", _)) [ct] = SOME (mk_uminus ct)
+ | z3_mk_builtin_fun (Z3_Interface.Sym ("+", _)) cts = SOME (mk_nary add real0 cts)
+ | z3_mk_builtin_fun (Z3_Interface.Sym ("-", _)) [ct, cu] = SOME (mk_sub ct cu)
+ | z3_mk_builtin_fun (Z3_Interface.Sym ("*", _)) [ct, cu] = SOME (mk_mul ct cu)
+ | z3_mk_builtin_fun (Z3_Interface.Sym ("/", _)) [ct, cu] = SOME (mk_div ct cu)
+ | z3_mk_builtin_fun (Z3_Interface.Sym ("<", _)) [ct, cu] = SOME (mk_lt ct cu)
+ | z3_mk_builtin_fun (Z3_Interface.Sym ("<=", _)) [ct, cu] = SOME (mk_le ct cu)
+ | z3_mk_builtin_fun (Z3_Interface.Sym (">", _)) [ct, cu] = SOME (mk_lt cu ct)
+ | z3_mk_builtin_fun (Z3_Interface.Sym (">=", _)) [ct, cu] = SOME (mk_le cu ct)
+ | z3_mk_builtin_fun _ _ = NONE
+in
+
+val z3_mk_builtins = {
+ mk_builtin_typ = z3_mk_builtin_typ,
+ mk_builtin_num = z3_mk_builtin_num,
+ mk_builtin_fun = (fn _ => fn sym => fn cts =>
+ (case try (#T o Thm.rep_cterm o hd) cts of
+ SOME @{typ real} => z3_mk_builtin_fun sym cts
+ | _ => NONE)) }
+
+end
+
+
+(* Z3 proof replay *)
+
+val real_linarith_proc = Simplifier.simproc_global @{theory} "fast_real_arith" [
+ "(m::real) < n", "(m::real) <= n", "(m::real) = n"] Lin_Arith.simproc
+
+
+(* setup *)
+
+val _ = Theory.setup (Context.theory_map (
+ SMTLIB_Interface.add_logic (10, smtlib_logic) #>
+ setup_builtins #>
+ Z3_Interface.add_mk_builtins z3_mk_builtins #>
+ Z3_Replay_Util.add_simproc real_linarith_proc))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_solver.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,306 @@
+(* Title: HOL/Tools/SMT/smt_solver.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT solvers registry and SMT tactic.
+*)
+
+signature SMT_SOLVER =
+sig
+ (*configuration*)
+ datatype outcome = Unsat | Sat | Unknown
+
+ type parsed_proof =
+ {outcome: SMT_Failure.failure option,
+ fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list,
+ atp_proof: unit -> (term, string) ATP_Proof.atp_step list}
+
+ type solver_config =
+ {name: string,
+ class: Proof.context -> SMT_Util.class,
+ avail: unit -> bool,
+ command: unit -> string list,
+ options: Proof.context -> string list,
+ smt_options: (string * string) list,
+ default_max_relevant: int,
+ outcome: string -> string list -> outcome * string list,
+ parse_proof: (Proof.context -> SMT_Translate.replay_data ->
+ ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
+ parsed_proof) option,
+ replay: (Proof.context -> SMT_Translate.replay_data -> string list -> thm) option}
+
+ (*registry*)
+ val add_solver: solver_config -> theory -> theory
+ val default_max_relevant: Proof.context -> string -> int
+
+ (*filter*)
+ val smt_filter: Proof.context -> thm -> ((string * ATP_Problem_Generate.stature) * thm) list ->
+ int -> Time.time -> parsed_proof
+
+ (*tactic*)
+ val smt_tac: Proof.context -> thm list -> int -> tactic
+ val smt_tac': Proof.context -> thm list -> int -> tactic
+end;
+
+structure SMT_Solver: SMT_SOLVER =
+struct
+
+(* interface to external solvers *)
+
+local
+
+fun make_command command options problem_path proof_path =
+ "(exec 2>&1;" :: map File.shell_quote (command () @ options) @
+ [File.shell_path problem_path, ")", ">", File.shell_path proof_path]
+ |> space_implode " "
+
+fun with_trace ctxt msg f x =
+ let val _ = SMT_Config.trace_msg ctxt (fn () => msg) ()
+ in f x end
+
+fun run ctxt name mk_cmd input =
+ (case SMT_Config.certificates_of ctxt of
+ NONE =>
+ if not (SMT_Config.is_available ctxt name) then
+ error ("The SMT solver " ^ quote name ^ " is not installed")
+ else if Config.get ctxt SMT_Config.debug_files = "" then
+ with_trace ctxt ("Invoking SMT solver " ^ quote name ^ " ...") (Cache_IO.run mk_cmd) input
+ else
+ let
+ val base_path = Path.explode (Config.get ctxt SMT_Config.debug_files)
+ val in_path = Path.ext "smt_in" base_path
+ val out_path = Path.ext "smt_out" base_path
+ in Cache_IO.raw_run mk_cmd input in_path out_path end
+ | SOME certs =>
+ (case Cache_IO.lookup certs input of
+ (NONE, key) =>
+ if Config.get ctxt SMT_Config.read_only_certificates then
+ error ("Bad certificate cache: missing certificate")
+ else
+ Cache_IO.run_and_cache certs key mk_cmd input
+ | (SOME output, _) =>
+ with_trace ctxt ("Using cached certificate from " ^
+ File.shell_path (Cache_IO.cache_path_of certs) ^ " ...") I output))
+
+(* Z3 returns 1 if "get-model" or "get-model" fails *)
+val normal_return_codes = [0, 1]
+
+fun run_solver ctxt name mk_cmd input =
+ let
+ fun pretty tag lines = Pretty.string_of (Pretty.big_list tag (map Pretty.str lines))
+
+ val _ = SMT_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input
+
+ val {redirected_output = res, output = err, return_code} =
+ SMT_Config.with_timeout ctxt (run ctxt name mk_cmd) input
+ val _ = SMT_Config.trace_msg ctxt (pretty "Solver:") err
+
+ val output = fst (take_suffix (equal "") res)
+ val _ = SMT_Config.trace_msg ctxt (pretty "Result:") output
+
+ val _ = member (op =) normal_return_codes return_code orelse
+ raise SMT_Failure.SMT (SMT_Failure.Abnormal_Termination return_code)
+ in output end
+
+fun trace_assms ctxt =
+ SMT_Config.trace_msg ctxt (Pretty.string_of o
+ Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd))
+
+fun trace_replay_data ({context = ctxt, typs, terms, ...} : SMT_Translate.replay_data) =
+ let
+ fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]
+ fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)
+ fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)
+ in
+ SMT_Config.trace_msg ctxt (fn () =>
+ Pretty.string_of (Pretty.big_list "Names:" [
+ Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)),
+ Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) ()
+ end
+
+in
+
+fun invoke name command smt_options ithms ctxt =
+ let
+ val options = SMT_Config.solver_options_of ctxt
+ val comments = [space_implode " " options]
+
+ val (str, replay_data as {context = ctxt', ...}) =
+ ithms
+ |> tap (trace_assms ctxt)
+ |> SMT_Translate.translate ctxt smt_options comments
+ ||> tap trace_replay_data
+ in (run_solver ctxt' name (make_command command options) str, replay_data) end
+
+end
+
+
+(* configuration *)
+
+datatype outcome = Unsat | Sat | Unknown
+
+type parsed_proof =
+ {outcome: SMT_Failure.failure option,
+ fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list,
+ atp_proof: unit -> (term, string) ATP_Proof.atp_step list}
+
+type solver_config =
+ {name: string,
+ class: Proof.context -> SMT_Util.class,
+ avail: unit -> bool,
+ command: unit -> string list,
+ options: Proof.context -> string list,
+ smt_options: (string * string) list,
+ default_max_relevant: int,
+ outcome: string -> string list -> outcome * string list,
+ parse_proof: (Proof.context -> SMT_Translate.replay_data ->
+ ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
+ parsed_proof) option,
+ replay: (Proof.context -> SMT_Translate.replay_data -> string list -> thm) option}
+
+
+(* check well-sortedness *)
+
+val has_topsort = Term.exists_type (Term.exists_subtype (fn
+ TFree (_, []) => true
+ | TVar (_, []) => true
+ | _ => false))
+
+(* top sorts cause problems with atomization *)
+fun check_topsort ctxt thm =
+ if has_topsort (Thm.prop_of thm) then (SMT_Normalize.drop_fact_warning ctxt thm; TrueI) else thm
+
+
+(* registry *)
+
+type solver_info = {
+ command: unit -> string list,
+ smt_options: (string * string) list,
+ default_max_relevant: int,
+ parse_proof: Proof.context -> SMT_Translate.replay_data ->
+ ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
+ parsed_proof,
+ replay: Proof.context -> SMT_Translate.replay_data -> string list -> thm}
+
+structure Solvers = Generic_Data
+(
+ type T = solver_info Symtab.table
+ val empty = Symtab.empty
+ val extend = I
+ fun merge data = Symtab.merge (K true) data
+)
+
+local
+ fun parse_proof outcome parse_proof0 outer_ctxt replay_data xfacts prems concl output =
+ (case outcome output of
+ (Unsat, lines) =>
+ (case parse_proof0 of
+ SOME pp => pp outer_ctxt replay_data xfacts prems concl lines
+ | NONE => {outcome = NONE, fact_ids = [], atp_proof = K []})
+ | (result, _) => raise SMT_Failure.SMT (SMT_Failure.Counterexample (result = Sat)))
+
+ fun replay outcome replay0 oracle outer_ctxt
+ (replay_data as {context = ctxt, ...} : SMT_Translate.replay_data) output =
+ (case outcome output of
+ (Unsat, lines) =>
+ if not (Config.get ctxt SMT_Config.oracle) andalso is_some replay0
+ then the replay0 outer_ctxt replay_data lines
+ else oracle ()
+ | (result, _) => raise SMT_Failure.SMT (SMT_Failure.Counterexample (result = Sat)))
+
+ val cfalse = Thm.cterm_of @{theory} @{prop False}
+in
+
+fun add_solver ({name, class, avail, command, options, smt_options, default_max_relevant, outcome,
+ parse_proof = parse_proof0, replay = replay0} : solver_config) =
+ let
+ fun solver oracle = {
+ command = command,
+ smt_options = smt_options,
+ default_max_relevant = default_max_relevant,
+ parse_proof = parse_proof (outcome name) parse_proof0,
+ replay = replay (outcome name) replay0 oracle}
+
+ val info = {name = name, class = class, avail = avail, options = options}
+ in
+ Thm.add_oracle (Binding.name name, K cfalse) #-> (fn (_, oracle) =>
+ Context.theory_map (Solvers.map (Symtab.update_new (name, solver oracle)))) #>
+ Context.theory_map (SMT_Config.add_solver info)
+ end
+
+end
+
+fun get_info ctxt name = the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name)
+
+fun name_and_info_of ctxt =
+ let val name = SMT_Config.solver_of ctxt
+ in (name, get_info ctxt name) end
+
+val default_max_relevant = #default_max_relevant oo get_info
+
+fun apply_solver_and_replay ctxt thms0 =
+ let
+ val thms = map (check_topsort ctxt) thms0
+ val (name, {command, smt_options, replay, ...}) = name_and_info_of ctxt
+ val (output, replay_data) =
+ invoke name command smt_options (SMT_Normalize.normalize ctxt thms) ctxt
+ in replay ctxt replay_data output end
+
+
+(* filter *)
+
+fun smt_filter ctxt0 goal xfacts i time_limit =
+ let
+ val ctxt = ctxt0 |> Config.put SMT_Config.timeout (Time.toReal time_limit)
+
+ val ({context = ctxt, prems, concl, ...}, _) = Subgoal.focus ctxt i goal
+ fun negate ct = Thm.dest_comb ct ||> Thm.apply @{cterm Not} |-> Thm.apply
+ val cprop =
+ (case try negate (Thm.rhs_of (SMT_Normalize.atomize_conv ctxt concl)) of
+ SOME ct => ct
+ | NONE => raise SMT_Failure.SMT (SMT_Failure.Other_Failure "goal is not a HOL term"))
+
+ val conjecture = Thm.assume cprop
+ val facts = map snd xfacts
+ val thms = conjecture :: prems @ facts
+ val thms' = map (check_topsort ctxt) thms
+
+ val (name, {command, smt_options, parse_proof, ...}) = name_and_info_of ctxt
+ val (output, replay_data) =
+ invoke name command smt_options (SMT_Normalize.normalize ctxt thms') ctxt
+ in
+ parse_proof ctxt replay_data xfacts (map Thm.prop_of prems) (Thm.term_of concl) output
+ end
+ handle SMT_Failure.SMT fail => {outcome = SOME fail, fact_ids = [], atp_proof = K []}
+
+
+(* SMT tactic *)
+
+local
+ fun str_of ctxt fail =
+ "Solver " ^ SMT_Config.solver_of ctxt ^ ": " ^ SMT_Failure.string_of_failure fail
+
+ fun safe_solve ctxt facts = SOME (apply_solver_and_replay ctxt facts)
+ handle
+ SMT_Failure.SMT (fail as SMT_Failure.Counterexample _) =>
+ (SMT_Config.verbose_msg ctxt (str_of ctxt) fail; NONE)
+ | SMT_Failure.SMT (fail as SMT_Failure.Time_Out) =>
+ error ("SMT: Solver " ^ quote (SMT_Config.solver_of ctxt) ^ ": " ^
+ SMT_Failure.string_of_failure fail ^ " (setting the " ^
+ "configuration option " ^ quote (Config.name_of SMT_Config.timeout) ^ " might help)")
+ | SMT_Failure.SMT fail => error (str_of ctxt fail)
+
+ fun resolve (SOME thm) = rtac thm 1
+ | resolve NONE = no_tac
+
+ fun tac prove ctxt rules =
+ CONVERSION (SMT_Normalize.atomize_conv ctxt)
+ THEN' rtac @{thm ccontr}
+ THEN' SUBPROOF (fn {context = ctxt, prems, ...} => resolve (prove ctxt (rules @ prems))) ctxt
+in
+
+val smt_tac = tac safe_solve
+val smt_tac' = tac (SOME oo apply_solver_and_replay)
+
+end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_systems.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,188 @@
+(* Title: HOL/Tools/SMT/smt_systems.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Setup SMT solvers.
+*)
+
+signature SMT_SYSTEMS =
+sig
+ datatype z3_non_commercial =
+ Z3_Non_Commercial_Unknown |
+ Z3_Non_Commercial_Accepted |
+ Z3_Non_Commercial_Declined
+ val z3_non_commercial: unit -> z3_non_commercial
+ val z3_extensions: bool Config.T
+end;
+
+structure SMT_Systems: SMT_SYSTEMS =
+struct
+
+(* helper functions *)
+
+fun make_avail name () = getenv (name ^ "_SOLVER") <> ""
+
+fun make_command name () = [getenv (name ^ "_SOLVER")]
+
+fun outcome_of unsat sat unknown solver_name line =
+ if String.isPrefix unsat line then SMT_Solver.Unsat
+ else if String.isPrefix sat line then SMT_Solver.Sat
+ else if String.isPrefix unknown line then SMT_Solver.Unknown
+ else raise SMT_Failure.SMT (SMT_Failure.Other_Failure ("Solver " ^ quote solver_name ^
+ " failed -- enable tracing using the " ^ quote (Config.name_of SMT_Config.trace) ^
+ " option for details"))
+
+fun on_first_line test_outcome solver_name lines =
+ let
+ val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
+ val (l, ls) = split_first (snd (take_prefix (curry (op =) "") lines))
+ in (test_outcome solver_name l, ls) end
+
+fun on_first_non_unsupported_line test_outcome solver_name lines =
+ on_first_line test_outcome solver_name (filter (curry (op <>) "unsupported") lines)
+
+(* CVC3 *)
+
+local
+ fun cvc3_options ctxt = [
+ "-seed", string_of_int (Config.get ctxt SMT_Config.random_seed),
+ "-lang", "smt2",
+ "-timeout", string_of_int (Real.ceil (Config.get ctxt SMT_Config.timeout))]
+in
+
+val cvc3: SMT_Solver.solver_config = {
+ name = "cvc3",
+ class = K SMTLIB_Interface.smtlibC,
+ avail = make_avail "CVC3",
+ command = make_command "CVC3",
+ options = cvc3_options,
+ smt_options = [],
+ default_max_relevant = 400 (* FUDGE *),
+ outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
+ parse_proof = NONE,
+ replay = NONE }
+
+end
+
+
+(* CVC4 *)
+
+local
+ fun cvc4_options ctxt = [
+ "--random-seed=" ^ string_of_int (Config.get ctxt SMT_Config.random_seed),
+ "--lang=smt2",
+ "--tlimit", string_of_int (Real.ceil (1000.0 * Config.get ctxt SMT_Config.timeout))]
+in
+
+val cvc4: SMT_Solver.solver_config = {
+ name = "cvc4",
+ class = K SMTLIB_Interface.smtlibC,
+ avail = make_avail "CVC4",
+ command = make_command "CVC4",
+ options = cvc4_options,
+ smt_options = [],
+ default_max_relevant = 400 (* FUDGE *),
+ outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
+ parse_proof = NONE,
+ replay = NONE }
+
+end
+
+(* veriT *)
+
+val veriT: SMT_Solver.solver_config = {
+ name = "veriT",
+ class = K SMTLIB_Interface.smtlibC,
+ avail = make_avail "VERIT",
+ command = make_command "VERIT",
+ options = (fn ctxt => [
+ "--proof-version=1",
+ "--proof=-",
+ "--proof-prune",
+ "--proof-merge",
+ "--disable-print-success",
+ "--disable-banner",
+ "--max-time=" ^ string_of_int (Real.ceil (Config.get ctxt SMT_Config.timeout))]),
+ smt_options = [],
+ default_max_relevant = 120 (* FUDGE *),
+ outcome = on_first_non_unsupported_line (outcome_of "unsat" "sat"
+ "warning : proof_done: status is still open"),
+ parse_proof = SOME VeriT_Proof_Parse.parse_proof,
+ replay = NONE }
+
+(* Z3 *)
+
+datatype z3_non_commercial =
+ Z3_Non_Commercial_Unknown |
+ Z3_Non_Commercial_Accepted |
+ Z3_Non_Commercial_Declined
+
+local
+ val accepted = member (op =) ["yes", "Yes", "YES"]
+ val declined = member (op =) ["no", "No", "NO"]
+in
+
+fun z3_non_commercial () =
+ let
+ val flag1 = Options.default_string @{system_option z3_non_commercial}
+ val flag2 = getenv "Z3_NON_COMMERCIAL"
+ in
+ if accepted flag1 then Z3_Non_Commercial_Accepted
+ else if declined flag1 then Z3_Non_Commercial_Declined
+ else if accepted flag2 then Z3_Non_Commercial_Accepted
+ else if declined flag2 then Z3_Non_Commercial_Declined
+ else Z3_Non_Commercial_Unknown
+ end
+
+fun if_z3_non_commercial f =
+ (case z3_non_commercial () of
+ Z3_Non_Commercial_Accepted => f ()
+ | Z3_Non_Commercial_Declined =>
+ error (Pretty.string_of (Pretty.para
+ "The SMT solver Z3 may be used only for non-commercial applications."))
+ | Z3_Non_Commercial_Unknown =>
+ error (Pretty.string_of (Pretty.para
+ ("The SMT solver Z3 is not activated. To activate it, set the Isabelle \
+ \system option \"z3_non_commercial\" to \"yes\" (e.g. via \
+ \the Isabelle/jEdit menu Plugin Options / Isabelle / General)."))))
+
+end
+
+val z3_extensions = Attrib.setup_config_bool @{binding z3_extensions} (K false)
+
+local
+ fun z3_make_command name () = if_z3_non_commercial (make_command name)
+
+ fun z3_options ctxt =
+ ["smt.random_seed=" ^ string_of_int (Config.get ctxt SMT_Config.random_seed),
+ "smt.refine_inj_axioms=false",
+ "-T:" ^ string_of_int (Real.ceil (Config.get ctxt SMT_Config.timeout)),
+ "-smt2"]
+
+ fun select_class ctxt =
+ if Config.get ctxt z3_extensions then Z3_Interface.smtlib_z3C else SMTLIB_Interface.smtlibC
+in
+
+val z3: SMT_Solver.solver_config = {
+ name = "z3",
+ class = select_class,
+ avail = make_avail "Z3_NEW",
+ command = z3_make_command "Z3_NEW",
+ options = z3_options,
+ smt_options = [(":produce-proofs", "true")],
+ default_max_relevant = 350 (* FUDGE *),
+ outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
+ parse_proof = SOME Z3_Replay.parse_proof,
+ replay = SOME Z3_Replay.replay }
+
+end
+
+
+(* overall setup *)
+
+val _ = Theory.setup (
+ SMT_Solver.add_solver cvc3 #>
+ SMT_Solver.add_solver cvc4 #>
+ SMT_Solver.add_solver veriT #>
+ SMT_Solver.add_solver z3)
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_translate.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,522 @@
+(* Title: HOL/Tools/SMT/smt_translate.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Translate theorems into an SMT intermediate format and serialize them.
+*)
+
+signature SMT_TRANSLATE =
+sig
+ (*intermediate term structure*)
+ datatype squant = SForall | SExists
+ datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
+ datatype sterm =
+ SVar of int |
+ SApp of string * sterm list |
+ SLet of string * sterm * sterm |
+ SQua of squant * string list * sterm spattern list * sterm
+
+ (*translation configuration*)
+ type sign = {
+ logic: string,
+ sorts: string list,
+ dtyps: (string * (string * (string * string) list) list) list list,
+ funcs: (string * (string list * string)) list }
+ type config = {
+ logic: term list -> string,
+ has_datatypes: bool,
+ serialize: (string * string) list -> string list -> sign -> sterm list -> string }
+ type replay_data = {
+ context: Proof.context,
+ typs: typ Symtab.table,
+ terms: term Symtab.table,
+ ll_defs: term list,
+ rewrite_rules: thm list,
+ assms: (int * thm) list }
+
+ (*translation*)
+ val add_config: SMT_Util.class * (Proof.context -> config) -> Context.generic -> Context.generic
+ val translate: Proof.context -> (string * string) list -> string list -> (int * thm) list ->
+ string * replay_data
+end;
+
+structure SMT_Translate: SMT_TRANSLATE =
+struct
+
+
+(* intermediate term structure *)
+
+datatype squant = SForall | SExists
+
+datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
+
+datatype sterm =
+ SVar of int |
+ SApp of string * sterm list |
+ SLet of string * sterm * sterm |
+ SQua of squant * string list * sterm spattern list * sterm
+
+
+(* translation configuration *)
+
+type sign = {
+ logic: string,
+ sorts: string list,
+ dtyps: (string * (string * (string * string) list) list) list list,
+ funcs: (string * (string list * string)) list }
+
+type config = {
+ logic: term list -> string,
+ has_datatypes: bool,
+ serialize: (string * string) list -> string list -> sign -> sterm list -> string }
+
+type replay_data = {
+ context: Proof.context,
+ typs: typ Symtab.table,
+ terms: term Symtab.table,
+ ll_defs: term list,
+ rewrite_rules: thm list,
+ assms: (int * thm) list }
+
+
+(* translation context *)
+
+fun add_components_of_typ (Type (s, Ts)) =
+ cons (Long_Name.base_name s) #> fold_rev add_components_of_typ Ts
+ | add_components_of_typ (TFree (s, _)) = cons (perhaps (try (unprefix "'")) s)
+ | add_components_of_typ _ = I;
+
+fun suggested_name_of_typ T = space_implode "_" (add_components_of_typ T []);
+
+fun suggested_name_of_term (Const (s, _)) = Long_Name.base_name s
+ | suggested_name_of_term (Free (s, _)) = s
+ | suggested_name_of_term _ = Name.uu
+
+val empty_tr_context = (Name.context, Typtab.empty, Termtab.empty)
+val safe_suffix = "$"
+
+fun add_typ T proper (cx as (names, typs, terms)) =
+ (case Typtab.lookup typs T of
+ SOME (name, _) => (name, cx)
+ | NONE =>
+ let
+ val sugg = Name.desymbolize (SOME true) (suggested_name_of_typ T) ^ safe_suffix
+ val (name, names') = Name.variant sugg names
+ val typs' = Typtab.update (T, (name, proper)) typs
+ in (name, (names', typs', terms)) end)
+
+fun add_fun t sort (cx as (names, typs, terms)) =
+ (case Termtab.lookup terms t of
+ SOME (name, _) => (name, cx)
+ | NONE =>
+ let
+ val sugg = Name.desymbolize (SOME false) (suggested_name_of_term t) ^ safe_suffix
+ val (name, names') = Name.variant sugg names
+ val terms' = Termtab.update (t, (name, sort)) terms
+ in (name, (names', typs, terms')) end)
+
+fun sign_of logic dtyps (_, typs, terms) = {
+ logic = logic,
+ sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
+ dtyps = dtyps,
+ funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
+
+fun replay_data_of ctxt ll_defs rules assms (_, typs, terms) =
+ let
+ fun add_typ (T, (n, _)) = Symtab.update (n, T)
+ val typs' = Typtab.fold add_typ typs Symtab.empty
+
+ fun add_fun (t, (n, _)) = Symtab.update (n, t)
+ val terms' = Termtab.fold add_fun terms Symtab.empty
+ in
+ {context = ctxt, typs = typs', terms = terms', ll_defs = ll_defs, rewrite_rules = rules,
+ assms = assms}
+ end
+
+
+(* preprocessing *)
+
+(** datatype declarations **)
+
+fun collect_datatypes_and_records (tr_context, ctxt) ts =
+ let
+ val (declss, ctxt') = fold (Term.fold_types SMT_Datatypes.add_decls) ts ([], ctxt)
+
+ fun is_decl_typ T = exists (exists (equal T o fst)) declss
+
+ fun add_typ' T proper =
+ (case SMT_Builtin.dest_builtin_typ ctxt' T of
+ SOME n => pair n
+ | NONE => add_typ T proper)
+
+ fun tr_select sel =
+ let val T = Term.range_type (Term.fastype_of sel)
+ in add_fun sel NONE ##>> add_typ' T (not (is_decl_typ T)) end
+ fun tr_constr (constr, selects) =
+ add_fun constr NONE ##>> fold_map tr_select selects
+ fun tr_typ (T, cases) = add_typ' T false ##>> fold_map tr_constr cases
+ val (declss', tr_context') = fold_map (fold_map tr_typ) declss tr_context
+
+ fun add (constr, selects) =
+ Termtab.update (constr, length selects) #>
+ fold (Termtab.update o rpair 1) selects
+ val funcs = fold (fold (fold add o snd)) declss Termtab.empty
+ in ((funcs, declss', tr_context', ctxt'), ts) end
+ (* FIXME: also return necessary datatype and record theorems *)
+
+
+(** eta-expand quantifiers, let expressions and built-ins *)
+
+local
+ fun eta f T t = Abs (Name.uu, T, f (Term.incr_boundvars 1 t $ Bound 0))
+
+ fun exp f T = eta f (Term.domain_type (Term.domain_type T))
+
+ fun exp2 T q =
+ let val U = Term.domain_type T
+ in Abs (Name.uu, U, q $ eta I (Term.domain_type U) (Bound 0)) end
+
+ fun expf k i T t =
+ let val Ts = drop i (fst (SMT_Util.dest_funT k T))
+ in
+ Term.incr_boundvars (length Ts) t
+ |> fold_rev (fn i => fn u => u $ Bound i) (0 upto length Ts - 1)
+ |> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts
+ end
+in
+
+fun eta_expand ctxt funcs =
+ let
+ fun exp_func t T ts =
+ (case Termtab.lookup funcs t of
+ SOME k => Term.list_comb (t, ts) |> k <> length ts ? expf k (length ts) T
+ | NONE => Term.list_comb (t, ts))
+
+ fun expand ((q as Const (@{const_name All}, _)) $ Abs a) = q $ abs_expand a
+ | expand ((q as Const (@{const_name All}, T)) $ t) = q $ exp expand T t
+ | expand (q as Const (@{const_name All}, T)) = exp2 T q
+ | expand ((q as Const (@{const_name Ex}, _)) $ Abs a) = q $ abs_expand a
+ | expand ((q as Const (@{const_name Ex}, T)) $ t) = q $ exp expand T t
+ | expand (q as Const (@{const_name Ex}, T)) = exp2 T q
+ | expand (Const (@{const_name Let}, _) $ t $ u) = expand (Term.betapply (u, t))
+ | expand (Const (@{const_name Let}, T) $ t) =
+ let val U = Term.domain_type (Term.range_type T)
+ in Abs (Name.uu, U, Bound 0 $ Term.incr_boundvars 1 t) end
+ | expand (Const (@{const_name Let}, T)) =
+ let val U = Term.domain_type (Term.range_type T)
+ in Abs (Name.uu, Term.domain_type T, Abs (Name.uu, U, Bound 0 $ Bound 1)) end
+ | expand t =
+ (case Term.strip_comb t of
+ (u as Const (c as (_, T)), ts) =>
+ (case SMT_Builtin.dest_builtin ctxt c ts of
+ SOME (_, k, us, mk) =>
+ if k = length us then mk (map expand us)
+ else if k < length us then chop k (map expand us) |>> mk |> Term.list_comb
+ else expf k (length ts) T (mk (map expand us))
+ | NONE => exp_func u T (map expand ts))
+ | (u as Free (_, T), ts) => exp_func u T (map expand ts)
+ | (Abs a, ts) => Term.list_comb (abs_expand a, map expand ts)
+ | (u, ts) => Term.list_comb (u, map expand ts))
+
+ and abs_expand (n, T, t) = Abs (n, T, expand t)
+
+ in map expand end
+
+end
+
+
+(** introduce explicit applications **)
+
+local
+ (*
+ Make application explicit for functions with varying number of arguments.
+ *)
+
+ fun add t i = apfst (Termtab.map_default (t, i) (Integer.min i))
+ fun add_type T = apsnd (Typtab.update (T, ()))
+
+ fun min_arities t =
+ (case Term.strip_comb t of
+ (u as Const _, ts) => add u (length ts) #> fold min_arities ts
+ | (u as Free _, ts) => add u (length ts) #> fold min_arities ts
+ | (Abs (_, T, u), ts) => (can dest_funT T ? add_type T) #> min_arities u #> fold min_arities ts
+ | (_, ts) => fold min_arities ts)
+
+ fun minimize types t i =
+ let
+ fun find_min j [] _ = j
+ | find_min j (U :: Us) T =
+ if Typtab.defined types T then j else find_min (j + 1) Us (U --> T)
+
+ val (Ts, T) = Term.strip_type (Term.type_of t)
+ in find_min 0 (take i (rev Ts)) T end
+
+ fun app u (t, T) = (Const (@{const_name fun_app}, T --> T) $ t $ u, Term.range_type T)
+
+ fun apply i t T ts =
+ let
+ val (ts1, ts2) = chop i ts
+ val (_, U) = SMT_Util.dest_funT i T
+ in fst (fold app ts2 (Term.list_comb (t, ts1), U)) end
+in
+
+fun intro_explicit_application ctxt funcs ts =
+ let
+ val (arities, types) = fold min_arities ts (Termtab.empty, Typtab.empty)
+ val arities' = Termtab.map (minimize types) arities (* FIXME: highly suspicious *)
+
+ fun app_func t T ts =
+ if is_some (Termtab.lookup funcs t) then Term.list_comb (t, ts)
+ else apply (the (Termtab.lookup arities' t)) t T ts
+
+ fun in_list T f t = SMT_Util.mk_symb_list T (map f (SMT_Util.dest_symb_list t))
+
+ fun traverse Ts t =
+ (case Term.strip_comb t of
+ (q as Const (@{const_name All}, _), [Abs (x, T, u)]) =>
+ q $ Abs (x, T, in_trigger (T :: Ts) u)
+ | (q as Const (@{const_name Ex}, _), [Abs (x, T, u)]) =>
+ q $ Abs (x, T, in_trigger (T :: Ts) u)
+ | (q as Const (@{const_name Let}, _), [u1, u2 as Abs _]) =>
+ q $ traverse Ts u1 $ traverse Ts u2
+ | (u as Const (c as (_, T)), ts) =>
+ (case SMT_Builtin.dest_builtin ctxt c ts of
+ SOME (_, k, us, mk) =>
+ let
+ val (ts1, ts2) = chop k (map (traverse Ts) us)
+ val U = Term.strip_type T |>> snd o chop k |> (op --->)
+ in apply 0 (mk ts1) U ts2 end
+ | NONE => app_func u T (map (traverse Ts) ts))
+ | (u as Free (_, T), ts) => app_func u T (map (traverse Ts) ts)
+ | (u as Bound i, ts) => apply 0 u (nth Ts i) (map (traverse Ts) ts)
+ | (Abs (n, T, u), ts) => traverses Ts (Abs (n, T, traverse (T::Ts) u)) ts
+ | (u, ts) => traverses Ts u ts)
+ and in_trigger Ts ((c as @{const trigger}) $ p $ t) = c $ in_pats Ts p $ traverse Ts t
+ | in_trigger Ts t = traverse Ts t
+ and in_pats Ts ps =
+ in_list @{typ "pattern symb_list"} (in_list @{typ pattern} (in_pat Ts)) ps
+ and in_pat Ts ((p as Const (@{const_name pat}, _)) $ t) = p $ traverse Ts t
+ | in_pat Ts ((p as Const (@{const_name nopat}, _)) $ t) = p $ traverse Ts t
+ | in_pat _ t = raise TERM ("bad pattern", [t])
+ and traverses Ts t ts = Term.list_comb (t, map (traverse Ts) ts)
+ in map (traverse []) ts end
+
+val fun_app_eq = mk_meta_eq @{thm fun_app_def}
+
+end
+
+
+(** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
+
+local
+ val is_quant = member (op =) [@{const_name All}, @{const_name Ex}]
+
+ val fol_rules = [
+ Let_def,
+ @{lemma "P = True == P" by (rule eq_reflection) simp},
+ @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
+
+ exception BAD_PATTERN of unit
+
+ fun wrap_in_if pat t =
+ if pat then raise BAD_PATTERN () else @{const If (bool)} $ t $ @{const True} $ @{const False}
+
+ fun is_builtin_conn_or_pred ctxt c ts =
+ is_some (SMT_Builtin.dest_builtin_conn ctxt c ts) orelse
+ is_some (SMT_Builtin.dest_builtin_pred ctxt c ts)
+in
+
+fun folify ctxt =
+ let
+ fun in_list T f t = SMT_Util.mk_symb_list T (map_filter f (SMT_Util.dest_symb_list t))
+
+ fun in_term pat t =
+ (case Term.strip_comb t of
+ (@{const True}, []) => t
+ | (@{const False}, []) => t
+ | (u as Const (@{const_name If}, _), [t1, t2, t3]) =>
+ if pat then raise BAD_PATTERN () else u $ in_form t1 $ in_term pat t2 $ in_term pat t3
+ | (Const (c as (n, _)), ts) =>
+ if is_builtin_conn_or_pred ctxt c ts then wrap_in_if pat (in_form t)
+ else if is_quant n then wrap_in_if pat (in_form t)
+ else Term.list_comb (Const c, map (in_term pat) ts)
+ | (Free c, ts) => Term.list_comb (Free c, map (in_term pat) ts)
+ | _ => t)
+
+ and in_pat ((p as Const (@{const_name pat}, _)) $ t) =
+ p $ in_term true t
+ | in_pat ((p as Const (@{const_name nopat}, _)) $ t) =
+ p $ in_term true t
+ | in_pat t = raise TERM ("bad pattern", [t])
+
+ and in_pats ps =
+ in_list @{typ "pattern symb_list"} (SOME o in_list @{typ pattern} (try in_pat)) ps
+
+ and in_trigger ((c as @{const trigger}) $ p $ t) = c $ in_pats p $ in_form t
+ | in_trigger t = in_form t
+
+ and in_form t =
+ (case Term.strip_comb t of
+ (q as Const (qn, _), [Abs (n, T, u)]) =>
+ if is_quant qn then q $ Abs (n, T, in_trigger u)
+ else in_term false t
+ | (Const c, ts) =>
+ (case SMT_Builtin.dest_builtin_conn ctxt c ts of
+ SOME (_, _, us, mk) => mk (map in_form us)
+ | NONE =>
+ (case SMT_Builtin.dest_builtin_pred ctxt c ts of
+ SOME (_, _, us, mk) => mk (map (in_term false) us)
+ | NONE => in_term false t))
+ | _ => in_term false t)
+ in
+ map in_form #>
+ pair (fol_rules, I)
+ end
+
+end
+
+
+(* translation into intermediate format *)
+
+(** utility functions **)
+
+val quantifier = (fn
+ @{const_name All} => SOME SForall
+ | @{const_name Ex} => SOME SExists
+ | _ => NONE)
+
+fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
+ if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
+ | group_quant _ Ts t = (Ts, t)
+
+fun dest_pat (Const (@{const_name pat}, _) $ t) = (t, true)
+ | dest_pat (Const (@{const_name nopat}, _) $ t) = (t, false)
+ | dest_pat t = raise TERM ("bad pattern", [t])
+
+fun dest_pats [] = I
+ | dest_pats ts =
+ (case map dest_pat ts |> split_list ||> distinct (op =) of
+ (ps, [true]) => cons (SPat ps)
+ | (ps, [false]) => cons (SNoPat ps)
+ | _ => raise TERM ("bad multi-pattern", ts))
+
+fun dest_trigger (@{const trigger} $ tl $ t) =
+ (rev (fold (dest_pats o SMT_Util.dest_symb_list) (SMT_Util.dest_symb_list tl) []), t)
+ | dest_trigger t = ([], t)
+
+fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
+ let
+ val (Ts, u) = group_quant qn [T] t
+ val (ps, p) = dest_trigger u
+ in (q, rev Ts, ps, p) end)
+
+fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
+ | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
+
+
+(** translation from Isabelle terms into SMT intermediate terms **)
+
+fun intermediate logic dtyps builtin ctxt ts trx =
+ let
+ fun transT (T as TFree _) = add_typ T true
+ | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
+ | transT (T as Type _) =
+ (case SMT_Builtin.dest_builtin_typ ctxt T of
+ SOME n => pair n
+ | NONE => add_typ T true)
+
+ fun app n ts = SApp (n, ts)
+
+ fun trans t =
+ (case Term.strip_comb t of
+ (Const (qn, _), [Abs (_, T, t1)]) =>
+ (case dest_quant qn T t1 of
+ SOME (q, Ts, ps, b) =>
+ fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
+ trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', b'))
+ | NONE => raise TERM ("unsupported quantifier", [t]))
+ | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
+ transT T ##>> trans t1 ##>> trans t2 #>> (fn ((U, u1), u2) => SLet (U, u1, u2))
+ | (u as Const (c as (_, T)), ts) =>
+ (case builtin ctxt c ts of
+ SOME (n, _, us, _) => fold_map trans us #>> app n
+ | NONE => transs u T ts)
+ | (u as Free (_, T), ts) => transs u T ts
+ | (Bound i, []) => pair (SVar i)
+ | _ => raise TERM ("bad SMT term", [t]))
+
+ and transs t T ts =
+ let val (Us, U) = SMT_Util.dest_funT (length ts) T
+ in
+ fold_map transT Us ##>> transT U #-> (fn Up =>
+ add_fun t (SOME Up) ##>> fold_map trans ts #>> SApp)
+ end
+
+ val (us, trx') = fold_map trans ts trx
+ in ((sign_of (logic ts) dtyps trx', us), trx') end
+
+
+(* translation *)
+
+structure Configs = Generic_Data
+(
+ type T = (Proof.context -> config) SMT_Util.dict
+ val empty = []
+ val extend = I
+ fun merge data = SMT_Util.dict_merge fst data
+)
+
+fun add_config (cs, cfg) = Configs.map (SMT_Util.dict_update (cs, cfg))
+
+fun get_config ctxt =
+ let val cs = SMT_Config.solver_class_of ctxt
+ in
+ (case SMT_Util.dict_get (Configs.get (Context.Proof ctxt)) cs of
+ SOME cfg => cfg ctxt
+ | NONE => error ("SMT: no translation configuration found " ^
+ "for solver class " ^ quote (SMT_Util.string_of_class cs)))
+ end
+
+fun translate ctxt smt_options comments ithms =
+ let
+ val {logic, has_datatypes, serialize} = get_config ctxt
+
+ fun no_dtyps (tr_context, ctxt) ts =
+ ((Termtab.empty, [], tr_context, ctxt), ts)
+
+ val ts1 = map (Envir.beta_eta_contract o SMT_Util.prop_of o snd) ithms
+
+ val ((funcs, dtyps, tr_context, ctxt1), ts2) =
+ ((empty_tr_context, ctxt), ts1)
+ |-> (if has_datatypes then collect_datatypes_and_records else no_dtyps)
+
+ fun is_binder (Const (@{const_name Let}, _) $ _) = true
+ | is_binder t = Lambda_Lifting.is_quantifier t
+
+ fun mk_trigger ((q as Const (@{const_name All}, _)) $ Abs (n, T, t)) =
+ q $ Abs (n, T, mk_trigger t)
+ | mk_trigger (eq as (Const (@{const_name HOL.eq}, T) $ lhs $ _)) =
+ Term.domain_type T --> @{typ pattern}
+ |> (fn T => Const (@{const_name pat}, T) $ lhs)
+ |> SMT_Util.mk_symb_list @{typ pattern} o single
+ |> SMT_Util.mk_symb_list @{typ "pattern symb_list"} o single
+ |> (fn t => @{const trigger} $ t $ eq)
+ | mk_trigger t = t
+
+ val (ctxt2, (ts3, ll_defs)) =
+ ts2
+ |> eta_expand ctxt1 funcs
+ |> rpair ctxt1
+ |-> Lambda_Lifting.lift_lambdas NONE is_binder
+ |-> (fn (ts', ll_defs) => fn ctxt' =>
+ (ctxt', (intro_explicit_application ctxt' funcs (map mk_trigger ll_defs @ ts'), ll_defs)))
+
+ val ((rewrite_rules, builtin), ts4) = folify ctxt2 ts3
+ |>> apfst (cons fun_app_eq)
+ in
+ (ts4, tr_context)
+ |-> intermediate logic dtyps (builtin SMT_Builtin.dest_builtin) ctxt2
+ |>> uncurry (serialize smt_options comments)
+ ||> replay_data_of ctxt2 ll_defs rewrite_rules ithms
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smt_util.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,246 @@
+(* Title: HOL/Tools/SMT/smt_util.ML
+ Author: Sascha Boehme, TU Muenchen
+
+General utility functions.
+*)
+
+signature SMT_UTIL =
+sig
+ (*basic combinators*)
+ val repeat: ('a -> 'a option) -> 'a -> 'a
+ val repeat_yield: ('a -> 'b -> ('a * 'b) option) -> 'a -> 'b -> 'a * 'b
+
+ (*class dictionaries*)
+ type class = string list
+ val basicC: class
+ val string_of_class: class -> string
+ type 'a dict = (class * 'a) Ord_List.T
+ val dict_map_default: class * 'a -> ('a -> 'a) -> 'a dict -> 'a dict
+ val dict_update: class * 'a -> 'a dict -> 'a dict
+ val dict_merge: ('a * 'a -> 'a) -> 'a dict * 'a dict -> 'a dict
+ val dict_lookup: 'a dict -> class -> 'a list
+ val dict_get: 'a dict -> class -> 'a option
+
+ (*types*)
+ val dest_funT: int -> typ -> typ list * typ
+
+ (*terms*)
+ val dest_conj: term -> term * term
+ val dest_disj: term -> term * term
+ val under_quant: (term -> 'a) -> term -> 'a
+ val is_number: term -> bool
+
+ (*symbolic lists*)
+ val symb_nil_const: typ -> term
+ val symb_cons_const: typ -> term
+ val mk_symb_list: typ -> term list -> term
+ val dest_symb_list: term -> term list
+
+ (*patterns and instantiations*)
+ val mk_const_pat: theory -> string -> (ctyp -> 'a) -> 'a * cterm
+ val destT1: ctyp -> ctyp
+ val destT2: ctyp -> ctyp
+ val instTs: ctyp list -> ctyp list * cterm -> cterm
+ val instT: ctyp -> ctyp * cterm -> cterm
+ val instT': cterm -> ctyp * cterm -> cterm
+
+ (*certified terms*)
+ val certify: Proof.context -> term -> cterm
+ val typ_of: cterm -> typ
+ val dest_cabs: cterm -> Proof.context -> cterm * Proof.context
+ val dest_all_cabs: cterm -> Proof.context -> cterm * Proof.context
+ val dest_cbinder: cterm -> Proof.context -> cterm * Proof.context
+ val dest_all_cbinders: cterm -> Proof.context -> cterm * Proof.context
+ val mk_cprop: cterm -> cterm
+ val dest_cprop: cterm -> cterm
+ val mk_cequals: cterm -> cterm -> cterm
+ val term_of: cterm -> term
+ val prop_of: thm -> term
+
+ (*conversions*)
+ val if_conv: (term -> bool) -> conv -> conv -> conv
+ val if_true_conv: (term -> bool) -> conv -> conv
+ val if_exists_conv: (term -> bool) -> conv -> conv
+ val binders_conv: (Proof.context -> conv) -> Proof.context -> conv
+ val under_quant_conv: (Proof.context * cterm list -> conv) ->
+ Proof.context -> conv
+ val prop_conv: conv -> conv
+end;
+
+structure SMT_Util: SMT_UTIL =
+struct
+
+(* basic combinators *)
+
+fun repeat f =
+ let fun rep x = (case f x of SOME y => rep y | NONE => x)
+ in rep end
+
+fun repeat_yield f =
+ let fun rep x y = (case f x y of SOME (x', y') => rep x' y' | NONE => (x, y))
+ in rep end
+
+
+(* class dictionaries *)
+
+type class = string list
+
+val basicC = []
+
+fun string_of_class [] = "basic"
+ | string_of_class cs = "basic." ^ space_implode "." cs
+
+type 'a dict = (class * 'a) Ord_List.T
+
+fun class_ord ((cs1, _), (cs2, _)) =
+ rev_order (list_ord fast_string_ord (cs1, cs2))
+
+fun dict_insert (cs, x) d =
+ if AList.defined (op =) d cs then d
+ else Ord_List.insert class_ord (cs, x) d
+
+fun dict_map_default (cs, x) f =
+ dict_insert (cs, x) #> AList.map_entry (op =) cs f
+
+fun dict_update (e as (_, x)) = dict_map_default e (K x)
+
+fun dict_merge val_merge = sort class_ord o AList.join (op =) (K val_merge)
+
+fun dict_lookup d cs =
+ let fun match (cs', x) = if is_prefix (op =) cs' cs then SOME x else NONE
+ in map_filter match d end
+
+fun dict_get d cs =
+ (case AList.lookup (op =) d cs of
+ NONE => (case cs of [] => NONE | _ => dict_get d (take (length cs - 1) cs))
+ | SOME x => SOME x)
+
+
+(* types *)
+
+val dest_funT =
+ let
+ fun dest Ts 0 T = (rev Ts, T)
+ | dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
+ | dest _ _ T = raise TYPE ("not a function type", [T], [])
+ in dest [] end
+
+
+(* terms *)
+
+fun dest_conj (@{const HOL.conj} $ t $ u) = (t, u)
+ | dest_conj t = raise TERM ("not a conjunction", [t])
+
+fun dest_disj (@{const HOL.disj} $ t $ u) = (t, u)
+ | dest_disj t = raise TERM ("not a disjunction", [t])
+
+fun under_quant f t =
+ (case t of
+ Const (@{const_name All}, _) $ Abs (_, _, u) => under_quant f u
+ | Const (@{const_name Ex}, _) $ Abs (_, _, u) => under_quant f u
+ | _ => f t)
+
+val is_number =
+ let
+ fun is_num env (Const (@{const_name Let}, _) $ t $ Abs (_, _, u)) = is_num (t :: env) u
+ | is_num env (Bound i) = i < length env andalso is_num env (nth env i)
+ | is_num _ t = can HOLogic.dest_number t
+ in is_num [] end
+
+
+(* symbolic lists *)
+
+fun symb_listT T = Type (@{type_name symb_list}, [T])
+
+fun symb_nil_const T = Const (@{const_name Symb_Nil}, symb_listT T)
+
+fun symb_cons_const T =
+ let val listT = symb_listT T in Const (@{const_name Symb_Cons}, T --> listT --> listT) end
+
+fun mk_symb_list T ts =
+ fold_rev (fn t => fn u => symb_cons_const T $ t $ u) ts (symb_nil_const T)
+
+fun dest_symb_list (Const (@{const_name Symb_Nil}, _)) = []
+ | dest_symb_list (Const (@{const_name Symb_Cons}, _) $ t $ u) = t :: dest_symb_list u
+
+
+(* patterns and instantiations *)
+
+fun mk_const_pat thy name destT =
+ let val cpat = Thm.cterm_of thy (Const (name, Sign.the_const_type thy name))
+ in (destT (Thm.ctyp_of_term cpat), cpat) end
+
+val destT1 = hd o Thm.dest_ctyp
+val destT2 = hd o tl o Thm.dest_ctyp
+
+fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (cTs ~~ cUs, []) ct
+fun instT cU (cT, ct) = instTs [cU] ([cT], ct)
+fun instT' ct = instT (Thm.ctyp_of_term ct)
+
+
+(* certified terms *)
+
+fun certify ctxt = Thm.cterm_of (Proof_Context.theory_of ctxt)
+
+fun typ_of ct = #T (Thm.rep_cterm ct)
+
+fun dest_cabs ct ctxt =
+ (case Thm.term_of ct of
+ Abs _ =>
+ let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
+ in (snd (Thm.dest_abs (SOME n) ct), ctxt') end
+ | _ => raise CTERM ("no abstraction", [ct]))
+
+val dest_all_cabs = repeat_yield (try o dest_cabs)
+
+fun dest_cbinder ct ctxt =
+ (case Thm.term_of ct of
+ Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt
+ | _ => raise CTERM ("not a binder", [ct]))
+
+val dest_all_cbinders = repeat_yield (try o dest_cbinder)
+
+val mk_cprop = Thm.apply (Thm.cterm_of @{theory} @{const Trueprop})
+
+fun dest_cprop ct =
+ (case Thm.term_of ct of
+ @{const Trueprop} $ _ => Thm.dest_arg ct
+ | _ => raise CTERM ("not a property", [ct]))
+
+val equals = mk_const_pat @{theory} @{const_name Pure.eq} destT1
+fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu
+
+val dest_prop = (fn @{const Trueprop} $ t => t | t => t)
+fun term_of ct = dest_prop (Thm.term_of ct)
+fun prop_of thm = dest_prop (Thm.prop_of thm)
+
+
+(* conversions *)
+
+fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct
+
+fun if_true_conv pred cv = if_conv pred cv Conv.all_conv
+
+fun if_exists_conv pred = if_true_conv (Term.exists_subterm pred)
+
+fun binders_conv cv ctxt =
+ Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt
+
+fun under_quant_conv cv ctxt =
+ let
+ fun quant_conv inside ctxt cvs ct =
+ (case Thm.term_of ct of
+ Const (@{const_name All}, _) $ Abs _ =>
+ Conv.binder_conv (under_conv cvs) ctxt
+ | Const (@{const_name Ex}, _) $ Abs _ =>
+ Conv.binder_conv (under_conv cvs) ctxt
+ | _ => if inside then cv (ctxt, cvs) else Conv.all_conv) ct
+ and under_conv cvs (cv, ctxt) = quant_conv true ctxt (cv :: cvs)
+ in quant_conv false ctxt [] end
+
+fun prop_conv cv ct =
+ (case Thm.term_of ct of
+ @{const Trueprop} $ _ => Conv.arg_conv cv ct
+ | _ => raise CTERM ("not a property", [ct]))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smtlib.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,191 @@
+(* Title: HOL/Tools/SMT/smtlib.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Parsing and generating SMT-LIB 2.
+*)
+
+signature SMTLIB =
+sig
+ exception PARSE of int * string
+ datatype tree =
+ Num of int |
+ Dec of int * int |
+ Str of string |
+ Sym of string |
+ Key of string |
+ S of tree list
+ val parse: string list -> tree
+ val pretty_tree: tree -> Pretty.T
+ val str_of: tree -> string
+end;
+
+structure SMTLIB: SMTLIB =
+struct
+
+(* data structures *)
+
+exception PARSE of int * string
+
+datatype tree =
+ Num of int |
+ Dec of int * int |
+ Str of string |
+ Sym of string |
+ Key of string |
+ S of tree list
+
+datatype unfinished = None | String of string | Symbol of string
+
+
+(* utilities *)
+
+fun read_raw pred l cs =
+ (case take_prefix pred cs of
+ ([], []) => raise PARSE (l, "empty token")
+ | ([], c :: _) => raise PARSE (l, "unexpected character " ^ quote c)
+ | x => x)
+
+
+(* numerals and decimals *)
+
+fun int_of cs = fst (read_int cs)
+
+fun read_num l cs =
+ (case read_raw Symbol.is_ascii_digit l cs of
+ (cs1, "." :: cs') =>
+ let val (cs2, cs'') = read_raw Symbol.is_ascii_digit l cs'
+ in (Dec (int_of cs1, int_of cs2), cs'') end
+ | (cs1, cs2) => (Num (int_of cs1), cs2))
+
+
+(* binary numbers *)
+
+fun is_bin c = (c = "0" orelse c = "1")
+
+fun read_bin l cs = read_raw is_bin l cs |>> Num o fst o read_radix_int 2
+
+
+(* hex numbers *)
+
+val is_hex = member (op =) (raw_explode "0123456789abcdefABCDEF")
+
+fun within c1 c2 c = (ord c1 <= ord c andalso ord c <= ord c2)
+
+fun unhex i [] = i
+ | unhex i (c :: cs) =
+ if within "0" "9" c then unhex (i * 16 + (ord c - ord "0")) cs
+ else if within "a" "f" c then unhex (i * 16 + (ord c - ord "a" + 10)) cs
+ else if within "A" "F" c then unhex (i * 16 + (ord c - ord "A" + 10)) cs
+ else raise Fail ("bad hex character " ^ quote c)
+
+fun read_hex l cs = read_raw is_hex l cs |>> Num o unhex 0
+
+
+(* symbols *)
+
+val symbol_chars = raw_explode "~!@$%^&*_+=<>.?/-"
+
+fun is_sym c =
+ Symbol.is_ascii_letter c orelse
+ Symbol.is_ascii_digit c orelse
+ member (op =) symbol_chars c
+
+fun read_sym f l cs = read_raw is_sym l cs |>> f o implode
+
+
+(* quoted tokens *)
+
+fun read_quoted stop (escape, replacement) cs =
+ let
+ fun read _ [] = NONE
+ | read rs (cs as (c :: cs')) =
+ if is_prefix (op =) stop cs then
+ SOME (implode (rev rs), drop (length stop) cs)
+ else if not (null escape) andalso is_prefix (op =) escape cs then
+ read (replacement :: rs) (drop (length escape) cs)
+ else read (c :: rs) cs'
+ in read [] cs end
+
+fun read_string cs = read_quoted ["\\", "\""] (["\\", "\\"], "\\") cs
+fun read_symbol cs = read_quoted ["|"] ([], "") cs
+
+
+(* core parser *)
+
+fun read _ [] rest tss = (rest, tss)
+ | read l ("(" :: cs) None tss = read l cs None ([] :: tss)
+ | read l (")" :: cs) None (ts1 :: ts2 :: tss) =
+ read l cs None ((S (rev ts1) :: ts2) :: tss)
+ | read l ("#" :: "x" :: cs) None (ts :: tss) =
+ token read_hex l cs ts tss
+ | read l ("#" :: "b" :: cs) None (ts :: tss) =
+ token read_bin l cs ts tss
+ | read l (":" :: cs) None (ts :: tss) =
+ token (read_sym Key) l cs ts tss
+ | read l ("\"" :: cs) None (ts :: tss) =
+ quoted read_string String Str l "" cs ts tss
+ | read l ("|" :: cs) None (ts :: tss) =
+ quoted read_symbol Symbol Sym l "" cs ts tss
+ | read l ((c as "!") :: cs) None (ts :: tss) =
+ token (fn _ => pair (Sym c)) l cs ts tss
+ | read l (c :: cs) None (ts :: tss) =
+ if Symbol.is_ascii_blank c then read l cs None (ts :: tss)
+ else if Symbol.is_digit c then token read_num l (c :: cs) ts tss
+ else token (read_sym Sym) l (c :: cs) ts tss
+ | read l cs (String s) (ts :: tss) =
+ quoted read_string String Str l s cs ts tss
+ | read l cs (Symbol s) (ts :: tss) =
+ quoted read_symbol Symbol Sym l s cs ts tss
+ | read l _ _ [] = raise PARSE (l, "bad parser state")
+
+and token f l cs ts tss =
+ let val (t, cs') = f l cs
+ in read l cs' None ((t :: ts) :: tss) end
+
+and quoted r f g l s cs ts tss =
+ (case r cs of
+ NONE => (f (s ^ implode cs), ts :: tss)
+ | SOME (s', cs') => read l cs' None ((g (s ^ s') :: ts) :: tss))
+
+
+
+(* overall parser *)
+
+fun read_line l line = read l (raw_explode line)
+
+fun add_line line (l, (None, tss)) =
+ if size line = 0 orelse nth_string line 0 = ";" then (l + 1, (None, tss))
+ else (l + 1, read_line l line None tss)
+ | add_line line (l, (unfinished, tss)) =
+ (l + 1, read_line l line unfinished tss)
+
+fun finish (_, (None, [[t]])) = t
+ | finish (l, _) = raise PARSE (l, "bad nesting")
+
+fun parse lines = finish (fold add_line lines (1, (None, [[]])))
+
+
+(* pretty printer *)
+
+fun pretty_tree (Num i) = Pretty.str (string_of_int i)
+ | pretty_tree (Dec (i, j)) =
+ Pretty.str (string_of_int i ^ "." ^ string_of_int j)
+ | pretty_tree (Str s) =
+ raw_explode s
+ |> maps (fn "\"" => ["\\", "\""] | "\\" => ["\\", "\\"] | c => [c])
+ |> implode
+ |> enclose "\"" "\""
+ |> Pretty.str
+ | pretty_tree (Sym s) =
+ if String.isPrefix "(" s (* for bit vector functions *) orelse
+ forall is_sym (raw_explode s) then
+ Pretty.str s
+ else
+ Pretty.str ("|" ^ s ^ "|")
+ | pretty_tree (Key s) = Pretty.str (":" ^ s)
+ | pretty_tree (S trees) =
+ Pretty.enclose "(" ")" (Pretty.separate "" (map pretty_tree trees))
+
+val str_of = Pretty.str_of o pretty_tree
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smtlib_interface.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,163 @@
+(* Title: HOL/Tools/SMT/smtlib_interface.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Interface to SMT solvers based on the SMT-LIB 2 format.
+*)
+
+signature SMTLIB_INTERFACE =
+sig
+ val smtlibC: SMT_Util.class
+ val add_logic: int * (term list -> string option) -> Context.generic -> Context.generic
+ val translate_config: Proof.context -> SMT_Translate.config
+ val assert_index_of_name: string -> int
+ val assert_prefix : string
+end;
+
+structure SMTLIB_Interface: SMTLIB_INTERFACE =
+struct
+
+val smtlibC = ["smtlib"]
+
+
+(* builtins *)
+
+local
+ fun int_num _ i = SOME (string_of_int i)
+
+ fun is_linear [t] = SMT_Util.is_number t
+ | is_linear [t, u] = SMT_Util.is_number t orelse SMT_Util.is_number u
+ | is_linear _ = false
+
+ fun times _ _ ts =
+ let val mk = Term.list_comb o pair @{const times (int)}
+ in if is_linear ts then SOME ("*", 2, ts, mk) else NONE end
+in
+
+val setup_builtins =
+ fold (SMT_Builtin.add_builtin_typ smtlibC) [
+ (@{typ bool}, K (SOME "Bool"), K (K NONE)),
+ (@{typ int}, K (SOME "Int"), int_num)] #>
+ fold (SMT_Builtin.add_builtin_fun' smtlibC) [
+ (@{const True}, "true"),
+ (@{const False}, "false"),
+ (@{const Not}, "not"),
+ (@{const HOL.conj}, "and"),
+ (@{const HOL.disj}, "or"),
+ (@{const HOL.implies}, "=>"),
+ (@{const HOL.eq ('a)}, "="),
+ (@{const If ('a)}, "ite"),
+ (@{const less (int)}, "<"),
+ (@{const less_eq (int)}, "<="),
+ (@{const uminus (int)}, "-"),
+ (@{const plus (int)}, "+"),
+ (@{const minus (int)}, "-")] #>
+ SMT_Builtin.add_builtin_fun smtlibC
+ (Term.dest_Const @{const times (int)}, times)
+
+end
+
+
+(* serialization *)
+
+(** logic **)
+
+fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
+
+structure Logics = Generic_Data
+(
+ type T = (int * (term list -> string option)) list
+ val empty = []
+ val extend = I
+ fun merge data = Ord_List.merge fst_int_ord data
+)
+
+fun add_logic pf = Logics.map (Ord_List.insert fst_int_ord pf)
+
+fun choose_logic ctxt ts =
+ let
+ fun choose [] = "AUFLIA"
+ | choose ((_, f) :: fs) = (case f ts of SOME s => s | NONE => choose fs)
+ in
+ (case choose (Logics.get (Context.Proof ctxt)) of
+ "" => "" (* for default Z3 logic, a subset of everything *)
+ | logic => "(set-logic " ^ logic ^ ")\n")
+ end
+
+
+(** serialization **)
+
+fun var i = "?v" ^ string_of_int i
+
+fun tree_of_sterm l (SMT_Translate.SVar i) = SMTLIB.Sym (var (l - i - 1))
+ | tree_of_sterm _ (SMT_Translate.SApp (n, [])) = SMTLIB.Sym n
+ | tree_of_sterm l (SMT_Translate.SApp (n, ts)) =
+ SMTLIB.S (SMTLIB.Sym n :: map (tree_of_sterm l) ts)
+ | tree_of_sterm _ (SMT_Translate.SLet _) =
+ raise Fail "SMT-LIB: unsupported let expression"
+ | tree_of_sterm l (SMT_Translate.SQua (q, ss, pats, t)) =
+ let
+ val l' = l + length ss
+
+ fun quant_name SMT_Translate.SForall = "forall"
+ | quant_name SMT_Translate.SExists = "exists"
+
+ fun gen_trees_of_pat keyword ps =
+ [SMTLIB.Key keyword, (case map (tree_of_sterm l') ps of [t] => t | ts => SMTLIB.S ts)]
+ fun trees_of_pat (SMT_Translate.SPat ps) = gen_trees_of_pat "pattern" ps
+ | trees_of_pat (SMT_Translate.SNoPat ps) = gen_trees_of_pat "no-pattern" ps
+ fun tree_of_pats [] t = t
+ | tree_of_pats pats t = SMTLIB.S (SMTLIB.Sym "!" :: t :: maps trees_of_pat pats)
+
+ val vs = map_index (fn (i, ty) =>
+ SMTLIB.S [SMTLIB.Sym (var (l + i)), SMTLIB.Sym ty]) ss
+
+ val body = t
+ |> tree_of_sterm l'
+ |> tree_of_pats pats
+ in
+ SMTLIB.S [SMTLIB.Sym (quant_name q), SMTLIB.S vs, body]
+ end
+
+
+fun sctrarg (sel, typ) = "(" ^ sel ^ " " ^ typ ^ ")"
+fun sctr (name, args) = enclose "(" ")" (space_implode " " (name :: map sctrarg args))
+fun sdatatype (name, ctrs) = enclose "(" ")" (space_implode " " (name :: map sctr ctrs))
+
+fun string_of_fun (f, (ss, s)) = f ^ " (" ^ space_implode " " ss ^ ") " ^ s
+
+fun named_sterm s t = SMTLIB.S [SMTLIB.Sym "!", t, SMTLIB.Key "named", SMTLIB.Sym s]
+
+val assert_prefix = "a"
+
+fun assert_name_of_index i = assert_prefix ^ string_of_int i
+fun assert_index_of_name s = the_default ~1 (Int.fromString (unprefix assert_prefix s))
+
+fun serialize smt_options comments {logic, sorts, dtyps, funcs} ts =
+ Buffer.empty
+ |> fold (Buffer.add o enclose "; " "\n") comments
+ |> fold (fn (k, v) => Buffer.add ("(set-option " ^ k ^ " " ^ v ^ ")\n")) smt_options
+ |> Buffer.add logic
+ |> fold (Buffer.add o enclose "(declare-sort " " 0)\n") (sort fast_string_ord sorts)
+ |> (if null dtyps then I
+ else Buffer.add (enclose "(declare-datatypes () (" "))\n"
+ (space_implode "\n " (maps (map sdatatype) dtyps))))
+ |> fold (Buffer.add o enclose "(declare-fun " ")\n" o string_of_fun)
+ (sort (fast_string_ord o pairself fst) funcs)
+ |> fold (fn (i, t) => Buffer.add (enclose "(assert " ")\n"
+ (SMTLIB.str_of (named_sterm (assert_name_of_index i) (tree_of_sterm 0 t))))) (map_index I ts)
+ |> Buffer.add "(check-sat)\n(get-proof)\n"
+ |> Buffer.content
+
+(* interface *)
+
+fun translate_config ctxt = {
+ logic = choose_logic ctxt,
+ has_datatypes = false,
+ serialize = serialize}
+
+val _ = Theory.setup (Context.theory_map
+ (setup_builtins #>
+ SMT_Translate.add_config (smtlibC, translate_config)))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smtlib_isar.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,71 @@
+(* Title: HOL/Tools/SMT/smtlib_isar.ML
+ Author: Jasmin Blanchette, TU Muenchen
+ Author: Mathias Fleury, ENS Rennes
+
+General tools for Isar proof reconstruction.
+*)
+
+signature SMTLIB_ISAR =
+sig
+ val unlift_term: term list -> term -> term
+ val postprocess_step_conclusion: theory -> thm list -> term list -> term -> term
+ val normalizing_prems : Proof.context -> term -> (string * string list) list
+ val distinguish_conjecture_and_hypothesis : ''a list -> ''b -> ''b -> ''b list ->
+ (''a * 'c) list -> 'c list -> 'c -> (ATP_Problem.atp_formula_role * 'c) option
+ val unskolemize_names: term -> term
+end;
+
+structure SMTLIB_Isar: SMTLIB_ISAR =
+struct
+
+open ATP_Util
+open ATP_Problem
+open ATP_Proof_Reconstruct
+
+fun unlift_term ll_defs =
+ let
+ val lifted = map (ATP_Util.extract_lambda_def dest_Free o ATP_Util.hol_open_form I) ll_defs
+
+ fun un_free (t as Free (s, _)) =
+ (case AList.lookup (op =) lifted s of
+ SOME t => un_term t
+ | NONE => t)
+ | un_free t = t
+ and un_term t = map_aterms un_free t
+ in un_term end
+
+(* It is not entirely clear why this should be necessary, especially for abstractions variables. *)
+val unskolemize_names =
+ Term.map_abs_vars (perhaps (try Name.dest_skolem))
+ #> Term.map_aterms (perhaps (try (fn Free (s, T) => Free (Name.dest_skolem s, T))))
+
+fun postprocess_step_conclusion thy rewrite_rules ll_defs =
+ Raw_Simplifier.rewrite_term thy rewrite_rules []
+ #> Object_Logic.atomize_term thy
+ #> not (null ll_defs) ? unlift_term ll_defs
+ #> simplify_bool
+ #> unskolemize_names
+ #> HOLogic.mk_Trueprop
+
+fun normalizing_prems ctxt concl0 =
+ SMT_Normalize.case_bool_entry :: SMT_Normalize.special_quant_table @
+ SMT_Normalize.abs_min_max_table
+ |> map_filter (fn (c, th) =>
+ if exists_Const (curry (op =) c o fst) concl0 then
+ let val s = short_thm_name ctxt th in SOME (s, [s]) end
+ else
+ NONE)
+
+fun distinguish_conjecture_and_hypothesis ss id conjecture_id prem_ids fact_helper_ts hyp_ts
+ concl_t =
+ (case ss of
+ [s] => SOME (Axiom, the (AList.lookup (op =) fact_helper_ts s))
+ | _ =>
+ if id = conjecture_id then
+ SOME (Conjecture, concl_t)
+ else
+ (case find_index (curry (op =) id) prem_ids of
+ ~1 => NONE (* lambda-lifting definition *)
+ | i => SOME (Hypothesis, nth hyp_ts i)))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/smtlib_proof.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,298 @@
+(* Title: HOL/Tools/SMT/smtlib_proof.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Mathias Fleury, ENS Rennes
+ Author: Jasmin Blanchette, TU Muenchen
+
+SMT-LIB-2-style proofs: parsing and abstract syntax tree.
+*)
+
+signature SMTLIB_PROOF =
+sig
+ datatype 'b shared = Tree of SMTLIB.tree | Term of term | Proof of 'b | None
+ type ('a, 'b) context
+
+ val mk_context: Proof.context -> int -> 'b shared Symtab.table -> typ Symtab.table ->
+ term Symtab.table -> 'a -> ('a, 'b) context
+ val empty_context: Proof.context -> typ Symtab.table -> term Symtab.table -> ('a list, 'b) context
+ val ctxt_of: ('a, 'b) context -> Proof.context
+ val lookup_binding: ('a, 'b) context -> string -> 'b shared
+ val update_binding: string * 'b shared -> ('a, 'b) context -> ('a, 'b) context
+ val with_bindings: (string * 'b shared) list -> (('a, 'b) context -> 'c * ('d, 'b) context) ->
+ ('a, 'b) context -> 'c * ('d, 'b) context
+ val next_id: ('a, 'b) context -> int * ('a, 'b) context
+ val with_fresh_names: (('a list, 'b) context ->
+ term * ((string * (string * typ)) list, 'b) context) -> ('c, 'b) context -> (term * string list)
+
+ (*type and term parsers*)
+ type type_parser = SMTLIB.tree * typ list -> typ option
+ type term_parser = SMTLIB.tree * term list -> term option
+ val add_type_parser: type_parser -> Context.generic -> Context.generic
+ val add_term_parser: term_parser -> Context.generic -> Context.generic
+
+ exception SMTLIB_PARSE of string * SMTLIB.tree
+
+ val declare_fun: string -> typ -> ((string * typ) list, 'a) context ->
+ ((string * typ) list, 'a) context
+ val dest_binding: SMTLIB.tree -> string * 'a shared
+ val type_of: ('a, 'b) context -> SMTLIB.tree -> typ
+ val term_of: SMTLIB.tree -> ((string * (string * typ)) list, 'a) context ->
+ term * ((string * (string * typ)) list, 'a) context
+end;
+
+structure SMTLIB_Proof: SMTLIB_PROOF =
+struct
+
+(* proof parser context *)
+
+datatype 'b shared = Tree of SMTLIB.tree | Term of term | Proof of 'b | None
+
+type ('a, 'b) context = {
+ ctxt: Proof.context,
+ id: int,
+ syms: 'b shared Symtab.table,
+ typs: typ Symtab.table,
+ funs: term Symtab.table,
+ extra: 'a}
+
+fun mk_context ctxt id syms typs funs extra: ('a, 'b) context =
+ {ctxt = ctxt, id = id, syms = syms, typs = typs, funs = funs, extra = extra}
+
+fun empty_context ctxt typs funs = mk_context ctxt 1 Symtab.empty typs funs []
+
+fun ctxt_of ({ctxt, ...}: ('a, 'b) context) = ctxt
+
+fun lookup_binding ({syms, ...}: ('a, 'b) context) =
+ the_default None o Symtab.lookup syms
+
+fun map_syms f ({ctxt, id, syms, typs, funs, extra}: ('a, 'b) context) =
+ mk_context ctxt id (f syms) typs funs extra
+
+fun update_binding b = map_syms (Symtab.update b)
+
+fun with_bindings bs f cx =
+ let val bs' = map (lookup_binding cx o fst) bs
+ in
+ cx
+ |> fold update_binding bs
+ |> f
+ ||> fold2 (fn (name, _) => update_binding o pair name) bs bs'
+ end
+
+fun next_id ({ctxt, id, syms, typs, funs, extra}: ('a, 'b) context) =
+ (id, mk_context ctxt (id + 1) syms typs funs extra)
+
+fun with_fresh_names f ({ctxt, id, syms, typs, funs, ...}: ('a, 'b) context) =
+ let
+ fun bind (_, v as (_, T)) t = Logic.all_const T $ Term.absfree v t
+
+ val needs_inferT = equal Term.dummyT orf Term.is_TVar
+ val needs_infer = Term.exists_type (Term.exists_subtype needs_inferT)
+ fun infer_types ctxt =
+ singleton (Type_Infer_Context.infer_types ctxt) #>
+ singleton (Proof_Context.standard_term_check_finish ctxt)
+ fun infer ctxt t = if needs_infer t then infer_types ctxt t else t
+
+ val (t, {ctxt = ctxt', extra = names, ...}: ((string * (string * typ)) list, 'b) context) =
+ f (mk_context ctxt id syms typs funs [])
+ val t' = infer ctxt' (fold_rev bind names (HOLogic.mk_Trueprop t))
+ in
+ (t', map fst names)
+ end
+
+fun lookup_typ ({typs, ...}: ('a, 'b) context) = Symtab.lookup typs
+fun lookup_fun ({funs, ...}: ('a, 'b) context) = Symtab.lookup funs
+
+
+(* core type and term parser *)
+
+fun core_type_parser (SMTLIB.Sym "Bool", []) = SOME @{typ HOL.bool}
+ | core_type_parser (SMTLIB.Sym "Int", []) = SOME @{typ Int.int}
+ | core_type_parser _ = NONE
+
+fun mk_unary n t =
+ let val T = fastype_of t
+ in Const (n, T --> T) $ t end
+
+fun mk_binary' n T U t1 t2 = Const (n, [T, T] ---> U) $ t1 $ t2
+
+fun mk_binary n t1 t2 =
+ let val T = fastype_of t1
+ in mk_binary' n T T t1 t2 end
+
+fun mk_rassoc f t ts =
+ let val us = rev (t :: ts)
+ in fold f (tl us) (hd us) end
+
+fun mk_lassoc f t ts = fold (fn u1 => fn u2 => f u2 u1) ts t
+
+fun mk_lassoc' n = mk_lassoc (mk_binary n)
+
+fun mk_binary_pred n S t1 t2 =
+ let
+ val T1 = fastype_of t1
+ val T2 = fastype_of t2
+ val T =
+ if T1 <> Term.dummyT then T1
+ else if T2 <> Term.dummyT then T2
+ else TVar (("?a", serial ()), S)
+ in mk_binary' n T @{typ HOL.bool} t1 t2 end
+
+fun mk_less t1 t2 = mk_binary_pred @{const_name ord_class.less} @{sort linorder} t1 t2
+fun mk_less_eq t1 t2 = mk_binary_pred @{const_name ord_class.less_eq} @{sort linorder} t1 t2
+
+fun core_term_parser (SMTLIB.Sym "true", _) = SOME @{const HOL.True}
+ | core_term_parser (SMTLIB.Sym "false", _) = SOME @{const HOL.False}
+ | core_term_parser (SMTLIB.Sym "not", [t]) = SOME (HOLogic.mk_not t)
+ | core_term_parser (SMTLIB.Sym "and", t :: ts) = SOME (mk_rassoc (curry HOLogic.mk_conj) t ts)
+ | core_term_parser (SMTLIB.Sym "or", t :: ts) = SOME (mk_rassoc (curry HOLogic.mk_disj) t ts)
+ | core_term_parser (SMTLIB.Sym "=>", [t1, t2]) = SOME (HOLogic.mk_imp (t1, t2))
+ | core_term_parser (SMTLIB.Sym "implies", [t1, t2]) = SOME (HOLogic.mk_imp (t1, t2))
+ | core_term_parser (SMTLIB.Sym "=", [t1, t2]) = SOME (HOLogic.mk_eq (t1, t2))
+ | core_term_parser (SMTLIB.Sym "~", [t1, t2]) = SOME (HOLogic.mk_eq (t1, t2))
+ | core_term_parser (SMTLIB.Sym "ite", [t1, t2, t3]) =
+ let
+ val T = fastype_of t2
+ val c = Const (@{const_name HOL.If}, [@{typ HOL.bool}, T, T] ---> T)
+ in SOME (c $ t1 $ t2 $ t3) end
+ | core_term_parser (SMTLIB.Num i, []) = SOME (HOLogic.mk_number @{typ Int.int} i)
+ | core_term_parser (SMTLIB.Sym "-", [t]) = SOME (mk_unary @{const_name uminus_class.uminus} t)
+ | core_term_parser (SMTLIB.Sym "~", [t]) = SOME (mk_unary @{const_name uminus_class.uminus} t)
+ | core_term_parser (SMTLIB.Sym "+", t :: ts) =
+ SOME (mk_lassoc' @{const_name plus_class.plus} t ts)
+ | core_term_parser (SMTLIB.Sym "-", t :: ts) =
+ SOME (mk_lassoc' @{const_name minus_class.minus} t ts)
+ | core_term_parser (SMTLIB.Sym "*", t :: ts) =
+ SOME (mk_lassoc' @{const_name times_class.times} t ts)
+ | core_term_parser (SMTLIB.Sym "div", [t1, t2]) = SOME (mk_binary @{const_name z3div} t1 t2)
+ | core_term_parser (SMTLIB.Sym "mod", [t1, t2]) = SOME (mk_binary @{const_name z3mod} t1 t2)
+ | core_term_parser (SMTLIB.Sym "<", [t1, t2]) = SOME (mk_less t1 t2)
+ | core_term_parser (SMTLIB.Sym ">", [t1, t2]) = SOME (mk_less t2 t1)
+ | core_term_parser (SMTLIB.Sym "<=", [t1, t2]) = SOME (mk_less_eq t1 t2)
+ | core_term_parser (SMTLIB.Sym ">=", [t1, t2]) = SOME (mk_less_eq t2 t1)
+ | core_term_parser _ = NONE
+
+
+(* custom type and term parsers *)
+
+type type_parser = SMTLIB.tree * typ list -> typ option
+
+type term_parser = SMTLIB.tree * term list -> term option
+
+fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
+
+structure Parsers = Generic_Data
+(
+ type T = (int * type_parser) list * (int * term_parser) list
+ val empty : T = ([(serial (), core_type_parser)], [(serial (), core_term_parser)])
+ val extend = I
+ fun merge ((tys1, ts1), (tys2, ts2)) =
+ (Ord_List.merge id_ord (tys1, tys2), Ord_List.merge id_ord (ts1, ts2))
+)
+
+fun add_type_parser type_parser =
+ Parsers.map (apfst (Ord_List.insert id_ord (serial (), type_parser)))
+
+fun add_term_parser term_parser =
+ Parsers.map (apsnd (Ord_List.insert id_ord (serial (), term_parser)))
+
+fun get_type_parsers ctxt = map snd (fst (Parsers.get (Context.Proof ctxt)))
+fun get_term_parsers ctxt = map snd (snd (Parsers.get (Context.Proof ctxt)))
+
+fun apply_parsers parsers x =
+ let
+ fun apply [] = NONE
+ | apply (parser :: parsers) =
+ (case parser x of
+ SOME y => SOME y
+ | NONE => apply parsers)
+ in apply parsers end
+
+
+(* type and term parsing *)
+
+exception SMTLIB_PARSE of string * SMTLIB.tree
+
+val desymbolize = Name.desymbolize (SOME false) o perhaps (try (unprefix "?"))
+
+fun fresh_fun add name n T ({ctxt, id, syms, typs, funs, extra}: ('a, 'b) context) =
+ let
+ val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
+ val t = Free (n', T)
+ val funs' = Symtab.update (name, t) funs
+ in (t, mk_context ctxt' id syms typs funs' (add (n', T) extra)) end
+
+fun declare_fun name = snd oo fresh_fun cons name (desymbolize name)
+fun declare_free name = fresh_fun (cons o pair name) name (desymbolize name)
+
+fun parse_type cx ty Ts =
+ (case apply_parsers (get_type_parsers (ctxt_of cx)) (ty, Ts) of
+ SOME T => T
+ | NONE =>
+ (case ty of
+ SMTLIB.Sym name =>
+ (case lookup_typ cx name of
+ SOME T => T
+ | NONE => raise SMTLIB_PARSE ("unknown SMT type", ty))
+ | _ => raise SMTLIB_PARSE ("bad SMT type format", ty)))
+
+fun parse_term t ts cx =
+ (case apply_parsers (get_term_parsers (ctxt_of cx)) (t, ts) of
+ SOME u => (u, cx)
+ | NONE =>
+ (case t of
+ SMTLIB.Sym name =>
+ (case lookup_fun cx name of
+ SOME u => (Term.list_comb (u, ts), cx)
+ | NONE =>
+ if null ts then declare_free name Term.dummyT cx
+ else raise SMTLIB_PARSE ("bad SMT term", t))
+ | _ => raise SMTLIB_PARSE ("bad SMT term format", t)))
+
+fun type_of cx ty =
+ (case try (parse_type cx ty) [] of
+ SOME T => T
+ | NONE =>
+ (case ty of
+ SMTLIB.S (ty' :: tys) => parse_type cx ty' (map (type_of cx) tys)
+ | _ => raise SMTLIB_PARSE ("bad SMT type", ty)))
+
+fun dest_var cx (SMTLIB.S [SMTLIB.Sym name, ty]) = (name, (desymbolize name, type_of cx ty))
+ | dest_var _ v = raise SMTLIB_PARSE ("bad SMT quantifier variable format", v)
+
+fun dest_body (SMTLIB.S (SMTLIB.Sym "!" :: body :: _)) = dest_body body
+ | dest_body body = body
+
+fun dest_binding (SMTLIB.S [SMTLIB.Sym name, t]) = (name, Tree t)
+ | dest_binding b = raise SMTLIB_PARSE ("bad SMT let binding format", b)
+
+fun term_of t cx =
+ (case t of
+ SMTLIB.S [SMTLIB.Sym "forall", SMTLIB.S vars, body] => quant HOLogic.mk_all vars body cx
+ | SMTLIB.S [SMTLIB.Sym "exists", SMTLIB.S vars, body] => quant HOLogic.mk_exists vars body cx
+ | SMTLIB.S [SMTLIB.Sym "let", SMTLIB.S bindings, body] =>
+ with_bindings (map dest_binding bindings) (term_of body) cx
+ | SMTLIB.S (SMTLIB.Sym "!" :: t :: _) => term_of t cx
+ | SMTLIB.S (f :: args) =>
+ cx
+ |> fold_map term_of args
+ |-> parse_term f
+ | SMTLIB.Sym name =>
+ (case lookup_binding cx name of
+ Tree u =>
+ cx
+ |> term_of u
+ |-> (fn u' => pair u' o update_binding (name, Term u'))
+ | Term u => (u, cx)
+ | None => parse_term t [] cx
+ | _ => raise SMTLIB_PARSE ("bad SMT term format", t))
+ | _ => parse_term t [] cx)
+
+and quant q vars body cx =
+ let val vs = map (dest_var cx) vars
+ in
+ cx
+ |> with_bindings (map (apsnd (Term o Free)) vs) (term_of (dest_body body))
+ |>> fold_rev (fn (_, (n, T)) => fn t => q (n, T, t)) vs
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/verit_isar.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,59 @@
+(* Title: HOL/Tools/SMT/verit_isar.ML
+ Author: Mathias Fleury, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+VeriT proofs as generic ATP proofs for Isar proof reconstruction.
+*)
+
+signature VERIT_ISAR =
+sig
+ type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
+ val atp_proof_of_veriT_proof: Proof.context -> term list -> thm list -> term list -> term ->
+ (string * term) list -> int list -> int -> (int * string) list -> VeriT_Proof.veriT_step list ->
+ (term, string) ATP_Proof.atp_step list
+end;
+
+structure VeriT_Isar: VERIT_ISAR =
+struct
+
+open ATP_Util
+open ATP_Problem
+open ATP_Proof
+open ATP_Proof_Reconstruct
+open SMTLIB_Isar
+open VeriT_Proof
+
+fun atp_proof_of_veriT_proof ctxt ll_defs rewrite_rules hyp_ts concl_t fact_helper_ts prem_ids
+ conjecture_id fact_helper_ids proof =
+ let
+ val thy = Proof_Context.theory_of ctxt
+ fun steps_of (VeriT_Proof.VeriT_Step {id, rule, prems, concl, ...}) =
+ let
+ val concl' = postprocess_step_conclusion thy rewrite_rules ll_defs concl
+ fun standard_step role = ((id, []), role, concl', rule, map (fn id => (id, [])) prems)
+ in
+ if rule = veriT_input_rule then
+ let val ss = the_list (AList.lookup (op =) fact_helper_ids (the (Int.fromString id))) in
+ (case distinguish_conjecture_and_hypothesis ss (the (Int.fromString id))
+ conjecture_id prem_ids fact_helper_ts hyp_ts concl_t of
+ NONE => []
+ | SOME (role0, concl00) =>
+ let
+ val name0 = (id ^ "a", ss)
+ val concl0 = unskolemize_names concl00
+ in
+ [(name0, role0, concl0, rule, []),
+ ((id, []), Plain, concl', veriT_rewrite_rule,
+ name0 :: normalizing_prems ctxt concl0)]
+ end)
+ end
+ else if rule = veriT_tmp_ite_elim_rule then
+ [standard_step Lemma]
+ else
+ [standard_step Plain]
+ end
+ in
+ maps steps_of proof
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/verit_proof.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,333 @@
+(* Title: HOL/Tools/SMT/verit_proof.ML
+ Author: Mathias Fleury, ENS Rennes
+ Author: Sascha Boehme, TU Muenchen
+
+VeriT proofs: parsing and abstract syntax tree.
+*)
+
+signature VERIT_PROOF =
+sig
+ (*proofs*)
+ datatype veriT_step = VeriT_Step of {
+ id: string,
+ rule: string,
+ prems: string list,
+ concl: term,
+ fixes: string list}
+
+ (*proof parser*)
+ val parse: typ Symtab.table -> term Symtab.table -> string list ->
+ Proof.context -> veriT_step list * Proof.context
+
+ val veriT_step_prefix : string
+ val veriT_input_rule: string
+ val veriT_la_generic_rule : string
+ val veriT_rewrite_rule : string
+ val veriT_simp_arith_rule : string
+ val veriT_tmp_ite_elim_rule : string
+ val veriT_tmp_skolemize_rule : string
+end;
+
+structure VeriT_Proof: VERIT_PROOF =
+struct
+
+open SMTLIB_Proof
+
+datatype veriT_node = VeriT_Node of {
+ id: string,
+ rule: string,
+ prems: string list,
+ concl: term,
+ bounds: string list}
+
+fun mk_node id rule prems concl bounds =
+ VeriT_Node {id = id, rule = rule, prems = prems, concl = concl, bounds = bounds}
+
+datatype veriT_step = VeriT_Step of {
+ id: string,
+ rule: string,
+ prems: string list,
+ concl: term,
+ fixes: string list}
+
+fun mk_step id rule prems concl fixes =
+ VeriT_Step {id = id, rule = rule, prems = prems, concl = concl, fixes = fixes}
+
+val veriT_step_prefix = ".c"
+val veriT_alpha_conv_rule = "tmp_alphaconv"
+val veriT_input_rule = "input"
+val veriT_la_generic_rule = "la_generic"
+val veriT_rewrite_rule = "__rewrite" (* arbitrary *)
+val veriT_simp_arith_rule = "simp_arith"
+val veriT_tmp_ite_elim_rule = "tmp_ite_elim"
+val veriT_tmp_skolemize_rule = "tmp_skolemize"
+
+(* proof parser *)
+
+fun node_of p cx =
+ ([], cx)
+ ||>> `(with_fresh_names (term_of p))
+ |>> snd
+
+(*in order to get Z3-style quantification*)
+fun repair_quantification (SMTLIB.S (SMTLIB.Sym "forall" :: l)) =
+ let val (quantified_vars, t) = split_last (map repair_quantification l)
+ in
+ SMTLIB.S (SMTLIB.Sym "forall" :: SMTLIB.S quantified_vars :: t :: [])
+ end
+ | repair_quantification (SMTLIB.S (SMTLIB.Sym "exists" :: l)) =
+ let val (quantified_vars, t) = split_last (map repair_quantification l)
+ in
+ SMTLIB.S (SMTLIB.Sym "exists" :: SMTLIB.S quantified_vars :: t :: [])
+ end
+ | repair_quantification (SMTLIB.S l) = SMTLIB.S (map repair_quantification l)
+ | repair_quantification x = x
+
+fun replace_bound_var_by_free_var (q $ Abs (var, ty, u)) free_var =
+ (case List.find (fn v => String.isPrefix v var) free_var of
+ NONE => q $ Abs (var, ty, replace_bound_var_by_free_var u free_var)
+ | SOME _ => replace_bound_var_by_free_var (Term.subst_bound (Free (var, ty), u)) free_var)
+ | replace_bound_var_by_free_var (u $ v) free_vars = replace_bound_var_by_free_var u free_vars $
+ replace_bound_var_by_free_var v free_vars
+ | replace_bound_var_by_free_var u _ = u
+
+fun find_type_in_formula (Abs(v, ty, u)) var_name =
+ if String.isPrefix var_name v then SOME ty else find_type_in_formula u var_name
+ | find_type_in_formula (u $ v) var_name =
+ (case find_type_in_formula u var_name of
+ NONE => find_type_in_formula v var_name
+ | a => a)
+ | find_type_in_formula _ _ = NONE
+
+fun add_bound_variables_to_ctxt cx bounds concl =
+ fold (fn a => fn b => update_binding a b)
+ (map (fn s => ((s, Term (Free (s, the_default dummyT (find_type_in_formula concl s))))))
+ bounds) cx
+
+fun update_step_and_cx (st as VeriT_Node {id, rule, prems, concl, bounds}) cx =
+ if rule = veriT_tmp_ite_elim_rule then
+ (mk_node id rule prems concl bounds, add_bound_variables_to_ctxt cx bounds concl)
+ else if rule = veriT_tmp_skolemize_rule then
+ let
+ val concl' = replace_bound_var_by_free_var concl bounds
+ in
+ (mk_node id rule prems concl' [], add_bound_variables_to_ctxt cx bounds concl)
+ end
+ else
+ (st, cx)
+
+(*FIXME: using a reference would be better to know th numbers of the steps to add*)
+fun fix_subproof_steps ((((id_of_father_step, rule), prems), subproof), ((step_concl, bounds),
+ cx)) =
+ let
+ fun mk_prop_of_term concl = (fastype_of concl = @{typ "bool"} ?
+ curry (op $) @{term "Trueprop"}) concl
+ fun inline_assumption assumption assumption_id (st as VeriT_Node {id, rule, prems, concl,
+ bounds}) =
+ if List.find (curry (op =) assumption_id) prems <> NONE then
+ let
+ val prems' = filter_out (curry (op =) assumption_id) prems
+ in
+ mk_node id rule (filter_out (curry (op =) assumption_id) prems')
+ (Const (@{const_name "Pure.imp"}, @{typ "prop"} --> @{typ "prop"} --> @{typ "prop"})
+ $ mk_prop_of_term assumption $ mk_prop_of_term concl) bounds
+ end
+ else
+ st
+ fun find_input_steps_and_inline [] last_step = ([], last_step)
+ | find_input_steps_and_inline (VeriT_Node {id = id', rule, prems, concl, bounds} :: steps)
+ last_step =
+ if rule = veriT_input_rule then
+ find_input_steps_and_inline (map (inline_assumption concl id') steps) last_step
+ else
+ apfst (cons (mk_node (id_of_father_step ^ id') rule prems concl bounds))
+ (find_input_steps_and_inline steps (id_of_father_step ^ id'))
+ val (subproof', last_step_id) = find_input_steps_and_inline subproof ""
+ val prems' =
+ if last_step_id = "" then prems
+ else
+ (case prems of
+ NONE => SOME [last_step_id]
+ | SOME l => SOME (last_step_id :: l))
+ in
+ (subproof', (((((id_of_father_step, rule), prems'), step_concl), bounds), cx))
+ end
+
+(*
+(set id rule :clauses(...) :args(..) :conclusion (...)).
+or
+(set id subproof (set ...) :conclusion (...)).
+*)
+
+fun parse_proof_step cx =
+ let
+ fun rotate_pair (a, (b, c)) = ((a, b), c)
+ fun get_id (SMTLIB.S [SMTLIB.Sym "set", SMTLIB.Sym id, SMTLIB.S l]) = (id, l)
+ | get_id t = raise Fail ("unrecognized VeriT Proof" ^ PolyML.makestring t)
+ fun parse_rule (SMTLIB.Sym rule :: l) = (rule, l)
+ fun parse_source (SMTLIB.Key "clauses" :: SMTLIB.S source ::l) =
+ (SOME (map (fn (SMTLIB.Sym id) => id) source), l)
+ | parse_source l = (NONE, l)
+ fun parse_subproof cx id_of_father_step ((subproof_step as SMTLIB.S (SMTLIB.Sym "set" :: _)) :: l) =
+ let val (subproof_steps, cx') = parse_proof_step cx subproof_step in
+ apfst (apfst (curry (op @) subproof_steps)) (parse_subproof cx' id_of_father_step l)
+ end
+ | parse_subproof cx _ l = (([], cx), l)
+ fun skip_args (SMTLIB.Key "args" :: SMTLIB.S _ :: l) = l
+ | skip_args l = l
+ fun parse_conclusion (SMTLIB.Key "conclusion" :: SMTLIB.S concl :: []) = concl
+ fun make_or_from_clausification l =
+ foldl1 (fn ((concl1, bounds1), (concl2, bounds2)) =>
+ (HOLogic.mk_disj (perhaps (try HOLogic.dest_Trueprop) concl1,
+ perhaps (try HOLogic.dest_Trueprop) concl2), bounds1 @ bounds2)) l
+ fun to_node (((((id, rule), prems), concl), bounds), cx) = (mk_node id rule
+ (the_default [] prems) concl bounds, cx)
+ in
+ get_id
+ ##> parse_rule
+ #> rotate_pair
+ ##> parse_source
+ #> rotate_pair
+ ##> skip_args
+ #> (fn (((id, rule), prems), sub) => (((id, rule), prems), parse_subproof cx id sub))
+ #> rotate_pair
+ ##> parse_conclusion
+ ##> map repair_quantification
+ #> (fn ((((id, rule), prems), (subproof, cx)), terms) =>
+ (((((id, rule), prems), subproof), fold_map (fn t => fn cx => node_of t cx) terms cx)))
+ ##> apfst (fn [] => (@{const False}, []) | concls => make_or_from_clausification concls)
+ #> fix_subproof_steps
+ ##> to_node
+ #> (fn (subproof, (step, cx)) => (subproof @ [step], cx))
+ #-> fold_map update_step_and_cx
+ end
+
+(*subproofs are written on multiple lines: SMTLIB can not parse then, because parentheses are
+unbalanced on each line*)
+fun seperate_into_steps lines =
+ let
+ fun count ("(" :: l) n = count l (n+1)
+ | count (")" :: l) n = count l (n-1)
+ | count (_ :: l) n = count l n
+ | count [] n = n
+ fun seperate (line :: l) actual_lines m =
+ let val n = count (raw_explode line) 0 in
+ if m + n = 0 then
+ [actual_lines ^ line] :: seperate l "" 0
+ else seperate l (actual_lines ^ line) (m + n)
+ end
+ | seperate [] _ 0 = []
+ in
+ seperate lines "" 0
+ end
+
+ (* VeriT adds @ before every variable. *)
+fun remove_all_at (SMTLIB.Sym v :: l) = SMTLIB.Sym (perhaps (try (unprefix "@")) v) :: remove_all_at l
+ | remove_all_at (SMTLIB.S l :: l') = SMTLIB.S (remove_all_at l) :: remove_all_at l'
+ | remove_all_at (SMTLIB.Key v :: l) = SMTLIB.Key v :: remove_all_at l
+ | remove_all_at (v :: l) = v :: remove_all_at l
+ | remove_all_at [] = []
+
+fun find_in_which_step_defined var (VeriT_Node {id, bounds, ...} :: l) =
+ (case List.find (fn v => String.isPrefix v var) bounds of
+ NONE => find_in_which_step_defined var l
+ | SOME _ => id)
+ | find_in_which_step_defined var _ = raise Fail ("undefined " ^ var)
+
+(*Yes every case is possible: the introduced var is not on a special size of the equality sign.*)
+fun find_ite_var_in_term (Const ("HOL.If", _) $ _ $
+ (Const (@{const_name "HOL.eq"}, _) $ Free (var1, _) $ Free (var2, _) ) $
+ (Const (@{const_name "HOL.eq"}, _) $ Free (var3, _) $ Free (var4, _) )) =
+ let
+ fun get_number_of_ite_transformed_var var =
+ perhaps (try (unprefix "ite")) var
+ |> Int.fromString
+ fun is_equal_and_has_correct_substring var var' var'' =
+ if var = var' andalso String.isPrefix "ite" var then SOME var'
+ else if var = var'' andalso String.isPrefix "ite" var then SOME var'' else NONE
+ val var1_introduced_var = is_equal_and_has_correct_substring var1 var3 var4
+ val var2_introduced_var = is_equal_and_has_correct_substring var3 var1 var2
+ in
+ (case (var1_introduced_var, var2_introduced_var) of
+ (SOME a, SOME b) =>
+ (*ill-generated case, might be possible when applying the rule to max a a. Only if the
+ variable have been introduced before. Probably an impossible edge case*)
+ (case (get_number_of_ite_transformed_var a, get_number_of_ite_transformed_var b) of
+ (SOME a, SOME b) => if a < b then var2_introduced_var else var1_introduced_var
+ (*Otherwise, it is a name clase between a parameter name and the introduced variable.
+ Or the name convention has been changed.*)
+ | (NONE, SOME _) => var2_introduced_var
+ | (SOME _, NONE) => var2_introduced_var)
+ | (_, SOME _) => var2_introduced_var
+ | (SOME _, _) => var1_introduced_var)
+ end
+ | find_ite_var_in_term (Const (@{const_name "If"}, _) $ _ $
+ (Const (@{const_name "HOL.eq"}, _) $ Free (var, _) $ _ ) $
+ (Const (@{const_name "HOL.eq"}, _) $ Free (var', _) $ _ )) =
+ if var = var' then SOME var else NONE
+ | find_ite_var_in_term (Const (@{const_name "If"}, _) $ _ $
+ (Const (@{const_name "HOL.eq"}, _) $ _ $ Free (var, _)) $
+ (Const (@{const_name "HOL.eq"}, _) $ _ $ Free (var', _))) =
+ if var = var' then SOME var else NONE
+ | find_ite_var_in_term (p $ q) =
+ (case find_ite_var_in_term p of
+ NONE => find_ite_var_in_term q
+ | x => x)
+ | find_ite_var_in_term (Abs (_, _, body)) = find_ite_var_in_term body
+ | find_ite_var_in_term _ = NONE
+
+fun correct_veriT_step steps (st as VeriT_Node {id, rule, prems, concl, bounds}) =
+ if rule = veriT_tmp_ite_elim_rule then
+ if bounds = [] then
+ (*if the introduced var has already been defined, adding the definition as a dependency*)
+ let
+ val new_prems =
+ (case find_ite_var_in_term concl of
+ NONE => prems
+ | SOME var => find_in_which_step_defined var steps :: prems)
+ in
+ VeriT_Node {id = id, rule = rule, prems = new_prems, concl = concl, bounds = bounds}
+ end
+ else
+ (*some new variables are created*)
+ let
+ val concl' = replace_bound_var_by_free_var concl bounds
+ in
+ mk_node id rule prems concl' []
+ end
+ else
+ st
+
+fun remove_alpha_conversion _ [] = []
+ | remove_alpha_conversion replace_table (VeriT_Node {id, rule, prems, concl, bounds} :: steps) =
+ let
+ fun correct_dependency prems =
+ map (fn x => perhaps (Symtab.lookup replace_table) x) prems
+ fun find_predecessor prem = perhaps (Symtab.lookup replace_table) prem
+ in
+ if rule = veriT_alpha_conv_rule then
+ remove_alpha_conversion (Symtab.update (id, find_predecessor (hd prems))
+ replace_table) steps
+ else
+ VeriT_Node {id = id, rule = rule, prems = correct_dependency prems,
+ concl = concl, bounds = bounds} :: remove_alpha_conversion replace_table steps
+ end
+
+fun correct_veriT_steps steps =
+ steps
+ |> map (correct_veriT_step steps)
+ |> remove_alpha_conversion Symtab.empty
+
+fun parse typs funs lines ctxt =
+ let
+ val smtlib_lines_without_at = remove_all_at (map SMTLIB.parse (seperate_into_steps lines))
+ val (u, env) = apfst flat (fold_map (fn l => fn cx => parse_proof_step cx l)
+ smtlib_lines_without_at (empty_context ctxt typs funs))
+ val t = correct_veriT_steps u
+ fun node_to_step (VeriT_Node {id, rule, prems, concl, bounds, ...}) =
+ mk_step id rule prems concl bounds
+ in
+ (map node_to_step t, ctxt_of env)
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/verit_proof_parse.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,104 @@
+(* Title: HOL/Tools/SMT/verit_proof_parse.ML
+ Author: Mathias Fleury, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+VeriT proof parsing.
+*)
+
+signature VERIT_PROOF_PARSE =
+sig
+ type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
+ val parse_proof: Proof.context -> SMT_Translate.replay_data ->
+ ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
+ SMT_Solver.parsed_proof
+end;
+
+structure VeriT_Proof_Parse: VERIT_PROOF_PARSE =
+struct
+
+open ATP_Util
+open ATP_Problem
+open ATP_Proof
+open ATP_Proof_Reconstruct
+open VeriT_Isar
+open VeriT_Proof
+
+fun find_and_add_missing_dependances steps assms ll_offset =
+ let
+ fun prems_to_theorem_number [] id repl = (([], []), (id, repl))
+ | prems_to_theorem_number (x :: ths) id replaced =
+ (case Int.fromString (perhaps (try (unprefix SMTLIB_Interface.assert_prefix)) x) of
+ NONE =>
+ let
+ val ((prems, iidths), (id', replaced')) = prems_to_theorem_number ths id replaced
+ in
+ ((x :: prems, iidths), (id', replaced'))
+ end
+ | SOME th =>
+ (case Option.map snd (List.find (fst #> curry (op =) x) replaced) of
+ NONE =>
+ let
+ val id' = if th = ll_offset then 0 else id - ll_offset (* 0: for the conjecture*)
+ val ((prems, iidths), (id'', replaced')) =
+ prems_to_theorem_number ths (if th <> ll_offset then id + 1 else id)
+ ((x, string_of_int id') :: replaced)
+ in
+ ((string_of_int id' :: prems, (th, (id', th - ll_offset)) :: iidths),
+ (id'', replaced'))
+ end
+ | SOME x =>
+ let
+ val ((prems, iidths), (id', replaced')) = prems_to_theorem_number ths id replaced
+ in ((x :: prems, iidths), (id', replaced')) end))
+ fun update_step (VeriT_Proof.VeriT_Step {prems, id = id0, rule = rule0,
+ concl = concl0, fixes = fixes0}) (id, replaced) =
+ let val ((prems', iidths), (id', replaced)) = prems_to_theorem_number prems id replaced
+ in
+ ((VeriT_Proof.VeriT_Step {id = id0, rule = rule0, prems = prems', concl = concl0,
+ fixes = fixes0}, iidths), (id', replaced))
+ end
+ in
+ fold_map update_step steps (1, [])
+ |> fst
+ |> `(map snd)
+ ||> (map fst)
+ |>> flat
+ |>> map (fn (_, (id, tm_id)) => let val (i, tm) = nth assms tm_id in (i, (id, tm)) end)
+ end
+
+fun add_missing_steps iidths =
+ let
+ fun add_single_step (_, (id, th)) = VeriT_Proof.VeriT_Step {id = string_of_int id,
+ rule = veriT_input_rule, prems = [], concl = prop_of th, fixes = []}
+ in map add_single_step iidths end
+
+fun parse_proof _
+ ({context = ctxt, typs, terms, ll_defs, rewrite_rules, assms} : SMT_Translate.replay_data)
+ xfacts prems concl output =
+ let
+ val (steps, _) = VeriT_Proof.parse typs terms output ctxt
+ val (iidths, steps'') = find_and_add_missing_dependances steps assms (length ll_defs)
+ val steps' = add_missing_steps iidths @ steps''
+ fun id_of_index i = the_default ~1 (Option.map fst (AList.lookup (op =) iidths i))
+
+ val prems_i = 1
+ val facts_i = prems_i + length prems
+ val conjecture_i = 0
+ val ll_offset = id_of_index conjecture_i
+ val prem_ids = map id_of_index (prems_i upto facts_i - 1)
+ val helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths
+
+ val fact_ids = map_filter (fn (i, (id, _)) =>
+ (try (apsnd (nth xfacts)) (id, i - facts_i))) iidths
+ val fact_helper_ts =
+ map (fn (_, th) => (ATP_Util.short_thm_name ctxt th, prop_of th)) helper_ids @
+ map (fn (_, ((s, _), th)) => (s, prop_of th)) fact_ids
+ val fact_helper_ids =
+ map (apsnd (ATP_Util.short_thm_name ctxt)) helper_ids @ map (apsnd (fst o fst)) fact_ids
+ in
+ {outcome = NONE, fact_ids = fact_ids,
+ atp_proof = fn () => atp_proof_of_veriT_proof ctxt ll_defs rewrite_rules prems concl
+ fact_helper_ts prem_ids ll_offset fact_helper_ids steps'}
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_interface.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,192 @@
+(* Title: HOL/Tools/SMT/z3_interface.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Interface to Z3 based on a relaxed version of SMT-LIB.
+*)
+
+signature Z3_INTERFACE =
+sig
+ val smtlib_z3C: SMT_Util.class
+
+ datatype sym = Sym of string * sym list
+ type mk_builtins = {
+ mk_builtin_typ: sym -> typ option,
+ mk_builtin_num: theory -> int -> typ -> cterm option,
+ mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
+ val add_mk_builtins: mk_builtins -> Context.generic -> Context.generic
+ val mk_builtin_typ: Proof.context -> sym -> typ option
+ val mk_builtin_num: Proof.context -> int -> typ -> cterm option
+ val mk_builtin_fun: Proof.context -> sym -> cterm list -> cterm option
+
+ val is_builtin_theory_term: Proof.context -> term -> bool
+end;
+
+structure Z3_Interface: Z3_INTERFACE =
+struct
+
+val smtlib_z3C = SMTLIB_Interface.smtlibC @ ["z3"]
+
+
+(* interface *)
+
+local
+ fun translate_config ctxt =
+ {logic = K "", has_datatypes = true,
+ serialize = #serialize (SMTLIB_Interface.translate_config ctxt)}
+
+ fun is_div_mod @{const div (int)} = true
+ | is_div_mod @{const mod (int)} = true
+ | is_div_mod _ = false
+
+ val have_int_div_mod = exists (Term.exists_subterm is_div_mod o Thm.prop_of)
+
+ fun add_div_mod _ (thms, extra_thms) =
+ if have_int_div_mod thms orelse have_int_div_mod extra_thms then
+ (thms, @{thms div_as_z3div mod_as_z3mod} @ extra_thms)
+ else (thms, extra_thms)
+
+ val setup_builtins =
+ SMT_Builtin.add_builtin_fun' smtlib_z3C (@{const times (int)}, "*") #>
+ SMT_Builtin.add_builtin_fun' smtlib_z3C (@{const z3div}, "div") #>
+ SMT_Builtin.add_builtin_fun' smtlib_z3C (@{const z3mod}, "mod")
+in
+
+val _ = Theory.setup (Context.theory_map (
+ setup_builtins #>
+ SMT_Normalize.add_extra_norm (smtlib_z3C, add_div_mod) #>
+ SMT_Translate.add_config (smtlib_z3C, translate_config)))
+
+end
+
+
+(* constructors *)
+
+datatype sym = Sym of string * sym list
+
+
+(** additional constructors **)
+
+type mk_builtins = {
+ mk_builtin_typ: sym -> typ option,
+ mk_builtin_num: theory -> int -> typ -> cterm option,
+ mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
+
+fun chained _ [] = NONE
+ | chained f (b :: bs) = (case f b of SOME y => SOME y | NONE => chained f bs)
+
+fun chained_mk_builtin_typ bs sym =
+ chained (fn {mk_builtin_typ=mk, ...} : mk_builtins => mk sym) bs
+
+fun chained_mk_builtin_num ctxt bs i T =
+ let val thy = Proof_Context.theory_of ctxt
+ in chained (fn {mk_builtin_num=mk, ...} : mk_builtins => mk thy i T) bs end
+
+fun chained_mk_builtin_fun ctxt bs s cts =
+ let val thy = Proof_Context.theory_of ctxt
+ in chained (fn {mk_builtin_fun=mk, ...} : mk_builtins => mk thy s cts) bs end
+
+fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
+
+structure Mk_Builtins = Generic_Data
+(
+ type T = (int * mk_builtins) list
+ val empty = []
+ val extend = I
+ fun merge data = Ord_List.merge fst_int_ord data
+)
+
+fun add_mk_builtins mk = Mk_Builtins.map (Ord_List.insert fst_int_ord (serial (), mk))
+
+fun get_mk_builtins ctxt = map snd (Mk_Builtins.get (Context.Proof ctxt))
+
+
+(** basic and additional constructors **)
+
+fun mk_builtin_typ _ (Sym ("Bool", _)) = SOME @{typ bool}
+ | mk_builtin_typ _ (Sym ("Int", _)) = SOME @{typ int}
+ | mk_builtin_typ _ (Sym ("bool", _)) = SOME @{typ bool} (*FIXME: legacy*)
+ | mk_builtin_typ _ (Sym ("int", _)) = SOME @{typ int} (*FIXME: legacy*)
+ | mk_builtin_typ ctxt sym = chained_mk_builtin_typ (get_mk_builtins ctxt) sym
+
+fun mk_builtin_num _ i @{typ int} = SOME (Numeral.mk_cnumber @{ctyp int} i)
+ | mk_builtin_num ctxt i T =
+ chained_mk_builtin_num ctxt (get_mk_builtins ctxt) i T
+
+val mk_true = Thm.cterm_of @{theory} (@{const Not} $ @{const False})
+val mk_false = Thm.cterm_of @{theory} @{const False}
+val mk_not = Thm.apply (Thm.cterm_of @{theory} @{const Not})
+val mk_implies = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.implies})
+val mk_iff = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.eq (bool)})
+val conj = Thm.cterm_of @{theory} @{const HOL.conj}
+val disj = Thm.cterm_of @{theory} @{const HOL.disj}
+
+fun mk_nary _ cu [] = cu
+ | mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
+
+val eq = SMT_Util.mk_const_pat @{theory} @{const_name HOL.eq} SMT_Util.destT1
+fun mk_eq ct cu = Thm.mk_binop (SMT_Util.instT' ct eq) ct cu
+
+val if_term =
+ SMT_Util.mk_const_pat @{theory} @{const_name If} (SMT_Util.destT1 o SMT_Util.destT2)
+fun mk_if cc ct = Thm.mk_binop (Thm.apply (SMT_Util.instT' ct if_term) cc) ct
+
+val access = SMT_Util.mk_const_pat @{theory} @{const_name fun_app} SMT_Util.destT1
+fun mk_access array = Thm.apply (SMT_Util.instT' array access) array
+
+val update =
+ SMT_Util.mk_const_pat @{theory} @{const_name fun_upd} (Thm.dest_ctyp o SMT_Util.destT1)
+fun mk_update array index value =
+ let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array)
+ in Thm.apply (Thm.mk_binop (SMT_Util.instTs cTs update) array index) value end
+
+val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (int)})
+val add = Thm.cterm_of @{theory} @{const plus (int)}
+val int0 = Numeral.mk_cnumber @{ctyp int} 0
+val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (int)})
+val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (int)})
+val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3div})
+val mk_mod = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3mod})
+val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (int)})
+val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (int)})
+
+fun mk_builtin_fun ctxt sym cts =
+ (case (sym, cts) of
+ (Sym ("true", _), []) => SOME mk_true
+ | (Sym ("false", _), []) => SOME mk_false
+ | (Sym ("not", _), [ct]) => SOME (mk_not ct)
+ | (Sym ("and", _), _) => SOME (mk_nary conj mk_true cts)
+ | (Sym ("or", _), _) => SOME (mk_nary disj mk_false cts)
+ | (Sym ("implies", _), [ct, cu]) => SOME (mk_implies ct cu)
+ | (Sym ("iff", _), [ct, cu]) => SOME (mk_iff ct cu)
+ | (Sym ("~", _), [ct, cu]) => SOME (mk_iff ct cu)
+ | (Sym ("xor", _), [ct, cu]) => SOME (mk_not (mk_iff ct cu))
+ | (Sym ("if", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3)
+ | (Sym ("ite", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3) (* FIXME: remove *)
+ | (Sym ("=", _), [ct, cu]) => SOME (mk_eq ct cu)
+ | (Sym ("select", _), [ca, ck]) => SOME (Thm.apply (mk_access ca) ck)
+ | (Sym ("store", _), [ca, ck, cv]) => SOME (mk_update ca ck cv)
+ | _ =>
+ (case (sym, try (#T o Thm.rep_cterm o hd) cts, cts) of
+ (Sym ("+", _), SOME @{typ int}, _) => SOME (mk_nary add int0 cts)
+ | (Sym ("-", _), SOME @{typ int}, [ct]) => SOME (mk_uminus ct)
+ | (Sym ("-", _), SOME @{typ int}, [ct, cu]) => SOME (mk_sub ct cu)
+ | (Sym ("*", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mul ct cu)
+ | (Sym ("div", _), SOME @{typ int}, [ct, cu]) => SOME (mk_div ct cu)
+ | (Sym ("mod", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mod ct cu)
+ | (Sym ("<", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt ct cu)
+ | (Sym ("<=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le ct cu)
+ | (Sym (">", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt cu ct)
+ | (Sym (">=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le cu ct)
+ | _ => chained_mk_builtin_fun ctxt (get_mk_builtins ctxt) sym cts))
+
+
+(* abstraction *)
+
+fun is_builtin_theory_term ctxt t =
+ if SMT_Builtin.is_builtin_num ctxt t then true
+ else
+ (case Term.strip_comb t of
+ (Const c, ts) => SMT_Builtin.is_builtin_fun ctxt c ts
+ | _ => false)
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_isar.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,123 @@
+(* Title: HOL/Tools/SMT/z3_isar.ML
+ Author: Jasmin Blanchette, TU Muenchen
+
+Z3 proofs as generic ATP proofs for Isar proof reconstruction.
+*)
+
+signature Z3_ISAR =
+sig
+ val atp_proof_of_z3_proof: Proof.context -> term list -> thm list -> term list -> term ->
+ (string * term) list -> int list -> int -> (int * string) list -> Z3_Proof.z3_step list ->
+ (term, string) ATP_Proof.atp_step list
+end;
+
+structure Z3_Isar: Z3_ISAR =
+struct
+
+open ATP_Util
+open ATP_Problem
+open ATP_Proof
+open ATP_Proof_Reconstruct
+open SMTLIB_Isar
+
+val z3_apply_def_rule = Z3_Proof.string_of_rule Z3_Proof.Apply_Def
+val z3_hypothesis_rule = Z3_Proof.string_of_rule Z3_Proof.Hypothesis
+val z3_intro_def_rule = Z3_Proof.string_of_rule Z3_Proof.Intro_Def
+val z3_lemma_rule = Z3_Proof.string_of_rule Z3_Proof.Lemma
+
+fun inline_z3_defs _ [] = []
+ | inline_z3_defs defs ((name, role, t, rule, deps) :: lines) =
+ if rule = z3_intro_def_rule then
+ let val def = t |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> swap in
+ inline_z3_defs (insert (op =) def defs)
+ (map (replace_dependencies_in_line (name, [])) lines)
+ end
+ else if rule = z3_apply_def_rule then
+ inline_z3_defs defs (map (replace_dependencies_in_line (name, [])) lines)
+ else
+ (name, role, Term.subst_atomic defs t, rule, deps) :: inline_z3_defs defs lines
+
+fun add_z3_hypotheses [] = I
+ | add_z3_hypotheses hyps =
+ HOLogic.dest_Trueprop
+ #> curry s_imp (Library.foldr1 s_conj (map HOLogic.dest_Trueprop hyps))
+ #> HOLogic.mk_Trueprop
+
+fun inline_z3_hypotheses _ _ [] = []
+ | inline_z3_hypotheses hyp_names hyps ((name, role, t, rule, deps) :: lines) =
+ if rule = z3_hypothesis_rule then
+ inline_z3_hypotheses (name :: hyp_names) (AList.map_default (op =) (t, []) (cons name) hyps)
+ lines
+ else
+ let val deps' = subtract (op =) hyp_names deps in
+ if rule = z3_lemma_rule then
+ (name, role, t, rule, deps') :: inline_z3_hypotheses hyp_names hyps lines
+ else
+ let
+ val add_hyps = filter_out (null o inter (op =) deps o snd) hyps
+ val t' = add_z3_hypotheses (map fst add_hyps) t
+ val deps' = subtract (op =) hyp_names deps
+ val hyps' = fold (AList.update (op =) o apsnd (insert (op =) name)) add_hyps hyps
+ in
+ (name, role, t', rule, deps') :: inline_z3_hypotheses hyp_names hyps' lines
+ end
+ end
+
+fun dest_alls (Const (@{const_name Pure.all}, _) $ Abs (abs as (_, T, _))) =
+ let val (s', t') = Term.dest_abs abs in
+ dest_alls t' |>> cons (s', T)
+ end
+ | dest_alls t = ([], t)
+
+val reorder_foralls =
+ dest_alls
+ #>> sort_wrt fst
+ #-> fold_rev (Logic.all o Free);
+
+fun atp_proof_of_z3_proof ctxt ll_defs rewrite_rules hyp_ts concl_t fact_helper_ts prem_ids
+ conjecture_id fact_helper_ids proof =
+ let
+ val thy = Proof_Context.theory_of ctxt
+
+ fun steps_of (Z3_Proof.Z3_Step {id, rule, prems, concl, ...}) =
+ let
+ val sid = string_of_int id
+
+ val concl' = concl
+ |> reorder_foralls (* crucial for skolemization steps *)
+ |> postprocess_step_conclusion thy rewrite_rules ll_defs
+ fun standard_step role =
+ ((sid, []), role, concl', Z3_Proof.string_of_rule rule,
+ map (fn id => (string_of_int id, [])) prems)
+ in
+ (case rule of
+ Z3_Proof.Asserted =>
+ let val ss = the_list (AList.lookup (op =) fact_helper_ids id) in
+ (case distinguish_conjecture_and_hypothesis ss id conjecture_id prem_ids fact_helper_ts
+ hyp_ts concl_t of
+ NONE => []
+ | SOME (role0, concl00) =>
+ let
+ val name0 = (sid ^ "a", ss)
+ val concl0 = unskolemize_names concl00
+ in
+ (if role0 = Axiom then []
+ else [(name0, role0, concl0, Z3_Proof.string_of_rule rule, [])]) @
+ [((sid, []), Plain, concl', Z3_Proof.string_of_rule Z3_Proof.Rewrite,
+ name0 :: normalizing_prems ctxt concl0)]
+ end)
+ end
+ | Z3_Proof.Rewrite => [standard_step Lemma]
+ | Z3_Proof.Rewrite_Star => [standard_step Lemma]
+ | Z3_Proof.Skolemize => [standard_step Lemma]
+ | Z3_Proof.Th_Lemma _ => [standard_step Lemma]
+ | _ => [standard_step Plain])
+ end
+ in
+ proof
+ |> maps steps_of
+ |> inline_z3_defs []
+ |> inline_z3_hypotheses [] []
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_proof.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,303 @@
+(* Title: HOL/Tools/SMT/z3_proof.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Z3 proofs: parsing and abstract syntax tree.
+*)
+
+signature Z3_PROOF =
+sig
+ (*proof rules*)
+ datatype z3_rule =
+ True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity | Symmetry | Transitivity |
+ Transitivity_Star | Monotonicity | Quant_Intro | Distributivity | And_Elim | Not_Or_Elim |
+ Rewrite | Rewrite_Star | Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
+ Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
+ Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star |
+ Cnf_Star | Skolemize | Modus_Ponens_Oeq | Th_Lemma of string
+
+ val is_assumption: z3_rule -> bool
+ val string_of_rule: z3_rule -> string
+
+ (*proofs*)
+ datatype z3_step = Z3_Step of {
+ id: int,
+ rule: z3_rule,
+ prems: int list,
+ concl: term,
+ fixes: string list,
+ is_fix_step: bool}
+
+ (*proof parser*)
+ val parse: typ Symtab.table -> term Symtab.table -> string list ->
+ Proof.context -> z3_step list * Proof.context
+end;
+
+structure Z3_Proof: Z3_PROOF =
+struct
+
+open SMTLIB_Proof
+
+
+(* proof rules *)
+
+datatype z3_rule =
+ True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity | Symmetry | Transitivity |
+ Transitivity_Star | Monotonicity | Quant_Intro | Distributivity | And_Elim | Not_Or_Elim |
+ Rewrite | Rewrite_Star | Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
+ Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
+ Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star |
+ Cnf_Star | Skolemize | Modus_Ponens_Oeq | Th_Lemma of string
+ (* some proof rules include further information that is currently dropped by the parser *)
+
+val rule_names = Symtab.make [
+ ("true-axiom", True_Axiom),
+ ("asserted", Asserted),
+ ("goal", Goal),
+ ("mp", Modus_Ponens),
+ ("refl", Reflexivity),
+ ("symm", Symmetry),
+ ("trans", Transitivity),
+ ("trans*", Transitivity_Star),
+ ("monotonicity", Monotonicity),
+ ("quant-intro", Quant_Intro),
+ ("distributivity", Distributivity),
+ ("and-elim", And_Elim),
+ ("not-or-elim", Not_Or_Elim),
+ ("rewrite", Rewrite),
+ ("rewrite*", Rewrite_Star),
+ ("pull-quant", Pull_Quant),
+ ("pull-quant*", Pull_Quant_Star),
+ ("push-quant", Push_Quant),
+ ("elim-unused", Elim_Unused_Vars),
+ ("der", Dest_Eq_Res),
+ ("quant-inst", Quant_Inst),
+ ("hypothesis", Hypothesis),
+ ("lemma", Lemma),
+ ("unit-resolution", Unit_Resolution),
+ ("iff-true", Iff_True),
+ ("iff-false", Iff_False),
+ ("commutativity", Commutativity),
+ ("def-axiom", Def_Axiom),
+ ("intro-def", Intro_Def),
+ ("apply-def", Apply_Def),
+ ("iff~", Iff_Oeq),
+ ("nnf-pos", Nnf_Pos),
+ ("nnf-neg", Nnf_Neg),
+ ("nnf*", Nnf_Star),
+ ("cnf*", Cnf_Star),
+ ("sk", Skolemize),
+ ("mp~", Modus_Ponens_Oeq)]
+
+fun is_assumption Asserted = true
+ | is_assumption Goal = true
+ | is_assumption Hypothesis = true
+ | is_assumption Intro_Def = true
+ | is_assumption Skolemize = true
+ | is_assumption _ = false
+
+fun rule_of_string name =
+ (case Symtab.lookup rule_names name of
+ SOME rule => rule
+ | NONE => error ("unknown Z3 proof rule " ^ quote name))
+
+fun string_of_rule (Th_Lemma kind) = "th-lemma" ^ (if kind = "" then "" else " " ^ kind)
+ | string_of_rule r =
+ let fun eq_rule (s, r') = if r = r' then SOME s else NONE
+ in the (Symtab.get_first eq_rule rule_names) end
+
+
+(* proofs *)
+
+datatype z3_node = Z3_Node of {
+ id: int,
+ rule: z3_rule,
+ prems: z3_node list,
+ concl: term,
+ bounds: string list}
+
+fun mk_node id rule prems concl bounds =
+ Z3_Node {id = id, rule = rule, prems = prems, concl = concl, bounds = bounds}
+
+datatype z3_step = Z3_Step of {
+ id: int,
+ rule: z3_rule,
+ prems: int list,
+ concl: term,
+ fixes: string list,
+ is_fix_step: bool}
+
+fun mk_step id rule prems concl fixes is_fix_step =
+ Z3_Step {id = id, rule = rule, prems = prems, concl = concl, fixes = fixes,
+ is_fix_step = is_fix_step}
+
+
+(* proof parser *)
+
+fun rule_of (SMTLIB.Sym name) = rule_of_string name
+ | rule_of (SMTLIB.S (SMTLIB.Sym "_" :: SMTLIB.Sym name :: args)) =
+ (case (name, args) of
+ ("th-lemma", SMTLIB.Sym kind :: _) => Th_Lemma kind
+ | _ => rule_of_string name)
+ | rule_of r = raise SMTLIB_PARSE ("bad Z3 proof rule format", r)
+
+fun node_of p cx =
+ (case p of
+ SMTLIB.Sym name =>
+ (case lookup_binding cx name of
+ Proof node => (node, cx)
+ | Tree p' =>
+ cx
+ |> node_of p'
+ |-> (fn node => pair node o update_binding (name, Proof node))
+ | _ => raise SMTLIB_PARSE ("bad Z3 proof format", p))
+ | SMTLIB.S [SMTLIB.Sym "let", SMTLIB.S bindings, p] =>
+ with_bindings (map dest_binding bindings) (node_of p) cx
+ | SMTLIB.S (name :: parts) =>
+ let
+ val (ps, p) = split_last parts
+ val r = rule_of name
+ in
+ cx
+ |> fold_map node_of ps
+ ||>> `(with_fresh_names (term_of p))
+ ||>> next_id
+ |>> (fn ((prems, (t, ns)), id) => mk_node id r prems t ns)
+ end
+ | _ => raise SMTLIB_PARSE ("bad Z3 proof format", p))
+
+fun dest_name (SMTLIB.Sym name) = name
+ | dest_name t = raise SMTLIB_PARSE ("bad name", t)
+
+fun dest_seq (SMTLIB.S ts) = ts
+ | dest_seq t = raise SMTLIB_PARSE ("bad Z3 proof format", t)
+
+fun parse' (SMTLIB.S (SMTLIB.Sym "set-logic" :: _) :: ts) cx = parse' ts cx
+ | parse' (SMTLIB.S [SMTLIB.Sym "declare-fun", n, tys, ty] :: ts) cx =
+ let
+ val name = dest_name n
+ val Ts = map (type_of cx) (dest_seq tys)
+ val T = type_of cx ty
+ in parse' ts (declare_fun name (Ts ---> T) cx) end
+ | parse' (SMTLIB.S [SMTLIB.Sym "proof", p] :: _) cx = node_of p cx
+ | parse' ts _ = raise SMTLIB_PARSE ("bad Z3 proof declarations", SMTLIB.S ts)
+
+fun parse_proof typs funs lines ctxt =
+ let
+ val ts = dest_seq (SMTLIB.parse lines)
+ val (node, cx) = parse' ts (empty_context ctxt typs funs)
+ in (node, ctxt_of cx) end
+ handle SMTLIB.PARSE (l, msg) => error ("parsing error at line " ^ string_of_int l ^ ": " ^ msg)
+ | SMTLIB_PARSE (msg, t) => error (msg ^ ": " ^ SMTLIB.str_of t)
+
+
+(* handling of bound variables *)
+
+fun subst_of tyenv =
+ let fun add (ix, (S, T)) = cons (TVar (ix, S), T)
+ in Vartab.fold add tyenv [] end
+
+fun substTs_same subst =
+ let val applyT = Same.function (AList.lookup (op =) subst)
+ in Term_Subst.map_atypsT_same applyT end
+
+fun subst_types ctxt env bounds t =
+ let
+ val match = Sign.typ_match (Proof_Context.theory_of ctxt)
+
+ val t' = singleton (Variable.polymorphic ctxt) t
+ val patTs = map snd (Term.strip_qnt_vars @{const_name Pure.all} t')
+ val objTs = map (the o Symtab.lookup env) bounds
+ val subst = subst_of (fold match (patTs ~~ objTs) Vartab.empty)
+ in Same.commit (Term_Subst.map_types_same (substTs_same subst)) t' end
+
+fun eq_quant (@{const_name HOL.All}, _) (@{const_name HOL.All}, _) = true
+ | eq_quant (@{const_name HOL.Ex}, _) (@{const_name HOL.Ex}, _) = true
+ | eq_quant _ _ = false
+
+fun opp_quant (@{const_name HOL.All}, _) (@{const_name HOL.Ex}, _) = true
+ | opp_quant (@{const_name HOL.Ex}, _) (@{const_name HOL.All}, _) = true
+ | opp_quant _ _ = false
+
+fun with_quant pred i (Const q1 $ Abs (_, T1, t1), Const q2 $ Abs (_, T2, t2)) =
+ if pred q1 q2 andalso T1 = T2 then
+ let val t = Var (("", i), T1)
+ in SOME (pairself Term.subst_bound ((t, t1), (t, t2))) end
+ else NONE
+ | with_quant _ _ _ = NONE
+
+fun dest_quant_pair i (@{term HOL.Not} $ t1, t2) =
+ Option.map (apfst HOLogic.mk_not) (with_quant opp_quant i (t1, t2))
+ | dest_quant_pair i (t1, t2) = with_quant eq_quant i (t1, t2)
+
+fun dest_quant i t =
+ (case dest_quant_pair i (HOLogic.dest_eq (HOLogic.dest_Trueprop t)) of
+ SOME (t1, t2) => HOLogic.mk_Trueprop (HOLogic.mk_eq (t1, t2))
+ | NONE => raise TERM ("lift_quant", [t]))
+
+fun match_types ctxt pat obj =
+ (Vartab.empty, Vartab.empty)
+ |> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, obj)
+
+fun strip_match ctxt pat i obj =
+ (case try (match_types ctxt pat) obj of
+ SOME (tyenv, _) => subst_of tyenv
+ | NONE => strip_match ctxt pat (i + 1) (dest_quant i obj))
+
+fun dest_all i (Const (@{const_name Pure.all}, _) $ (a as Abs (_, T, _))) =
+ dest_all (i + 1) (Term.betapply (a, Var (("", i), T)))
+ | dest_all i t = (i, t)
+
+fun dest_alls t = dest_all (Term.maxidx_of_term t + 1) t
+
+fun match_rule ctxt env (Z3_Node {bounds = bs', concl = t', ...}) bs t =
+ let
+ val t'' = singleton (Variable.polymorphic ctxt) t'
+ val (i, obj) = dest_alls (subst_types ctxt env bs t)
+ in
+ (case try (strip_match ctxt (snd (dest_alls t'')) i) obj of
+ NONE => NONE
+ | SOME subst =>
+ let
+ val applyT = Same.commit (substTs_same subst)
+ val patTs = map snd (Term.strip_qnt_vars @{const_name Pure.all} t'')
+ in SOME (Symtab.make (bs' ~~ map applyT patTs)) end)
+ end
+
+
+(* linearizing proofs and resolving types of bound variables *)
+
+fun has_step (tab, _) = Inttab.defined tab
+
+fun add_step id rule bounds concl is_fix_step ids (tab, sts) =
+ let val step = mk_step id rule ids concl bounds is_fix_step
+ in (id, (Inttab.update (id, ()) tab, step :: sts)) end
+
+fun is_fix_rule rule prems =
+ member (op =) [Quant_Intro, Nnf_Pos, Nnf_Neg] rule andalso length prems = 1
+
+fun lin_proof ctxt env (Z3_Node {id, rule, prems, concl, bounds}) steps =
+ if has_step steps id then (id, steps)
+ else
+ let
+ val t = subst_types ctxt env bounds concl
+ val add = add_step id rule bounds t
+ fun rec_apply e b = fold_map (lin_proof ctxt e) prems #-> add b
+ in
+ if is_fix_rule rule prems then
+ (case match_rule ctxt env (hd prems) bounds t of
+ NONE => rec_apply env false steps
+ | SOME env' => rec_apply env' true steps)
+ else rec_apply env false steps
+ end
+
+fun linearize ctxt node =
+ rev (snd (snd (lin_proof ctxt Symtab.empty node (Inttab.empty, []))))
+
+
+(* overall proof parser *)
+
+fun parse typs funs lines ctxt =
+ let val (node, ctxt') = parse_proof typs funs lines ctxt
+ in (linearize ctxt' node, ctxt') end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_real.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,32 @@
+(* Title: HOL/Tools/SMT/z3_real.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Z3 setup for reals.
+*)
+
+structure Z3_Real: sig end =
+struct
+
+fun real_type_parser (SMTLIB.Sym "Real", []) = SOME @{typ Real.real}
+ | real_type_parser _ = NONE
+
+fun real_term_parser (SMTLIB.Dec (i, 0), []) = SOME (HOLogic.mk_number @{typ Real.real} i)
+ | real_term_parser (SMTLIB.Sym "/", [t1, t2]) =
+ SOME (@{term "inverse_class.divide :: real => _"} $ t1 $ t2)
+ | real_term_parser (SMTLIB.Sym "to_real", [t]) = SOME (@{term "Real.real :: int => _"} $ t)
+ | real_term_parser _ = NONE
+
+fun abstract abs t =
+ (case t of
+ (c as @{term "inverse_class.divide :: real => _"}) $ t1 $ t2 =>
+ abs t1 ##>> abs t2 #>> (fn (u1, u2) => SOME (c $ u1 $ u2))
+ | (c as @{term "Real.real :: int => _"}) $ t =>
+ abs t #>> (fn u => SOME (c $ u))
+ | _ => pair NONE)
+
+val _ = Theory.setup (Context.theory_map (
+ SMTLIB_Proof.add_type_parser real_type_parser #>
+ SMTLIB_Proof.add_term_parser real_term_parser #>
+ Z3_Replay_Methods.add_arith_abstracter abstract))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_replay.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,217 @@
+(* Title: HOL/Tools/SMT/z3_replay.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Z3 proof parsing and replay.
+*)
+
+signature Z3_REPLAY =
+sig
+ val parse_proof: Proof.context -> SMT_Translate.replay_data ->
+ ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
+ SMT_Solver.parsed_proof
+ val replay: Proof.context -> SMT_Translate.replay_data -> string list -> thm
+end;
+
+structure Z3_Replay: Z3_REPLAY =
+struct
+
+fun params_of t = Term.strip_qnt_vars @{const_name Pure.all} t
+
+fun varify ctxt thm =
+ let
+ val maxidx = Thm.maxidx_of thm + 1
+ val vs = params_of (Thm.prop_of thm)
+ val vars = map_index (fn (i, (n, T)) => Var ((n, i + maxidx), T)) vs
+ in Drule.forall_elim_list (map (SMT_Util.certify ctxt) vars) thm end
+
+fun add_paramTs names t =
+ fold2 (fn n => fn (_, T) => AList.update (op =) (n, T)) names (params_of t)
+
+fun new_fixes ctxt nTs =
+ let
+ val (ns, ctxt') = Variable.variant_fixes (replicate (length nTs) "") ctxt
+ fun mk (n, T) n' = (n, SMT_Util.certify ctxt' (Free (n', T)))
+ in (ctxt', Symtab.make (map2 mk nTs ns)) end
+
+fun forall_elim_term ct (Const (@{const_name Pure.all}, _) $ (a as Abs _)) =
+ Term.betapply (a, Thm.term_of ct)
+ | forall_elim_term _ qt = raise TERM ("forall_elim'", [qt])
+
+fun apply_fixes elim env = fold (elim o the o Symtab.lookup env)
+
+val apply_fixes_prem = uncurry o apply_fixes Thm.forall_elim
+val apply_fixes_concl = apply_fixes forall_elim_term
+
+fun export_fixes env names = Drule.forall_intr_list (map (the o Symtab.lookup env) names)
+
+fun under_fixes f ctxt (prems, nthms) names concl =
+ let
+ val thms1 = map (varify ctxt) prems
+ val (ctxt', env) =
+ add_paramTs names concl []
+ |> fold (uncurry add_paramTs o apsnd Thm.prop_of) nthms
+ |> new_fixes ctxt
+ val thms2 = map (apply_fixes_prem env) nthms
+ val t = apply_fixes_concl env names concl
+ in export_fixes env names (f ctxt' (thms1 @ thms2) t) end
+
+fun replay_thm ctxt assumed nthms (Z3_Proof.Z3_Step {id, rule, concl, fixes, is_fix_step, ...}) =
+ if Z3_Proof.is_assumption rule then
+ (case Inttab.lookup assumed id of
+ SOME (_, thm) => thm
+ | NONE => Thm.assume (SMT_Util.certify ctxt concl))
+ else
+ under_fixes (Z3_Replay_Methods.method_for rule) ctxt
+ (if is_fix_step then (map snd nthms, []) else ([], nthms)) fixes concl
+
+fun replay_step ctxt assumed (step as Z3_Proof.Z3_Step {id, prems, fixes, ...}) proofs =
+ let val nthms = map (the o Inttab.lookup proofs) prems
+ in Inttab.update (id, (fixes, replay_thm ctxt assumed nthms step)) proofs end
+
+local
+ val remove_trigger = mk_meta_eq @{thm trigger_def}
+ val remove_fun_app = mk_meta_eq @{thm fun_app_def}
+
+ fun rewrite_conv _ [] = Conv.all_conv
+ | rewrite_conv ctxt eqs = Simplifier.full_rewrite (empty_simpset ctxt addsimps eqs)
+
+ val prep_rules = [@{thm Let_def}, remove_trigger, remove_fun_app, Z3_Replay_Literals.rewrite_true]
+
+ fun rewrite _ [] = I
+ | rewrite ctxt eqs = Conv.fconv_rule (rewrite_conv ctxt eqs)
+
+ fun lookup_assm assms_net ct =
+ Z3_Replay_Util.net_instances assms_net ct
+ |> map (fn ithm as (_, thm) => (ithm, Thm.cprop_of thm aconvc ct))
+in
+
+fun add_asserted outer_ctxt rewrite_rules assms steps ctxt =
+ let
+ val eqs = map (rewrite ctxt [Z3_Replay_Literals.rewrite_true]) rewrite_rules
+ val eqs' = union Thm.eq_thm eqs prep_rules
+
+ val assms_net =
+ assms
+ |> map (apsnd (rewrite ctxt eqs'))
+ |> map (apsnd (Conv.fconv_rule Thm.eta_conversion))
+ |> Z3_Replay_Util.thm_net_of snd
+
+ fun revert_conv ctxt = rewrite_conv ctxt eqs' then_conv Thm.eta_conversion
+
+ fun assume thm ctxt =
+ let
+ val ct = Thm.cprem_of thm 1
+ val (thm', ctxt') = yield_singleton Assumption.add_assumes ct ctxt
+ in (thm' RS thm, ctxt') end
+
+ fun add1 id fixes thm1 ((i, th), exact) ((iidths, thms), (ctxt, ptab)) =
+ let
+ val (thm, ctxt') = if exact then (Thm.implies_elim thm1 th, ctxt) else assume thm1 ctxt
+ val thms' = if exact then thms else th :: thms
+ in (((i, (id, th)) :: iidths, thms'), (ctxt', Inttab.update (id, (fixes, thm)) ptab)) end
+
+ fun add (Z3_Proof.Z3_Step {id, rule, concl, fixes, ...})
+ (cx as ((iidths, thms), (ctxt, ptab))) =
+ if Z3_Proof.is_assumption rule andalso rule <> Z3_Proof.Hypothesis then
+ let
+ val ct = SMT_Util.certify ctxt concl
+ val thm1 = Thm.trivial ct |> Conv.fconv_rule (Conv.arg1_conv (revert_conv outer_ctxt))
+ val thm2 = singleton (Variable.export ctxt outer_ctxt) thm1
+ in
+ (case lookup_assm assms_net (Thm.cprem_of thm2 1) of
+ [] =>
+ let val (thm, ctxt') = assume thm1 ctxt
+ in ((iidths, thms), (ctxt', Inttab.update (id, (fixes, thm)) ptab)) end
+ | ithms => fold (add1 id fixes thm1) ithms cx)
+ end
+ else
+ cx
+ in fold add steps (([], []), (ctxt, Inttab.empty)) end
+
+end
+
+(* |- (EX x. P x) = P c |- ~ (ALL x. P x) = ~ P c *)
+local
+ val sk_rules = @{lemma
+ "c = (SOME x. P x) ==> (EX x. P x) = P c"
+ "c = (SOME x. ~ P x) ==> (~ (ALL x. P x)) = (~ P c)"
+ by (metis someI_ex)+}
+in
+
+fun discharge_sk_tac i st =
+ (rtac @{thm trans} i
+ THEN resolve_tac sk_rules i
+ THEN (rtac @{thm refl} ORELSE' discharge_sk_tac) (i+1)
+ THEN rtac @{thm refl} i) st
+
+end
+
+fun make_discharge_rules rules = rules @ [@{thm allI}, @{thm refl}, @{thm reflexive},
+ Z3_Replay_Literals.true_thm]
+
+val intro_def_rules = @{lemma
+ "(~ P | P) & (P | ~ P)"
+ "(P | ~ P) & (~ P | P)"
+ by fast+}
+
+fun discharge_assms_tac rules =
+ REPEAT (HEADGOAL (resolve_tac (intro_def_rules @ rules) ORELSE' SOLVED' discharge_sk_tac))
+
+fun discharge_assms ctxt rules thm =
+ (if Thm.nprems_of thm = 0 then
+ thm
+ else
+ (case Seq.pull (discharge_assms_tac rules thm) of
+ SOME (thm', _) => thm'
+ | NONE => raise THM ("failed to discharge premise", 1, [thm])))
+ |> Goal.norm_result ctxt
+
+fun discharge rules outer_ctxt inner_ctxt =
+ singleton (Proof_Context.export inner_ctxt outer_ctxt)
+ #> discharge_assms outer_ctxt (make_discharge_rules rules)
+
+fun parse_proof outer_ctxt
+ ({context = ctxt, typs, terms, ll_defs, rewrite_rules, assms} : SMT_Translate.replay_data)
+ xfacts prems concl output =
+ let
+ val (steps, ctxt2) = Z3_Proof.parse typs terms output ctxt
+ val ((iidths, _), _) = add_asserted outer_ctxt rewrite_rules assms steps ctxt2
+
+ fun id_of_index i = the_default ~1 (Option.map fst (AList.lookup (op =) iidths i))
+
+ val conjecture_i = 0
+ val prems_i = 1
+ val facts_i = prems_i + length prems
+
+ val conjecture_id = id_of_index conjecture_i
+ val prem_ids = map id_of_index (prems_i upto facts_i - 1)
+ val helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths
+ val fact_ids = map_filter (fn (i, (id, _)) => try (apsnd (nth xfacts)) (id, i - facts_i)) iidths
+ val fact_helper_ts =
+ map (fn (_, th) => (ATP_Util.short_thm_name ctxt th, prop_of th)) helper_ids @
+ map (fn (_, ((s, _), th)) => (s, prop_of th)) fact_ids
+ val fact_helper_ids =
+ map (apsnd (ATP_Util.short_thm_name ctxt)) helper_ids @ map (apsnd (fst o fst)) fact_ids
+ in
+ {outcome = NONE, fact_ids = fact_ids,
+ atp_proof = fn () => Z3_Isar.atp_proof_of_z3_proof ctxt ll_defs rewrite_rules prems concl
+ fact_helper_ts prem_ids conjecture_id fact_helper_ids steps}
+ end
+
+fun replay outer_ctxt
+ ({context = ctxt, typs, terms, rewrite_rules, assms, ...} : SMT_Translate.replay_data) output =
+ let
+ val (steps, ctxt2) = Z3_Proof.parse typs terms output ctxt
+ val ((_, rules), (ctxt3, assumed)) = add_asserted outer_ctxt rewrite_rules assms steps ctxt2
+ val ctxt4 =
+ ctxt3
+ |> put_simpset (Z3_Replay_Util.make_simpset ctxt3 [])
+ |> Config.put SAT.solver (Config.get ctxt3 SMT_Config.sat_solver)
+ val proofs = fold (replay_step ctxt4 assumed) steps assumed
+ val (_, Z3_Proof.Z3_Step {id, ...}) = split_last steps
+ in
+ Inttab.lookup proofs id |> the |> snd |> discharge rules outer_ctxt ctxt4
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_replay_literals.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,351 @@
+(* Title: HOL/Tools/SMT/z3_replay_literals.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Proof tools related to conjunctions and disjunctions.
+*)
+
+signature Z3_REPLAY_LITERALS =
+sig
+ (*literal table*)
+ type littab = thm Termtab.table
+ val make_littab: thm list -> littab
+ val insert_lit: thm -> littab -> littab
+ val delete_lit: thm -> littab -> littab
+ val lookup_lit: littab -> term -> thm option
+ val get_first_lit: (term -> bool) -> littab -> thm option
+
+ (*rules*)
+ val true_thm: thm
+ val rewrite_true: thm
+
+ (*properties*)
+ val is_conj: term -> bool
+ val is_disj: term -> bool
+ val exists_lit: bool -> (term -> bool) -> term -> bool
+ val negate: cterm -> cterm
+
+ (*proof tools*)
+ val explode: bool -> bool -> bool -> term list -> thm -> thm list
+ val join: bool -> littab -> term -> thm
+ val prove_conj_disj_eq: cterm -> thm
+end;
+
+structure Z3_Replay_Literals: Z3_REPLAY_LITERALS =
+struct
+
+(* literal table *)
+
+type littab = thm Termtab.table
+
+fun make_littab thms = fold (Termtab.update o `SMT_Util.prop_of) thms Termtab.empty
+
+fun insert_lit thm = Termtab.update (`SMT_Util.prop_of thm)
+fun delete_lit thm = Termtab.delete (SMT_Util.prop_of thm)
+fun lookup_lit lits = Termtab.lookup lits
+fun get_first_lit f =
+ Termtab.get_first (fn (t, thm) => if f t then SOME thm else NONE)
+
+
+(* rules *)
+
+val true_thm = @{lemma "~False" by simp}
+val rewrite_true = @{lemma "True == ~ False" by simp}
+
+
+(* properties and term operations *)
+
+val is_neg = (fn @{const Not} $ _ => true | _ => false)
+fun is_neg' f = (fn @{const Not} $ t => f t | _ => false)
+val is_dneg = is_neg' is_neg
+val is_conj = (fn @{const HOL.conj} $ _ $ _ => true | _ => false)
+val is_disj = (fn @{const HOL.disj} $ _ $ _ => true | _ => false)
+
+fun dest_disj_term' f = (fn
+ @{const Not} $ (@{const HOL.disj} $ t $ u) => SOME (f t, f u)
+ | _ => NONE)
+
+val dest_conj_term = (fn @{const HOL.conj} $ t $ u => SOME (t, u) | _ => NONE)
+val dest_disj_term =
+ dest_disj_term' (fn @{const Not} $ t => t | t => @{const Not} $ t)
+
+fun exists_lit is_conj P =
+ let
+ val dest = if is_conj then dest_conj_term else dest_disj_term
+ fun exists t = P t orelse
+ (case dest t of
+ SOME (t1, t2) => exists t1 orelse exists t2
+ | NONE => false)
+ in exists end
+
+val negate = Thm.apply (Thm.cterm_of @{theory} @{const Not})
+
+
+(* proof tools *)
+
+(** explosion of conjunctions and disjunctions **)
+
+local
+ val precomp = Z3_Replay_Util.precompose2
+
+ fun destc ct = Thm.dest_binop (Thm.dest_arg ct)
+ val dest_conj1 = precomp destc @{thm conjunct1}
+ val dest_conj2 = precomp destc @{thm conjunct2}
+ fun dest_conj_rules t =
+ dest_conj_term t |> Option.map (K (dest_conj1, dest_conj2))
+
+ fun destd f ct = f (Thm.dest_binop (Thm.dest_arg (Thm.dest_arg ct)))
+ val dn1 = apfst Thm.dest_arg and dn2 = apsnd Thm.dest_arg
+ val dest_disj1 = precomp (destd I) @{lemma "~(P | Q) ==> ~P" by fast}
+ val dest_disj2 = precomp (destd dn1) @{lemma "~(~P | Q) ==> P" by fast}
+ val dest_disj3 = precomp (destd I) @{lemma "~(P | Q) ==> ~Q" by fast}
+ val dest_disj4 = precomp (destd dn2) @{lemma "~(P | ~Q) ==> Q" by fast}
+
+ fun dest_disj_rules t =
+ (case dest_disj_term' is_neg t of
+ SOME (true, true) => SOME (dest_disj2, dest_disj4)
+ | SOME (true, false) => SOME (dest_disj2, dest_disj3)
+ | SOME (false, true) => SOME (dest_disj1, dest_disj4)
+ | SOME (false, false) => SOME (dest_disj1, dest_disj3)
+ | NONE => NONE)
+
+ fun destn ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg ct))]
+ val dneg_rule = Z3_Replay_Util.precompose destn @{thm notnotD}
+in
+
+(*
+ explode a term into literals and collect all rules to be able to deduce
+ particular literals afterwards
+*)
+fun explode_term is_conj =
+ let
+ val dest = if is_conj then dest_conj_term else dest_disj_term
+ val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
+
+ fun add (t, rs) = Termtab.map_default (t, rs)
+ (fn rs' => if length rs' < length rs then rs' else rs)
+
+ fun explode1 rules t =
+ (case dest t of
+ SOME (t1, t2) =>
+ let val (rule1, rule2) = the (dest_rules t)
+ in
+ explode1 (rule1 :: rules) t1 #>
+ explode1 (rule2 :: rules) t2 #>
+ add (t, rev rules)
+ end
+ | NONE => add (t, rev rules))
+
+ fun explode0 (@{const Not} $ (@{const Not} $ t)) =
+ Termtab.make [(t, [dneg_rule])]
+ | explode0 t = explode1 [] t Termtab.empty
+
+ in explode0 end
+
+(*
+ extract a literal by applying previously collected rules
+*)
+fun extract_lit thm rules = fold Z3_Replay_Util.compose rules thm
+
+
+(*
+ explode a theorem into its literals
+*)
+fun explode is_conj full keep_intermediate stop_lits =
+ let
+ val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
+ val tab = fold (Termtab.update o rpair ()) stop_lits Termtab.empty
+
+ fun explode1 thm =
+ if Termtab.defined tab (SMT_Util.prop_of thm) then cons thm
+ else
+ (case dest_rules (SMT_Util.prop_of thm) of
+ SOME (rule1, rule2) =>
+ explode2 rule1 thm #>
+ explode2 rule2 thm #>
+ keep_intermediate ? cons thm
+ | NONE => cons thm)
+
+ and explode2 dest_rule thm =
+ if full orelse
+ exists_lit is_conj (Termtab.defined tab) (SMT_Util.prop_of thm)
+ then explode1 (Z3_Replay_Util.compose dest_rule thm)
+ else cons (Z3_Replay_Util.compose dest_rule thm)
+
+ fun explode0 thm =
+ if not is_conj andalso is_dneg (SMT_Util.prop_of thm)
+ then [Z3_Replay_Util.compose dneg_rule thm]
+ else explode1 thm []
+
+ in explode0 end
+
+end
+
+
+(** joining of literals to conjunctions or disjunctions **)
+
+local
+ fun on_cprem i f thm = f (Thm.cprem_of thm i)
+ fun on_cprop f thm = f (Thm.cprop_of thm)
+ fun precomp2 f g thm = (on_cprem 1 f thm, on_cprem 2 g thm, f, g, thm)
+ fun comp2 (cv1, cv2, f, g, rule) thm1 thm2 =
+ Thm.instantiate ([], [(cv1, on_cprop f thm1), (cv2, on_cprop g thm2)]) rule
+ |> Z3_Replay_Util.discharge thm1 |> Z3_Replay_Util.discharge thm2
+
+ fun d1 ct = Thm.dest_arg ct and d2 ct = Thm.dest_arg (Thm.dest_arg ct)
+
+ val conj_rule = precomp2 d1 d1 @{thm conjI}
+ fun comp_conj ((_, thm1), (_, thm2)) = comp2 conj_rule thm1 thm2
+
+ val disj1 = precomp2 d2 d2 @{lemma "~P ==> ~Q ==> ~(P | Q)" by fast}
+ val disj2 = precomp2 d2 d1 @{lemma "~P ==> Q ==> ~(P | ~Q)" by fast}
+ val disj3 = precomp2 d1 d2 @{lemma "P ==> ~Q ==> ~(~P | Q)" by fast}
+ val disj4 = precomp2 d1 d1 @{lemma "P ==> Q ==> ~(~P | ~Q)" by fast}
+
+ fun comp_disj ((false, thm1), (false, thm2)) = comp2 disj1 thm1 thm2
+ | comp_disj ((false, thm1), (true, thm2)) = comp2 disj2 thm1 thm2
+ | comp_disj ((true, thm1), (false, thm2)) = comp2 disj3 thm1 thm2
+ | comp_disj ((true, thm1), (true, thm2)) = comp2 disj4 thm1 thm2
+
+ fun dest_conj (@{const HOL.conj} $ t $ u) = ((false, t), (false, u))
+ | dest_conj t = raise TERM ("dest_conj", [t])
+
+ val neg = (fn @{const Not} $ t => (true, t) | t => (false, @{const Not} $ t))
+ fun dest_disj (@{const Not} $ (@{const HOL.disj} $ t $ u)) = (neg t, neg u)
+ | dest_disj t = raise TERM ("dest_disj", [t])
+
+ val precomp = Z3_Replay_Util.precompose
+ val dnegE = precomp (single o d2 o d1) @{thm notnotD}
+ val dnegI = precomp (single o d1) @{lemma "P ==> ~~P" by fast}
+ fun as_dneg f t = f (@{const Not} $ (@{const Not} $ t))
+
+ val precomp2 = Z3_Replay_Util.precompose2
+ fun dni f = apsnd f o Thm.dest_binop o f o d1
+ val negIffE = precomp2 (dni d1) @{lemma "~(P = (~Q)) ==> Q = P" by fast}
+ val negIffI = precomp2 (dni I) @{lemma "P = Q ==> ~(Q = (~P))" by fast}
+ val iff_const = @{const HOL.eq (bool)}
+ fun as_negIff f (@{const HOL.eq (bool)} $ t $ u) =
+ f (@{const Not} $ (iff_const $ u $ (@{const Not} $ t)))
+ | as_negIff _ _ = NONE
+in
+
+fun join is_conj littab t =
+ let
+ val comp = if is_conj then comp_conj else comp_disj
+ val dest = if is_conj then dest_conj else dest_disj
+
+ val lookup = lookup_lit littab
+
+ fun lookup_rule t =
+ (case t of
+ @{const Not} $ (@{const Not} $ t) => (Z3_Replay_Util.compose dnegI, lookup t)
+ | @{const Not} $ (@{const HOL.eq (bool)} $ t $ (@{const Not} $ u)) =>
+ (Z3_Replay_Util.compose negIffI, lookup (iff_const $ u $ t))
+ | @{const Not} $ ((eq as Const (@{const_name HOL.eq}, _)) $ t $ u) =>
+ let fun rewr lit = lit COMP @{thm not_sym}
+ in (rewr, lookup (@{const Not} $ (eq $ u $ t))) end
+ | _ =>
+ (case as_dneg lookup t of
+ NONE => (Z3_Replay_Util.compose negIffE, as_negIff lookup t)
+ | x => (Z3_Replay_Util.compose dnegE, x)))
+
+ fun join1 (s, t) =
+ (case lookup t of
+ SOME lit => (s, lit)
+ | NONE =>
+ (case lookup_rule t of
+ (rewrite, SOME lit) => (s, rewrite lit)
+ | (_, NONE) => (s, comp (pairself join1 (dest t)))))
+
+ in snd (join1 (if is_conj then (false, t) else (true, t))) end
+
+end
+
+
+(** proving equality of conjunctions or disjunctions **)
+
+fun iff_intro thm1 thm2 = thm2 COMP (thm1 COMP @{thm iffI})
+
+local
+ val cp1 = @{lemma "(~P) = (~Q) ==> P = Q" by simp}
+ val cp2 = @{lemma "(~P) = Q ==> P = (~Q)" by fastforce}
+ val cp3 = @{lemma "P = (~Q) ==> (~P) = Q" by simp}
+in
+fun contrapos1 prove (ct, cu) = prove (negate ct, negate cu) COMP cp1
+fun contrapos2 prove (ct, cu) = prove (negate ct, Thm.dest_arg cu) COMP cp2
+fun contrapos3 prove (ct, cu) = prove (Thm.dest_arg ct, negate cu) COMP cp3
+end
+
+local
+ val contra_rule = @{lemma "P ==> ~P ==> False" by (rule notE)}
+ fun contra_left conj thm =
+ let
+ val rules = explode_term conj (SMT_Util.prop_of thm)
+ fun contra_lits (t, rs) =
+ (case t of
+ @{const Not} $ u => Termtab.lookup rules u |> Option.map (pair rs)
+ | _ => NONE)
+ in
+ (case Termtab.lookup rules @{const False} of
+ SOME rs => extract_lit thm rs
+ | NONE =>
+ the (Termtab.get_first contra_lits rules)
+ |> pairself (extract_lit thm)
+ |> (fn (nlit, plit) => nlit COMP (plit COMP contra_rule)))
+ end
+
+ val falseE_v = Thm.dest_arg (Thm.dest_arg (Thm.cprop_of @{thm FalseE}))
+ fun contra_right ct = Thm.instantiate ([], [(falseE_v, ct)]) @{thm FalseE}
+in
+
+fun contradict conj ct =
+ iff_intro (Z3_Replay_Util.under_assumption (contra_left conj) ct) (contra_right ct)
+
+end
+
+local
+ fun prove_eq l r (cl, cr) =
+ let
+ fun explode' is_conj = explode is_conj true (l <> r) []
+ fun make_tab is_conj thm = make_littab (true_thm :: explode' is_conj thm)
+ fun prove is_conj ct tab = join is_conj tab (Thm.term_of ct)
+
+ val thm1 = Z3_Replay_Util.under_assumption (prove r cr o make_tab l) cl
+ val thm2 = Z3_Replay_Util.under_assumption (prove l cl o make_tab r) cr
+ in iff_intro thm1 thm2 end
+
+ datatype conj_disj = CONJ | DISJ | NCON | NDIS
+ fun kind_of t =
+ if is_conj t then SOME CONJ
+ else if is_disj t then SOME DISJ
+ else if is_neg' is_conj t then SOME NCON
+ else if is_neg' is_disj t then SOME NDIS
+ else NONE
+in
+
+fun prove_conj_disj_eq ct =
+ let val cp as (cl, cr) = Thm.dest_binop (Thm.dest_arg ct)
+ in
+ (case (kind_of (Thm.term_of cl), Thm.term_of cr) of
+ (SOME CONJ, @{const False}) => contradict true cl
+ | (SOME DISJ, @{const Not} $ @{const False}) =>
+ contrapos2 (contradict false o fst) cp
+ | (kl, _) =>
+ (case (kl, kind_of (Thm.term_of cr)) of
+ (SOME CONJ, SOME CONJ) => prove_eq true true cp
+ | (SOME CONJ, SOME NDIS) => prove_eq true false cp
+ | (SOME CONJ, _) => prove_eq true true cp
+ | (SOME DISJ, SOME DISJ) => contrapos1 (prove_eq false false) cp
+ | (SOME DISJ, SOME NCON) => contrapos2 (prove_eq false true) cp
+ | (SOME DISJ, _) => contrapos1 (prove_eq false false) cp
+ | (SOME NCON, SOME NCON) => contrapos1 (prove_eq true true) cp
+ | (SOME NCON, SOME DISJ) => contrapos3 (prove_eq true false) cp
+ | (SOME NCON, NONE) => contrapos3 (prove_eq true false) cp
+ | (SOME NDIS, SOME NDIS) => prove_eq false false cp
+ | (SOME NDIS, SOME CONJ) => prove_eq false true cp
+ | (SOME NDIS, NONE) => prove_eq false true cp
+ | _ => raise CTERM ("prove_conj_disj_eq", [ct])))
+ end
+
+end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_replay_methods.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,666 @@
+(* Title: HOL/Tools/SMT/z3_replay_methods.ML
+ Author: Sascha Boehme, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+
+Proof methods for replaying Z3 proofs.
+*)
+
+signature Z3_REPLAY_METHODS =
+sig
+ (*abstraction*)
+ type abs_context = int * term Termtab.table
+ type 'a abstracter = term -> abs_context -> 'a * abs_context
+ val add_arith_abstracter: (term abstracter -> term option abstracter) ->
+ Context.generic -> Context.generic
+
+ (*theory lemma methods*)
+ type th_lemma_method = Proof.context -> thm list -> term -> thm
+ val add_th_lemma_method: string * th_lemma_method -> Context.generic ->
+ Context.generic
+
+ (*methods for Z3 proof rules*)
+ type z3_method = Proof.context -> thm list -> term -> thm
+ val true_axiom: z3_method
+ val mp: z3_method
+ val refl: z3_method
+ val symm: z3_method
+ val trans: z3_method
+ val cong: z3_method
+ val quant_intro: z3_method
+ val distrib: z3_method
+ val and_elim: z3_method
+ val not_or_elim: z3_method
+ val rewrite: z3_method
+ val rewrite_star: z3_method
+ val pull_quant: z3_method
+ val push_quant: z3_method
+ val elim_unused: z3_method
+ val dest_eq_res: z3_method
+ val quant_inst: z3_method
+ val lemma: z3_method
+ val unit_res: z3_method
+ val iff_true: z3_method
+ val iff_false: z3_method
+ val comm: z3_method
+ val def_axiom: z3_method
+ val apply_def: z3_method
+ val iff_oeq: z3_method
+ val nnf_pos: z3_method
+ val nnf_neg: z3_method
+ val mp_oeq: z3_method
+ val th_lemma: string -> z3_method
+ val method_for: Z3_Proof.z3_rule -> z3_method
+end;
+
+structure Z3_Replay_Methods: Z3_REPLAY_METHODS =
+struct
+
+type z3_method = Proof.context -> thm list -> term -> thm
+
+
+(* utility functions *)
+
+fun trace ctxt f = SMT_Config.trace_msg ctxt f ()
+
+fun pretty_thm ctxt thm = Syntax.pretty_term ctxt (Thm.concl_of thm)
+
+fun pretty_goal ctxt msg rule thms t =
+ let
+ val full_msg = msg ^ ": " ^ quote (Z3_Proof.string_of_rule rule)
+ val assms =
+ if null thms then []
+ else [Pretty.big_list "assumptions:" (map (pretty_thm ctxt) thms)]
+ val concl = Pretty.big_list "proposition:" [Syntax.pretty_term ctxt t]
+ in Pretty.big_list full_msg (assms @ [concl]) end
+
+fun replay_error ctxt msg rule thms t = error (Pretty.string_of (pretty_goal ctxt msg rule thms t))
+
+fun replay_rule_error ctxt = replay_error ctxt "Failed to replay Z3 proof step"
+
+fun trace_goal ctxt rule thms t =
+ trace ctxt (fn () => Pretty.string_of (pretty_goal ctxt "Goal" rule thms t))
+
+fun as_prop (t as Const (@{const_name Trueprop}, _) $ _) = t
+ | as_prop t = HOLogic.mk_Trueprop t
+
+fun dest_prop (Const (@{const_name Trueprop}, _) $ t) = t
+ | dest_prop t = t
+
+fun dest_thm thm = dest_prop (Thm.concl_of thm)
+
+fun certify_prop ctxt t = SMT_Util.certify ctxt (as_prop t)
+
+fun try_provers ctxt rule [] thms t = replay_rule_error ctxt rule thms t
+ | try_provers ctxt rule ((name, prover) :: named_provers) thms t =
+ (case (trace ctxt (K ("Trying prover " ^ quote name)); try prover t) of
+ SOME thm => thm
+ | NONE => try_provers ctxt rule named_provers thms t)
+
+fun match ctxt pat t =
+ (Vartab.empty, Vartab.empty)
+ |> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, t)
+
+fun gen_certify_inst sel mk cert ctxt thm t =
+ let
+ val inst = match ctxt (dest_thm thm) (dest_prop t)
+ fun cert_inst (ix, (a, b)) = (cert (mk (ix, a)), cert b)
+ in Vartab.fold (cons o cert_inst) (sel inst) [] end
+
+fun match_instantiateT ctxt t thm =
+ if Term.exists_type (Term.exists_subtype Term.is_TVar) (dest_thm thm) then
+ let val certT = Thm.ctyp_of (Proof_Context.theory_of ctxt)
+ in Thm.instantiate (gen_certify_inst fst TVar certT ctxt thm t, []) thm end
+ else thm
+
+fun match_instantiate ctxt t thm =
+ let
+ val cert = SMT_Util.certify ctxt
+ val thm' = match_instantiateT ctxt t thm
+ in Thm.instantiate ([], gen_certify_inst snd Var cert ctxt thm' t) thm' end
+
+fun apply_rule ctxt t =
+ (case Z3_Replay_Rules.apply ctxt (certify_prop ctxt t) of
+ SOME thm => thm
+ | NONE => raise Fail "apply_rule")
+
+fun discharge _ [] thm = thm
+ | discharge i (rule :: rules) thm = discharge (i + Thm.nprems_of rule) rules (rule RSN (i, thm))
+
+fun by_tac ctxt thms ns ts t tac =
+ Goal.prove ctxt [] (map as_prop ts) (as_prop t)
+ (fn {context, prems} => HEADGOAL (tac context prems))
+ |> Drule.generalize ([], ns)
+ |> discharge 1 thms
+
+fun prove ctxt t tac = by_tac ctxt [] [] [] t (K o tac)
+
+fun prop_tac ctxt prems =
+ Method.insert_tac prems
+ THEN' SUBGOAL (fn (prop, i) =>
+ if Term.size_of_term prop > 100 then SAT.satx_tac ctxt i
+ else (Classical.fast_tac ctxt ORELSE' Clasimp.force_tac ctxt) i)
+
+fun quant_tac ctxt = Blast.blast_tac ctxt
+
+
+(* plug-ins *)
+
+type abs_context = int * term Termtab.table
+
+type 'a abstracter = term -> abs_context -> 'a * abs_context
+
+type th_lemma_method = Proof.context -> thm list -> term -> thm
+
+fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
+
+structure Plugins = Generic_Data
+(
+ type T =
+ (int * (term abstracter -> term option abstracter)) list *
+ th_lemma_method Symtab.table
+ val empty = ([], Symtab.empty)
+ val extend = I
+ fun merge ((abss1, ths1), (abss2, ths2)) = (
+ Ord_List.merge id_ord (abss1, abss2),
+ Symtab.merge (K true) (ths1, ths2))
+)
+
+fun add_arith_abstracter abs = Plugins.map (apfst (Ord_List.insert id_ord (serial (), abs)))
+fun get_arith_abstracters ctxt = map snd (fst (Plugins.get (Context.Proof ctxt)))
+
+fun add_th_lemma_method method = Plugins.map (apsnd (Symtab.update_new method))
+fun get_th_lemma_method ctxt = snd (Plugins.get (Context.Proof ctxt))
+
+
+(* abstraction *)
+
+fun prove_abstract ctxt thms t tac f =
+ let
+ val ((prems, concl), (_, ts)) = f (1, Termtab.empty)
+ val ns = Termtab.fold (fn (_, v) => cons (fst (Term.dest_Free v))) ts []
+ in
+ by_tac ctxt [] ns prems concl tac
+ |> match_instantiate ctxt t
+ |> discharge 1 thms
+ end
+
+fun prove_abstract' ctxt t tac f =
+ prove_abstract ctxt [] t tac (f #>> pair [])
+
+fun lookup_term (_, terms) t = Termtab.lookup terms t
+
+fun abstract_sub t f cx =
+ (case lookup_term cx t of
+ SOME v => (v, cx)
+ | NONE => f cx)
+
+fun mk_fresh_free t (i, terms) =
+ let val v = Free ("t" ^ string_of_int i, fastype_of t)
+ in (v, (i + 1, Termtab.update (t, v) terms)) end
+
+fun apply_abstracters _ [] _ cx = (NONE, cx)
+ | apply_abstracters abs (abstracter :: abstracters) t cx =
+ (case abstracter abs t cx of
+ (NONE, _) => apply_abstracters abs abstracters t cx
+ | x as (SOME _, _) => x)
+
+fun abstract_term (t as _ $ _) = abstract_sub t (mk_fresh_free t)
+ | abstract_term (t as Abs _) = abstract_sub t (mk_fresh_free t)
+ | abstract_term t = pair t
+
+fun abstract_bin abs f t t1 t2 = abstract_sub t (abs t1 ##>> abs t2 #>> f)
+
+fun abstract_ter abs f t t1 t2 t3 =
+ abstract_sub t (abs t1 ##>> abs t2 ##>> abs t3 #>> (Parse.triple1 #> f))
+
+fun abstract_lit (@{const HOL.Not} $ t) = abstract_term t #>> HOLogic.mk_not
+ | abstract_lit t = abstract_term t
+
+fun abstract_not abs (t as @{const HOL.Not} $ t1) =
+ abstract_sub t (abs t1 #>> HOLogic.mk_not)
+ | abstract_not _ t = abstract_lit t
+
+fun abstract_conj (t as @{const HOL.conj} $ t1 $ t2) =
+ abstract_bin abstract_conj HOLogic.mk_conj t t1 t2
+ | abstract_conj t = abstract_lit t
+
+fun abstract_disj (t as @{const HOL.disj} $ t1 $ t2) =
+ abstract_bin abstract_disj HOLogic.mk_disj t t1 t2
+ | abstract_disj t = abstract_lit t
+
+fun abstract_prop (t as (c as @{const If (bool)}) $ t1 $ t2 $ t3) =
+ abstract_ter abstract_prop (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
+ | abstract_prop (t as @{const HOL.disj} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_disj t t1 t2
+ | abstract_prop (t as @{const HOL.conj} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_conj t t1 t2
+ | abstract_prop (t as @{const HOL.implies} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_imp t t1 t2
+ | abstract_prop (t as @{term "HOL.eq :: bool => _"} $ t1 $ t2) =
+ abstract_bin abstract_prop HOLogic.mk_eq t t1 t2
+ | abstract_prop t = abstract_not abstract_prop t
+
+fun abstract_arith ctxt u =
+ let
+ fun abs (t as (c as Const _) $ Abs (s, T, t')) =
+ abstract_sub t (abs t' #>> (fn u' => c $ Abs (s, T, u')))
+ | abs (t as (c as Const (@{const_name If}, _)) $ t1 $ t2 $ t3) =
+ abstract_ter abs (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
+ | abs (t as @{const HOL.Not} $ t1) = abstract_sub t (abs t1 #>> HOLogic.mk_not)
+ | abs (t as @{const HOL.disj} $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> HOLogic.mk_disj)
+ | abs (t as (c as Const (@{const_name uminus_class.uminus}, _)) $ t1) =
+ abstract_sub t (abs t1 #>> (fn u => c $ u))
+ | abs (t as (c as Const (@{const_name plus_class.plus}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name minus_class.minus}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name times_class.times}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name z3div}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name z3mod}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name HOL.eq}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name ord_class.less}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs (t as (c as Const (@{const_name ord_class.less_eq}, _)) $ t1 $ t2) =
+ abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
+ | abs t = abstract_sub t (fn cx =>
+ if can HOLogic.dest_number t then (t, cx)
+ else
+ (case apply_abstracters abs (get_arith_abstracters ctxt) t cx of
+ (SOME u, cx') => (u, cx')
+ | (NONE, _) => abstract_term t cx))
+ in abs u end
+
+
+(* truth axiom *)
+
+fun true_axiom _ _ _ = @{thm TrueI}
+
+
+(* modus ponens *)
+
+fun mp _ [p, p_eq_q] _ = discharge 1 [p_eq_q, p] iffD1
+ | mp ctxt thms t = replay_rule_error ctxt Z3_Proof.Modus_Ponens thms t
+
+val mp_oeq = mp
+
+
+(* reflexivity *)
+
+fun refl ctxt _ t = match_instantiate ctxt t @{thm refl}
+
+
+(* symmetry *)
+
+fun symm _ [thm] _ = thm RS @{thm sym}
+ | symm ctxt thms t = replay_rule_error ctxt Z3_Proof.Reflexivity thms t
+
+
+(* transitivity *)
+
+fun trans _ [thm1, thm2] _ = thm1 RSN (1, thm2 RSN (2, @{thm trans}))
+ | trans ctxt thms t = replay_rule_error ctxt Z3_Proof.Transitivity thms t
+
+
+(* congruence *)
+
+fun ctac prems i st = st |> (
+ resolve_tac (@{thm refl} :: prems) i
+ ORELSE (cong_tac i THEN ctac prems (i + 1) THEN ctac prems i))
+
+fun cong_basic ctxt thms t =
+ let val st = Thm.trivial (certify_prop ctxt t)
+ in
+ (case Seq.pull (ctac thms 1 st) of
+ SOME (thm, _) => thm
+ | NONE => raise THM ("cong", 0, thms @ [st]))
+ end
+
+val cong_dest_rules = @{lemma
+ "(~ P | Q) & (P | ~ Q) ==> P = Q"
+ "(P | ~ Q) & (~ P | Q) ==> P = Q"
+ by fast+}
+
+fun cong_full ctxt thms t = prove ctxt t (fn ctxt' =>
+ Method.insert_tac thms
+ THEN' (Classical.fast_tac ctxt'
+ ORELSE' dresolve_tac cong_dest_rules
+ THEN' Classical.fast_tac ctxt'))
+
+fun cong ctxt thms = try_provers ctxt Z3_Proof.Monotonicity [
+ ("basic", cong_basic ctxt thms),
+ ("full", cong_full ctxt thms)] thms
+
+
+(* quantifier introduction *)
+
+val quant_intro_rules = @{lemma
+ "(!!x. P x = Q x) ==> (ALL x. P x) = (ALL x. Q x)"
+ "(!!x. P x = Q x) ==> (EX x. P x) = (EX x. Q x)"
+ "(!!x. (~ P x) = Q x) ==> (~ (EX x. P x)) = (ALL x. Q x)"
+ "(!!x. (~ P x) = Q x) ==> (~ (ALL x. P x)) = (EX x. Q x)"
+ by fast+}
+
+fun quant_intro ctxt [thm] t =
+ prove ctxt t (K (REPEAT_ALL_NEW (resolve_tac (thm :: quant_intro_rules))))
+ | quant_intro ctxt thms t = replay_rule_error ctxt Z3_Proof.Quant_Intro thms t
+
+
+(* distributivity of conjunctions and disjunctions *)
+
+(* TODO: there are no tests with this proof rule *)
+fun distrib ctxt _ t =
+ prove_abstract' ctxt t prop_tac (abstract_prop (dest_prop t))
+
+
+(* elimination of conjunctions *)
+
+fun and_elim ctxt [thm] t =
+ prove_abstract ctxt [thm] t prop_tac (
+ abstract_lit (dest_prop t) ##>>
+ abstract_conj (dest_thm thm) #>>
+ apfst single o swap)
+ | and_elim ctxt thms t = replay_rule_error ctxt Z3_Proof.And_Elim thms t
+
+
+(* elimination of negated disjunctions *)
+
+fun not_or_elim ctxt [thm] t =
+ prove_abstract ctxt [thm] t prop_tac (
+ abstract_lit (dest_prop t) ##>>
+ abstract_not abstract_disj (dest_thm thm) #>>
+ apfst single o swap)
+ | not_or_elim ctxt thms t =
+ replay_rule_error ctxt Z3_Proof.Not_Or_Elim thms t
+
+
+(* rewriting *)
+
+local
+
+fun dest_all (Const (@{const_name HOL.All}, _) $ Abs (_, T, t)) nctxt =
+ let
+ val (n, nctxt') = Name.variant "" nctxt
+ val f = Free (n, T)
+ val t' = Term.subst_bound (f, t)
+ in dest_all t' nctxt' |>> cons f end
+ | dest_all t _ = ([], t)
+
+fun dest_alls t =
+ let
+ val nctxt = Name.make_context (Term.add_free_names t [])
+ val (lhs, rhs) = HOLogic.dest_eq (dest_prop t)
+ val (ls, lhs') = dest_all lhs nctxt
+ val (rs, rhs') = dest_all rhs nctxt
+ in
+ if eq_list (op aconv) (ls, rs) then SOME (ls, (HOLogic.mk_eq (lhs', rhs')))
+ else NONE
+ end
+
+fun forall_intr ctxt t thm =
+ let val ct = Thm.cterm_of (Proof_Context.theory_of ctxt) t
+ in Thm.forall_intr ct thm COMP_INCR @{thm iff_allI} end
+
+in
+
+fun focus_eq f ctxt t =
+ (case dest_alls t of
+ NONE => f ctxt t
+ | SOME (vs, t') => fold (forall_intr ctxt) vs (f ctxt t'))
+
+end
+
+fun abstract_eq f (Const (@{const_name HOL.eq}, _) $ t1 $ t2) =
+ f t1 ##>> f t2 #>> HOLogic.mk_eq
+ | abstract_eq _ t = abstract_term t
+
+fun prove_prop_rewrite ctxt t =
+ prove_abstract' ctxt t prop_tac (
+ abstract_eq abstract_prop (dest_prop t))
+
+fun arith_rewrite_tac ctxt _ =
+ TRY o Simplifier.simp_tac ctxt
+ THEN_ALL_NEW (Arith_Data.arith_tac ctxt ORELSE' Clasimp.force_tac ctxt)
+
+fun prove_arith_rewrite ctxt t =
+ prove_abstract' ctxt t arith_rewrite_tac (
+ abstract_eq (abstract_arith ctxt) (dest_prop t))
+
+fun rewrite ctxt _ = try_provers ctxt Z3_Proof.Rewrite [
+ ("rules", apply_rule ctxt),
+ ("prop_rewrite", prove_prop_rewrite ctxt),
+ ("arith_rewrite", focus_eq prove_arith_rewrite ctxt)] []
+
+fun rewrite_star ctxt = rewrite ctxt
+
+
+(* pulling quantifiers *)
+
+fun pull_quant ctxt _ t = prove ctxt t quant_tac
+
+
+(* pushing quantifiers *)
+
+fun push_quant _ _ _ = raise Fail "unsupported" (* FIXME *)
+
+
+(* elimination of unused bound variables *)
+
+val elim_all = @{lemma "P = Q ==> (ALL x. P) = Q" by fast}
+val elim_ex = @{lemma "P = Q ==> (EX x. P) = Q" by fast}
+
+fun elim_unused_tac i st = (
+ match_tac [@{thm refl}]
+ ORELSE' (match_tac [elim_all, elim_ex] THEN' elim_unused_tac)
+ ORELSE' (
+ match_tac [@{thm iff_allI}, @{thm iff_exI}]
+ THEN' elim_unused_tac)) i st
+
+fun elim_unused ctxt _ t = prove ctxt t (fn _ => elim_unused_tac)
+
+
+(* destructive equality resolution *)
+
+fun dest_eq_res _ _ _ = raise Fail "dest_eq_res" (* FIXME *)
+
+
+(* quantifier instantiation *)
+
+val quant_inst_rule = @{lemma "~P x | Q ==> ~(ALL x. P x) | Q" by fast}
+
+fun quant_inst ctxt _ t = prove ctxt t (fn _ =>
+ REPEAT_ALL_NEW (rtac quant_inst_rule)
+ THEN' rtac @{thm excluded_middle})
+
+
+(* propositional lemma *)
+
+exception LEMMA of unit
+
+val intro_hyp_rule1 = @{lemma "(~P ==> Q) ==> P | Q" by fast}
+val intro_hyp_rule2 = @{lemma "(P ==> Q) ==> ~P | Q" by fast}
+
+fun norm_lemma thm =
+ (thm COMP_INCR intro_hyp_rule1)
+ handle THM _ => thm COMP_INCR intro_hyp_rule2
+
+fun negated_prop (@{const HOL.Not} $ t) = HOLogic.mk_Trueprop t
+ | negated_prop t = HOLogic.mk_Trueprop (HOLogic.mk_not t)
+
+fun intro_hyps tab (t as @{const HOL.disj} $ t1 $ t2) cx =
+ lookup_intro_hyps tab t (fold (intro_hyps tab) [t1, t2]) cx
+ | intro_hyps tab t cx =
+ lookup_intro_hyps tab t (fn _ => raise LEMMA ()) cx
+
+and lookup_intro_hyps tab t f (cx as (thm, terms)) =
+ (case Termtab.lookup tab (negated_prop t) of
+ NONE => f cx
+ | SOME hyp => (norm_lemma (Thm.implies_intr hyp thm), t :: terms))
+
+fun lemma ctxt (thms as [thm]) t =
+ (let
+ val tab = Termtab.make (map (`Thm.term_of) (#hyps (Thm.crep_thm thm)))
+ val (thm', terms) = intro_hyps tab (dest_prop t) (thm, [])
+ in
+ prove_abstract ctxt [thm'] t prop_tac (
+ fold (snd oo abstract_lit) terms #>
+ abstract_disj (dest_thm thm') #>> single ##>>
+ abstract_disj (dest_prop t))
+ end
+ handle LEMMA () => replay_error ctxt "Bad proof state" Z3_Proof.Lemma thms t)
+ | lemma ctxt thms t = replay_rule_error ctxt Z3_Proof.Lemma thms t
+
+
+(* unit resolution *)
+
+fun abstract_unit (t as (@{const HOL.Not} $ (@{const HOL.disj} $ t1 $ t2))) =
+ abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
+ HOLogic.mk_not o HOLogic.mk_disj)
+ | abstract_unit (t as (@{const HOL.disj} $ t1 $ t2)) =
+ abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
+ HOLogic.mk_disj)
+ | abstract_unit t = abstract_lit t
+
+fun unit_res ctxt thms t =
+ prove_abstract ctxt thms t prop_tac (
+ fold_map (abstract_unit o dest_thm) thms ##>>
+ abstract_unit (dest_prop t) #>>
+ (fn (prems, concl) => (prems, concl)))
+
+
+(* iff-true *)
+
+val iff_true_rule = @{lemma "P ==> P = True" by fast}
+
+fun iff_true _ [thm] _ = thm RS iff_true_rule
+ | iff_true ctxt thms t = replay_rule_error ctxt Z3_Proof.Iff_True thms t
+
+
+(* iff-false *)
+
+val iff_false_rule = @{lemma "~P ==> P = False" by fast}
+
+fun iff_false _ [thm] _ = thm RS iff_false_rule
+ | iff_false ctxt thms t = replay_rule_error ctxt Z3_Proof.Iff_False thms t
+
+
+(* commutativity *)
+
+fun comm ctxt _ t = match_instantiate ctxt t @{thm eq_commute}
+
+
+(* definitional axioms *)
+
+fun def_axiom_disj ctxt t =
+ (case dest_prop t of
+ @{const HOL.disj} $ u1 $ u2 =>
+ prove_abstract' ctxt t prop_tac (
+ abstract_prop u2 ##>> abstract_prop u1 #>> HOLogic.mk_disj o swap)
+ | u => prove_abstract' ctxt t prop_tac (abstract_prop u))
+
+fun def_axiom ctxt _ = try_provers ctxt Z3_Proof.Def_Axiom [
+ ("rules", apply_rule ctxt),
+ ("disj", def_axiom_disj ctxt)] []
+
+
+(* application of definitions *)
+
+fun apply_def _ [thm] _ = thm (* TODO: cover also the missing cases *)
+ | apply_def ctxt thms t = replay_rule_error ctxt Z3_Proof.Apply_Def thms t
+
+
+(* iff-oeq *)
+
+fun iff_oeq _ _ _ = raise Fail "iff_oeq" (* FIXME *)
+
+
+(* negation normal form *)
+
+fun nnf_prop ctxt thms t =
+ prove_abstract ctxt thms t prop_tac (
+ fold_map (abstract_prop o dest_thm) thms ##>>
+ abstract_prop (dest_prop t))
+
+fun nnf ctxt rule thms = try_provers ctxt rule [
+ ("prop", nnf_prop ctxt thms),
+ ("quant", quant_intro ctxt [hd thms])] thms
+
+fun nnf_pos ctxt = nnf ctxt Z3_Proof.Nnf_Pos
+fun nnf_neg ctxt = nnf ctxt Z3_Proof.Nnf_Neg
+
+
+(* theory lemmas *)
+
+fun arith_th_lemma_tac ctxt prems =
+ Method.insert_tac prems
+ THEN' SELECT_GOAL (Local_Defs.unfold_tac ctxt @{thms z3div_def z3mod_def})
+ THEN' Arith_Data.arith_tac ctxt
+
+fun arith_th_lemma ctxt thms t =
+ prove_abstract ctxt thms t arith_th_lemma_tac (
+ fold_map (abstract_arith ctxt o dest_thm) thms ##>>
+ abstract_arith ctxt (dest_prop t))
+
+val _ = Theory.setup (Context.theory_map (add_th_lemma_method ("arith", arith_th_lemma)))
+
+fun th_lemma name ctxt thms =
+ (case Symtab.lookup (get_th_lemma_method ctxt) name of
+ SOME method => method ctxt thms
+ | NONE => replay_error ctxt "Bad theory" (Z3_Proof.Th_Lemma name) thms)
+
+
+(* mapping of rules to methods *)
+
+fun unsupported rule ctxt = replay_error ctxt "Unsupported" rule
+fun assumed rule ctxt = replay_error ctxt "Assumed" rule
+
+fun choose Z3_Proof.True_Axiom = true_axiom
+ | choose (r as Z3_Proof.Asserted) = assumed r
+ | choose (r as Z3_Proof.Goal) = assumed r
+ | choose Z3_Proof.Modus_Ponens = mp
+ | choose Z3_Proof.Reflexivity = refl
+ | choose Z3_Proof.Symmetry = symm
+ | choose Z3_Proof.Transitivity = trans
+ | choose (r as Z3_Proof.Transitivity_Star) = unsupported r
+ | choose Z3_Proof.Monotonicity = cong
+ | choose Z3_Proof.Quant_Intro = quant_intro
+ | choose Z3_Proof.Distributivity = distrib
+ | choose Z3_Proof.And_Elim = and_elim
+ | choose Z3_Proof.Not_Or_Elim = not_or_elim
+ | choose Z3_Proof.Rewrite = rewrite
+ | choose Z3_Proof.Rewrite_Star = rewrite_star
+ | choose Z3_Proof.Pull_Quant = pull_quant
+ | choose (r as Z3_Proof.Pull_Quant_Star) = unsupported r
+ | choose Z3_Proof.Push_Quant = push_quant
+ | choose Z3_Proof.Elim_Unused_Vars = elim_unused
+ | choose Z3_Proof.Dest_Eq_Res = dest_eq_res
+ | choose Z3_Proof.Quant_Inst = quant_inst
+ | choose (r as Z3_Proof.Hypothesis) = assumed r
+ | choose Z3_Proof.Lemma = lemma
+ | choose Z3_Proof.Unit_Resolution = unit_res
+ | choose Z3_Proof.Iff_True = iff_true
+ | choose Z3_Proof.Iff_False = iff_false
+ | choose Z3_Proof.Commutativity = comm
+ | choose Z3_Proof.Def_Axiom = def_axiom
+ | choose (r as Z3_Proof.Intro_Def) = assumed r
+ | choose Z3_Proof.Apply_Def = apply_def
+ | choose Z3_Proof.Iff_Oeq = iff_oeq
+ | choose Z3_Proof.Nnf_Pos = nnf_pos
+ | choose Z3_Proof.Nnf_Neg = nnf_neg
+ | choose (r as Z3_Proof.Nnf_Star) = unsupported r
+ | choose (r as Z3_Proof.Cnf_Star) = unsupported r
+ | choose (r as Z3_Proof.Skolemize) = assumed r
+ | choose Z3_Proof.Modus_Ponens_Oeq = mp_oeq
+ | choose (Z3_Proof.Th_Lemma name) = th_lemma name
+
+fun with_tracing rule method ctxt thms t =
+ let val _ = trace_goal ctxt rule thms t
+ in method ctxt thms t end
+
+fun method_for rule = with_tracing rule (choose rule)
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_replay_rules.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,54 @@
+(* Title: HOL/Tools/SMT/z3_replay_rules.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Custom rules for Z3 proof replay.
+*)
+
+signature Z3_REPLAY_RULES =
+sig
+ val apply: Proof.context -> cterm -> thm option
+end;
+
+structure Z3_Replay_Rules: Z3_REPLAY_RULES =
+struct
+
+structure Data = Generic_Data
+(
+ type T = thm Net.net
+ val empty = Net.empty
+ val extend = I
+ val merge = Net.merge Thm.eq_thm
+)
+
+fun maybe_instantiate ct thm =
+ try Thm.first_order_match (Thm.cprop_of thm, ct)
+ |> Option.map (fn inst => Thm.instantiate inst thm)
+
+fun apply ctxt ct =
+ let
+ val net = Data.get (Context.Proof ctxt)
+ val xthms = Net.match_term net (Thm.term_of ct)
+
+ fun select ct = map_filter (maybe_instantiate ct) xthms
+ fun select' ct =
+ let val thm = Thm.trivial ct
+ in map_filter (try (fn rule => rule COMP thm)) xthms end
+
+ in try hd (case select ct of [] => select' ct | xthms' => xthms') end
+
+val prep = `Thm.prop_of
+
+fun ins thm net = Net.insert_term Thm.eq_thm (prep thm) net handle Net.INSERT => net
+fun del thm net = Net.delete_term Thm.eq_thm (prep thm) net handle Net.DELETE => net
+
+val add = Thm.declaration_attribute (Data.map o ins)
+val del = Thm.declaration_attribute (Data.map o del)
+
+val name = Binding.name "z3_rule"
+
+val description = "declaration of Z3 proof rules"
+
+val _ = Theory.setup (Attrib.setup name (Attrib.add_del add del) description #>
+ Global_Theory.add_thms_dynamic (name, Net.content o Data.get))
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/SMT/z3_replay_util.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,150 @@
+(* Title: HOL/Tools/SMT/z3_replay_util.ML
+ Author: Sascha Boehme, TU Muenchen
+
+Helper functions required for Z3 proof replay.
+*)
+
+signature Z3_REPLAY_UTIL =
+sig
+ (*theorem nets*)
+ val thm_net_of: ('a -> thm) -> 'a list -> 'a Net.net
+ val net_instances: (int * thm) Net.net -> cterm -> (int * thm) list
+
+ (*proof combinators*)
+ val under_assumption: (thm -> thm) -> cterm -> thm
+ val discharge: thm -> thm -> thm
+
+ (*a faster COMP*)
+ type compose_data
+ val precompose: (cterm -> cterm list) -> thm -> compose_data
+ val precompose2: (cterm -> cterm * cterm) -> thm -> compose_data
+ val compose: compose_data -> thm -> thm
+
+ (*simpset*)
+ val add_simproc: Simplifier.simproc -> Context.generic -> Context.generic
+ val make_simpset: Proof.context -> thm list -> simpset
+end;
+
+structure Z3_Replay_Util: Z3_REPLAY_UTIL =
+struct
+
+(* theorem nets *)
+
+fun thm_net_of f xthms =
+ let fun insert xthm = Net.insert_term (K false) (Thm.prop_of (f xthm), xthm)
+ in fold insert xthms Net.empty end
+
+fun maybe_instantiate ct thm =
+ try Thm.first_order_match (Thm.cprop_of thm, ct)
+ |> Option.map (fn inst => Thm.instantiate inst thm)
+
+local
+ fun instances_from_net match f net ct =
+ let
+ val lookup = if match then Net.match_term else Net.unify_term
+ val xthms = lookup net (Thm.term_of ct)
+ fun select ct = map_filter (f (maybe_instantiate ct)) xthms
+ fun select' ct =
+ let val thm = Thm.trivial ct
+ in map_filter (f (try (fn rule => rule COMP thm))) xthms end
+ in (case select ct of [] => select' ct | xthms' => xthms') end
+in
+
+fun net_instances net =
+ instances_from_net false (fn f => fn (i, thm) => Option.map (pair i) (f thm))
+ net
+
+end
+
+
+(* proof combinators *)
+
+fun under_assumption f ct =
+ let val ct' = SMT_Util.mk_cprop ct in Thm.implies_intr ct' (f (Thm.assume ct')) end
+
+fun discharge p pq = Thm.implies_elim pq p
+
+
+(* a faster COMP *)
+
+type compose_data = cterm list * (cterm -> cterm list) * thm
+
+fun list2 (x, y) = [x, y]
+
+fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule)
+fun precompose2 f rule = precompose (list2 o f) rule
+
+fun compose (cvs, f, rule) thm =
+ discharge thm (Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm)) rule)
+
+
+(* simpset *)
+
+local
+ val antisym_le1 = mk_meta_eq @{thm order_class.antisym_conv}
+ val antisym_le2 = mk_meta_eq @{thm linorder_class.antisym_conv2}
+ val antisym_less1 = mk_meta_eq @{thm linorder_class.antisym_conv1}
+ val antisym_less2 = mk_meta_eq @{thm linorder_class.antisym_conv3}
+
+ fun eq_prop t thm = HOLogic.mk_Trueprop t aconv Thm.prop_of thm
+ fun dest_binop ((c as Const _) $ t $ u) = (c, t, u)
+ | dest_binop t = raise TERM ("dest_binop", [t])
+
+ fun prove_antisym_le ctxt t =
+ let
+ val (le, r, s) = dest_binop t
+ val less = Const (@{const_name less}, Term.fastype_of le)
+ val prems = Simplifier.prems_of ctxt
+ in
+ (case find_first (eq_prop (le $ s $ r)) prems of
+ NONE =>
+ find_first (eq_prop (HOLogic.mk_not (less $ r $ s))) prems
+ |> Option.map (fn thm => thm RS antisym_less1)
+ | SOME thm => SOME (thm RS antisym_le1))
+ end
+ handle THM _ => NONE
+
+ fun prove_antisym_less ctxt t =
+ let
+ val (less, r, s) = dest_binop (HOLogic.dest_not t)
+ val le = Const (@{const_name less_eq}, Term.fastype_of less)
+ val prems = Simplifier.prems_of ctxt
+ in
+ (case find_first (eq_prop (le $ r $ s)) prems of
+ NONE =>
+ find_first (eq_prop (HOLogic.mk_not (less $ s $ r))) prems
+ |> Option.map (fn thm => thm RS antisym_less2)
+ | SOME thm => SOME (thm RS antisym_le2))
+ end
+ handle THM _ => NONE
+
+ val basic_simpset =
+ simpset_of (put_simpset HOL_ss @{context}
+ addsimps @{thms field_simps times_divide_eq_right times_divide_eq_left arith_special
+ arith_simps rel_simps array_rules z3div_def z3mod_def}
+ addsimprocs [@{simproc binary_int_div}, @{simproc binary_int_mod},
+ Simplifier.simproc_global @{theory} "fast_int_arith" [
+ "(m::int) < n", "(m::int) <= n", "(m::int) = n"] Lin_Arith.simproc,
+ Simplifier.simproc_global @{theory} "antisym_le" ["(x::'a::order) <= y"] prove_antisym_le,
+ Simplifier.simproc_global @{theory} "antisym_less" ["~ (x::'a::linorder) < y"]
+ prove_antisym_less])
+
+ structure Simpset = Generic_Data
+ (
+ type T = simpset
+ val empty = basic_simpset
+ val extend = I
+ val merge = Simplifier.merge_ss
+ )
+in
+
+fun add_simproc simproc context =
+ Simpset.map (simpset_map (Context.proof_of context)
+ (fn ctxt => ctxt addsimprocs [simproc])) context
+
+fun make_simpset ctxt rules =
+ simpset_of (put_simpset (Simpset.get (Context.Proof ctxt)) ctxt addsimps rules)
+
+end
+
+end;
--- a/src/HOL/Tools/SMT2/smt2_builtin.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,222 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_builtin.ML
- Author: Sascha Boehme, TU Muenchen
-
-Tables of types and terms directly supported by SMT solvers.
-*)
-
-signature SMT2_BUILTIN =
-sig
- (*for experiments*)
- val filter_builtins: (typ -> bool) -> Proof.context -> Proof.context
-
- (*built-in types*)
- val add_builtin_typ: SMT2_Util.class ->
- typ * (typ -> string option) * (typ -> int -> string option) -> Context.generic ->
- Context.generic
- val add_builtin_typ_ext: typ * (typ -> bool) -> Context.generic ->
- Context.generic
- val dest_builtin_typ: Proof.context -> typ -> string option
- val is_builtin_typ_ext: Proof.context -> typ -> bool
-
- (*built-in numbers*)
- val dest_builtin_num: Proof.context -> term -> (string * typ) option
- val is_builtin_num: Proof.context -> term -> bool
- val is_builtin_num_ext: Proof.context -> term -> bool
-
- (*built-in functions*)
- type 'a bfun = Proof.context -> typ -> term list -> 'a
- type bfunr = string * int * term list * (term list -> term)
- val add_builtin_fun: SMT2_Util.class -> (string * typ) * bfunr option bfun -> Context.generic ->
- Context.generic
- val add_builtin_fun': SMT2_Util.class -> term * string -> Context.generic -> Context.generic
- val add_builtin_fun_ext: (string * typ) * term list bfun -> Context.generic -> Context.generic
- val add_builtin_fun_ext': string * typ -> Context.generic -> Context.generic
- val add_builtin_fun_ext'': string -> Context.generic -> Context.generic
- val dest_builtin_fun: Proof.context -> string * typ -> term list -> bfunr option
- val dest_builtin_eq: Proof.context -> term -> term -> bfunr option
- val dest_builtin_pred: Proof.context -> string * typ -> term list -> bfunr option
- val dest_builtin_conn: Proof.context -> string * typ -> term list -> bfunr option
- val dest_builtin: Proof.context -> string * typ -> term list -> bfunr option
- val dest_builtin_ext: Proof.context -> string * typ -> term list -> term list option
- val is_builtin_fun: Proof.context -> string * typ -> term list -> bool
- val is_builtin_fun_ext: Proof.context -> string * typ -> term list -> bool
-end;
-
-structure SMT2_Builtin: SMT2_BUILTIN =
-struct
-
-
-(* built-in tables *)
-
-datatype ('a, 'b) kind = Ext of 'a | Int of 'b
-
-type ('a, 'b) ttab = ((typ * ('a, 'b) kind) Ord_List.T) SMT2_Util.dict
-
-fun typ_ord ((T, _), (U, _)) =
- let
- fun tord (TVar _, Type _) = GREATER
- | tord (Type _, TVar _) = LESS
- | tord (Type (n, Ts), Type (m, Us)) =
- if n = m then list_ord tord (Ts, Us)
- else Term_Ord.typ_ord (T, U)
- | tord TU = Term_Ord.typ_ord TU
- in tord (T, U) end
-
-fun insert_ttab cs T f =
- SMT2_Util.dict_map_default (cs, [])
- (Ord_List.insert typ_ord (perhaps (try Logic.varifyT_global) T, f))
-
-fun merge_ttab ttabp = SMT2_Util.dict_merge (Ord_List.merge typ_ord) ttabp
-
-fun lookup_ttab ctxt ttab T =
- let fun match (U, _) = Sign.typ_instance (Proof_Context.theory_of ctxt) (T, U)
- in
- get_first (find_first match) (SMT2_Util.dict_lookup ttab (SMT2_Config.solver_class_of ctxt))
- end
-
-type ('a, 'b) btab = ('a, 'b) ttab Symtab.table
-
-fun insert_btab cs n T f =
- Symtab.map_default (n, []) (insert_ttab cs T f)
-
-fun merge_btab btabp = Symtab.join (K merge_ttab) btabp
-
-fun lookup_btab ctxt btab (n, T) =
- (case Symtab.lookup btab n of
- NONE => NONE
- | SOME ttab => lookup_ttab ctxt ttab T)
-
-type 'a bfun = Proof.context -> typ -> term list -> 'a
-
-type bfunr = string * int * term list * (term list -> term)
-
-structure Builtins = Generic_Data
-(
- type T =
- (typ -> bool, (typ -> string option) * (typ -> int -> string option)) ttab *
- (term list bfun, bfunr option bfun) btab
- val empty = ([], Symtab.empty)
- val extend = I
- fun merge ((t1, b1), (t2, b2)) = (merge_ttab (t1, t2), merge_btab (b1, b2))
-)
-
-fun filter_ttab keep_T = map (apsnd (filter (keep_T o fst)))
-
-fun filter_builtins keep_T =
- Context.proof_map (Builtins.map (fn (ttab, btab) =>
- (filter_ttab keep_T ttab, Symtab.map (K (filter_ttab keep_T)) btab)))
-
-
-(* built-in types *)
-
-fun add_builtin_typ cs (T, f, g) =
- Builtins.map (apfst (insert_ttab cs T (Int (f, g))))
-
-fun add_builtin_typ_ext (T, f) = Builtins.map (apfst (insert_ttab SMT2_Util.basicC T (Ext f)))
-
-fun lookup_builtin_typ ctxt =
- lookup_ttab ctxt (fst (Builtins.get (Context.Proof ctxt)))
-
-fun dest_builtin_typ ctxt T =
- (case lookup_builtin_typ ctxt T of
- SOME (_, Int (f, _)) => f T
- | _ => NONE)
-
-fun is_builtin_typ_ext ctxt T =
- (case lookup_builtin_typ ctxt T of
- SOME (_, Int (f, _)) => is_some (f T)
- | SOME (_, Ext f) => f T
- | NONE => false)
-
-
-(* built-in numbers *)
-
-fun dest_builtin_num ctxt t =
- (case try HOLogic.dest_number t of
- NONE => NONE
- | SOME (T, i) =>
- if i < 0 then NONE else
- (case lookup_builtin_typ ctxt T of
- SOME (_, Int (_, g)) => g T i |> Option.map (rpair T)
- | _ => NONE))
-
-val is_builtin_num = is_some oo dest_builtin_num
-
-fun is_builtin_num_ext ctxt t =
- (case try HOLogic.dest_number t of
- NONE => false
- | SOME (T, _) => is_builtin_typ_ext ctxt T)
-
-
-(* built-in functions *)
-
-fun add_builtin_fun cs ((n, T), f) =
- Builtins.map (apsnd (insert_btab cs n T (Int f)))
-
-fun add_builtin_fun' cs (t, n) =
- let
- val c as (m, T) = Term.dest_Const t
- fun app U ts = Term.list_comb (Const (m, U), ts)
- fun bfun _ U ts = SOME (n, length (Term.binder_types T), ts, app U)
- in add_builtin_fun cs (c, bfun) end
-
-fun add_builtin_fun_ext ((n, T), f) =
- Builtins.map (apsnd (insert_btab SMT2_Util.basicC n T (Ext f)))
-
-fun add_builtin_fun_ext' c = add_builtin_fun_ext (c, fn _ => fn _ => I)
-
-fun add_builtin_fun_ext'' n context =
- let val thy = Context.theory_of context
- in add_builtin_fun_ext' (n, Sign.the_const_type thy n) context end
-
-fun lookup_builtin_fun ctxt =
- lookup_btab ctxt (snd (Builtins.get (Context.Proof ctxt)))
-
-fun dest_builtin_fun ctxt (c as (_, T)) ts =
- (case lookup_builtin_fun ctxt c of
- SOME (_, Int f) => f ctxt T ts
- | _ => NONE)
-
-fun dest_builtin_eq ctxt t u =
- let
- val aT = TFree (Name.aT, @{sort type})
- val c = (@{const_name HOL.eq}, aT --> aT --> @{typ bool})
- fun mk ts = Term.list_comb (HOLogic.eq_const (Term.fastype_of (hd ts)), ts)
- in
- dest_builtin_fun ctxt c []
- |> Option.map (fn (n, i, _, _) => (n, i, [t, u], mk))
- end
-
-fun special_builtin_fun pred ctxt (c as (_, T)) ts =
- if pred (Term.body_type T, Term.binder_types T) then
- dest_builtin_fun ctxt c ts
- else NONE
-
-fun dest_builtin_pred ctxt = special_builtin_fun (equal @{typ bool} o fst) ctxt
-
-fun dest_builtin_conn ctxt =
- special_builtin_fun (forall (equal @{typ bool}) o (op ::)) ctxt
-
-fun dest_builtin ctxt c ts =
- let val t = Term.list_comb (Const c, ts)
- in
- (case dest_builtin_num ctxt t of
- SOME (n, _) => SOME (n, 0, [], K t)
- | NONE => dest_builtin_fun ctxt c ts)
- end
-
-fun dest_builtin_fun_ext ctxt (c as (_, T)) ts =
- (case lookup_builtin_fun ctxt c of
- SOME (_, Int f) => f ctxt T ts |> Option.map (fn (_, _, us, _) => us)
- | SOME (_, Ext f) => SOME (f ctxt T ts)
- | NONE => NONE)
-
-fun dest_builtin_ext ctxt c ts =
- if is_builtin_num_ext ctxt (Term.list_comb (Const c, ts)) then SOME []
- else dest_builtin_fun_ext ctxt c ts
-
-fun is_builtin_fun ctxt c ts = is_some (dest_builtin_fun ctxt c ts)
-
-fun is_builtin_fun_ext ctxt c ts = is_some (dest_builtin_fun_ext ctxt c ts)
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_config.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,249 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_config.ML
- Author: Sascha Boehme, TU Muenchen
-
-Configuration options and diagnostic tools for SMT.
-*)
-
-signature SMT2_CONFIG =
-sig
- (*solver*)
- type solver_info = {
- name: string,
- class: Proof.context -> SMT2_Util.class,
- avail: unit -> bool,
- options: Proof.context -> string list }
- val add_solver: solver_info -> Context.generic -> Context.generic
- val set_solver_options: string * string -> Context.generic -> Context.generic
- val is_available: Proof.context -> string -> bool
- val available_solvers_of: Proof.context -> string list
- val select_solver: string -> Context.generic -> Context.generic
- val solver_of: Proof.context -> string
- val solver_class_of: Proof.context -> SMT2_Util.class
- val solver_options_of: Proof.context -> string list
-
- (*options*)
- val oracle: bool Config.T
- val timeout: real Config.T
- val random_seed: int Config.T
- val read_only_certificates: bool Config.T
- val verbose: bool Config.T
- val trace: bool Config.T
- val monomorph_limit: int Config.T
- val monomorph_instances: int Config.T
- val infer_triggers: bool Config.T
- val debug_files: string Config.T
- val sat_solver: string Config.T
-
- (*tools*)
- val with_timeout: Proof.context -> ('a -> 'b) -> 'a -> 'b
-
- (*diagnostics*)
- val trace_msg: Proof.context -> ('a -> string) -> 'a -> unit
- val verbose_msg: Proof.context -> ('a -> string) -> 'a -> unit
-
- (*certificates*)
- val select_certificates: string -> Context.generic -> Context.generic
- val certificates_of: Proof.context -> Cache_IO.cache option
-
- (*setup*)
- val print_setup: Proof.context -> unit
-end;
-
-structure SMT2_Config: SMT2_CONFIG =
-struct
-
-(* solver *)
-
-type solver_info = {
- name: string,
- class: Proof.context -> SMT2_Util.class,
- avail: unit -> bool,
- options: Proof.context -> string list}
-
-(* FIXME just one data slot (record) per program unit *)
-structure Solvers = Generic_Data
-(
- type T = (solver_info * string list) Symtab.table * string option
- val empty = (Symtab.empty, NONE)
- val extend = I
- fun merge ((ss1, s1), (ss2, s2)) =
- (Symtab.merge (K true) (ss1, ss2), merge_options (s1, s2))
-)
-
-fun set_solver_options (name, options) =
- let val opts = String.tokens (Symbol.is_ascii_blank o str) options
- in Solvers.map (apfst (Symtab.map_entry name (apsnd (K opts)))) end
-
-fun add_solver (info as {name, ...} : solver_info) context =
- if Symtab.defined (fst (Solvers.get context)) name then
- error ("Solver already registered: " ^ quote name)
- else
- context
- |> Solvers.map (apfst (Symtab.update (name, (info, []))))
- |> Context.map_theory (Attrib.setup (Binding.name (name ^ "_new_options"))
- (Scan.lift (@{keyword "="} |-- Args.name) >>
- (Thm.declaration_attribute o K o set_solver_options o pair name))
- ("Additional command line options for SMT solver " ^ quote name))
-
-fun all_solvers_of ctxt = Symtab.keys (fst (Solvers.get (Context.Proof ctxt)))
-
-fun solver_name_of ctxt = snd (Solvers.get (Context.Proof ctxt))
-
-fun is_available ctxt name =
- (case Symtab.lookup (fst (Solvers.get (Context.Proof ctxt))) name of
- SOME ({avail, ...}, _) => avail ()
- | NONE => false)
-
-fun available_solvers_of ctxt =
- filter (is_available ctxt) (all_solvers_of ctxt)
-
-fun warn_solver (Context.Proof ctxt) name =
- if Context_Position.is_visible ctxt then
- warning ("The SMT solver " ^ quote name ^ " is not installed")
- else ()
- | warn_solver _ _ = ()
-
-fun select_solver name context =
- let
- val ctxt = Context.proof_of context
- val upd = Solvers.map (apsnd (K (SOME name)))
- in
- if not (member (op =) (all_solvers_of ctxt) name) then
- error ("Trying to select unknown solver: " ^ quote name)
- else if not (is_available ctxt name) then
- (warn_solver context name; upd context)
- else upd context
- end
-
-fun no_solver_err () = error "No SMT solver selected"
-
-fun solver_of ctxt =
- (case solver_name_of ctxt of
- SOME name => name
- | NONE => no_solver_err ())
-
-fun solver_info_of default select ctxt =
- (case Solvers.get (Context.Proof ctxt) of
- (solvers, SOME name) => select (Symtab.lookup solvers name)
- | (_, NONE) => default ())
-
-fun solver_class_of ctxt =
- let fun class_of ({class, ...}: solver_info, _) = class ctxt
- in solver_info_of no_solver_err (class_of o the) ctxt end
-
-fun solver_options_of ctxt =
- let
- fun all_options NONE = []
- | all_options (SOME ({options, ...} : solver_info, opts)) =
- opts @ options ctxt
- in solver_info_of (K []) all_options ctxt end
-
-val setup_solver =
- Attrib.setup @{binding smt2_solver}
- (Scan.lift (@{keyword "="} |-- Args.name) >>
- (Thm.declaration_attribute o K o select_solver))
- "SMT solver configuration"
-
-
-(* options *)
-
-val oracle = Attrib.setup_config_bool @{binding smt2_oracle} (K true)
-val timeout = Attrib.setup_config_real @{binding smt2_timeout} (K 30.0)
-val random_seed = Attrib.setup_config_int @{binding smt2_random_seed} (K 1)
-val read_only_certificates = Attrib.setup_config_bool @{binding smt2_read_only_certificates} (K false)
-val verbose = Attrib.setup_config_bool @{binding smt2_verbose} (K true)
-val trace = Attrib.setup_config_bool @{binding smt2_trace} (K false)
-val monomorph_limit = Attrib.setup_config_int @{binding smt2_monomorph_limit} (K 10)
-val monomorph_instances = Attrib.setup_config_int @{binding smt2_monomorph_instances} (K 500)
-val infer_triggers = Attrib.setup_config_bool @{binding smt2_infer_triggers} (K false)
-val debug_files = Attrib.setup_config_string @{binding smt2_debug_files} (K "")
-val sat_solver = Attrib.setup_config_string @{binding smt2_sat_solver} (K "cdclite")
-
-
-(* diagnostics *)
-
-fun cond_trace flag f x = if flag then tracing ("SMT: " ^ f x) else ()
-
-fun verbose_msg ctxt = cond_trace (Config.get ctxt verbose)
-
-fun trace_msg ctxt = cond_trace (Config.get ctxt trace)
-
-
-(* tools *)
-
-fun with_timeout ctxt f x =
- TimeLimit.timeLimit (seconds (Config.get ctxt timeout)) f x
- handle TimeLimit.TimeOut => raise SMT2_Failure.SMT SMT2_Failure.Time_Out
-
-
-(* certificates *)
-
-(* FIXME just one data slot (record) per program unit *)
-structure Certificates = Generic_Data
-(
- type T = Cache_IO.cache option
- val empty = NONE
- val extend = I
- fun merge (s, _) = s (* FIXME merge options!? *)
-)
-
-val get_certificates_path =
- Option.map (Cache_IO.cache_path_of) o Certificates.get o Context.Proof
-
-fun select_certificates name context = context |> Certificates.put (
- if name = "" then NONE
- else
- Path.explode name
- |> Path.append (Resources.master_directory (Context.theory_of context))
- |> SOME o Cache_IO.unsynchronized_init)
-
-val certificates_of = Certificates.get o Context.Proof
-
-val setup_certificates =
- Attrib.setup @{binding smt2_certificates}
- (Scan.lift (@{keyword "="} |-- Args.name) >>
- (Thm.declaration_attribute o K o select_certificates))
- "SMT certificates configuration"
-
-
-(* setup *)
-
-val _ = Theory.setup (
- setup_solver #>
- setup_certificates)
-
-fun print_setup ctxt =
- let
- fun string_of_bool b = if b then "true" else "false"
-
- val names = available_solvers_of ctxt
- val ns = if null names then ["(none)"] else sort_strings names
- val n = the_default "(none)" (solver_name_of ctxt)
- val opts = solver_options_of ctxt
-
- val t = string_of_real (Config.get ctxt timeout)
-
- val certs_filename =
- (case get_certificates_path ctxt of
- SOME path => Path.print path
- | NONE => "(disabled)")
- in
- Pretty.writeln (Pretty.big_list "SMT setup:" [
- Pretty.str ("Current SMT solver: " ^ n),
- Pretty.str ("Current SMT solver options: " ^ space_implode " " opts),
- Pretty.str_list "Available SMT solvers: " "" ns,
- Pretty.str ("Current timeout: " ^ t ^ " seconds"),
- Pretty.str ("With proofs: " ^
- string_of_bool (not (Config.get ctxt oracle))),
- Pretty.str ("Certificates cache: " ^ certs_filename),
- Pretty.str ("Fixed certificates: " ^
- string_of_bool (Config.get ctxt read_only_certificates))])
- end
-
-val _ =
- Outer_Syntax.improper_command @{command_spec "smt2_status"}
- "show the available SMT solvers, the currently selected SMT solver, \
- \and the values of SMT configuration options"
- (Scan.succeed (Toplevel.keep (print_setup o Toplevel.context_of)))
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_datatypes.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,93 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_datatypes.ML
- Author: Sascha Boehme, TU Muenchen
-
-Collector functions for common type declarations and their representation
-as algebraic datatypes.
-*)
-
-signature SMT2_DATATYPES =
-sig
- val add_decls: typ ->
- (typ * (term * term list) list) list list * Proof.context ->
- (typ * (term * term list) list) list list * Proof.context
-end;
-
-structure SMT2_Datatypes: SMT2_DATATYPES =
-struct
-
-fun mk_selectors T Ts =
- Variable.variant_fixes (replicate (length Ts) "select")
- #>> map2 (fn U => fn n => Free (n, T --> U)) Ts
-
-
-(* free constructor type declarations *)
-
-fun get_ctr_sugar_decl ({ctrs, ...} : Ctr_Sugar.ctr_sugar) T Ts ctxt =
- let
- fun mk_constr ctr0 =
- let val ctr = Ctr_Sugar.mk_ctr Ts ctr0 in
- mk_selectors T (binder_types (fastype_of ctr)) #>> pair ctr
- end
- in
- fold_map mk_constr ctrs ctxt
- |>> (pair T #> single)
- end
-
-
-(* typedef declarations *)
-
-fun get_typedef_decl (({Abs_name, Rep_name, abs_type, rep_type, ...}, {Abs_inverse, ...})
- : Typedef.info) T Ts =
- if can (curry (op RS) @{thm UNIV_I}) Abs_inverse then
- let
- val env = snd (Term.dest_Type abs_type) ~~ Ts
- val instT = Term.map_atyps (perhaps (AList.lookup (op =) env))
-
- val constr = Const (Abs_name, instT (rep_type --> abs_type))
- val select = Const (Rep_name, instT (abs_type --> rep_type))
- in [(T, [(constr, [select])])] end
- else
- []
-
-
-(* collection of declarations *)
-
-fun declared declss T = exists (exists (equal T o fst)) declss
-fun declared' dss T = exists (exists (equal T o fst) o snd) dss
-
-fun get_decls T n Ts ctxt =
- (case Ctr_Sugar.ctr_sugar_of ctxt n of
- SOME ctr_sugar => get_ctr_sugar_decl ctr_sugar T Ts ctxt
- | NONE =>
- (case Typedef.get_info ctxt n of
- [] => ([], ctxt)
- | info :: _ => (get_typedef_decl info T Ts, ctxt)))
-
-fun add_decls T (declss, ctxt) =
- let
- fun depends Ts ds = exists (member (op =) (map fst ds)) Ts
-
- fun add (TFree _) = I
- | add (TVar _) = I
- | add (T as Type (@{type_name fun}, _)) =
- fold add (Term.body_type T :: Term.binder_types T)
- | add @{typ bool} = I
- | add (T as Type (n, Ts)) = (fn (dss, ctxt1) =>
- if declared declss T orelse declared' dss T then (dss, ctxt1)
- else if SMT2_Builtin.is_builtin_typ_ext ctxt1 T then (dss, ctxt1)
- else
- (case get_decls T n Ts ctxt1 of
- ([], _) => (dss, ctxt1)
- | (ds, ctxt2) =>
- let
- val constrTs = maps (map (snd o Term.dest_Const o fst) o snd) ds
- val Us = fold (union (op =) o Term.binder_types) constrTs []
-
- fun ins [] = [(Us, ds)]
- | ins ((Uds as (Us', _)) :: Udss) =
- if depends Us' ds then (Us, ds) :: Uds :: Udss
- else Uds :: ins Udss
- in fold add Us (ins dss, ctxt2) end))
- in add T ([], ctxt) |>> append declss o map snd end
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_failure.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,40 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_failure.ML
- Author: Sascha Boehme, TU Muenchen
-
-Failures and exception of SMT.
-*)
-
-signature SMT2_FAILURE =
-sig
- datatype failure =
- Counterexample of bool |
- Time_Out |
- Out_Of_Memory |
- Abnormal_Termination of int |
- Other_Failure of string
- val string_of_failure: failure -> string
- exception SMT of failure
-end;
-
-structure SMT2_Failure: SMT2_FAILURE =
-struct
-
-datatype failure =
- Counterexample of bool |
- Time_Out |
- Out_Of_Memory |
- Abnormal_Termination of int |
- Other_Failure of string
-
-fun string_of_failure (Counterexample genuine) =
- if genuine then "Counterexample found (possibly spurious)"
- else "Potential counterexample found"
- | string_of_failure Time_Out = "Timed out"
- | string_of_failure Out_Of_Memory = "Ran out of memory"
- | string_of_failure (Abnormal_Termination err) =
- "Solver terminated abnormally with error code " ^ string_of_int err
- | string_of_failure (Other_Failure msg) = msg
-
-exception SMT of failure
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_normalize.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,441 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_normalize.ML
- Author: Sascha Boehme, TU Muenchen
-
-Normalization steps on theorems required by SMT solvers.
-*)
-
-signature SMT2_NORMALIZE =
-sig
- val drop_fact_warning: Proof.context -> thm -> unit
- val atomize_conv: Proof.context -> conv
-
- val special_quant_table: (string * thm) list
- val case_bool_entry: string * thm
- val abs_min_max_table: (string * thm) list
-
- type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
- val add_extra_norm: SMT2_Util.class * extra_norm -> Context.generic -> Context.generic
- val normalize: Proof.context -> thm list -> (int * thm) list
-end;
-
-structure SMT2_Normalize: SMT2_NORMALIZE =
-struct
-
-fun drop_fact_warning ctxt =
- SMT2_Config.verbose_msg ctxt (prefix "Warning: dropping assumption: " o
- Display.string_of_thm ctxt)
-
-
-(* general theorem normalizations *)
-
-(** instantiate elimination rules **)
-
-local
- val (cpfalse, cfalse) = `SMT2_Util.mk_cprop (Thm.cterm_of @{theory} @{const False})
-
- fun inst f ct thm =
- let val cv = f (Drule.strip_imp_concl (Thm.cprop_of thm))
- in Thm.instantiate ([], [(cv, ct)]) thm end
-in
-
-fun instantiate_elim thm =
- (case Thm.concl_of thm of
- @{const Trueprop} $ Var (_, @{typ bool}) => inst Thm.dest_arg cfalse thm
- | Var _ => inst I cpfalse thm
- | _ => thm)
-
-end
-
-
-(** normalize definitions **)
-
-fun norm_def thm =
- (case Thm.prop_of thm of
- @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ _ $ Abs _) =>
- norm_def (thm RS @{thm fun_cong})
- | Const (@{const_name Pure.eq}, _) $ _ $ Abs _ => norm_def (thm RS @{thm meta_eq_to_obj_eq})
- | _ => thm)
-
-
-(** atomization **)
-
-fun atomize_conv ctxt ct =
- (case Thm.term_of ct of
- @{const Pure.imp} $ _ $ _ =>
- Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_imp}
- | Const (@{const_name Pure.eq}, _) $ _ $ _ =>
- Conv.binop_conv (atomize_conv ctxt) then_conv Conv.rewr_conv @{thm atomize_eq}
- | Const (@{const_name Pure.all}, _) $ Abs _ =>
- Conv.binder_conv (atomize_conv o snd) ctxt then_conv Conv.rewr_conv @{thm atomize_all}
- | _ => Conv.all_conv) ct
-
-val setup_atomize =
- fold SMT2_Builtin.add_builtin_fun_ext'' [@{const_name Pure.imp}, @{const_name Pure.eq},
- @{const_name Pure.all}, @{const_name Trueprop}]
-
-
-(** unfold special quantifiers **)
-
-val special_quant_table = [
- (@{const_name Ex1}, @{thm Ex1_def_raw}),
- (@{const_name Ball}, @{thm Ball_def_raw}),
- (@{const_name Bex}, @{thm Bex_def_raw})]
-
-local
- fun special_quant (Const (n, _)) = AList.lookup (op =) special_quant_table n
- | special_quant _ = NONE
-
- fun special_quant_conv _ ct =
- (case special_quant (Thm.term_of ct) of
- SOME thm => Conv.rewr_conv thm
- | NONE => Conv.all_conv) ct
-in
-
-fun unfold_special_quants_conv ctxt =
- SMT2_Util.if_exists_conv (is_some o special_quant) (Conv.top_conv special_quant_conv ctxt)
-
-val setup_unfolded_quants = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) special_quant_table
-
-end
-
-
-(** trigger inference **)
-
-local
- (*** check trigger syntax ***)
-
- fun dest_trigger (Const (@{const_name pat}, _) $ _) = SOME true
- | dest_trigger (Const (@{const_name nopat}, _) $ _) = SOME false
- | dest_trigger _ = NONE
-
- fun eq_list [] = false
- | eq_list (b :: bs) = forall (equal b) bs
-
- fun proper_trigger t =
- t
- |> these o try SMT2_Util.dest_symb_list
- |> map (map_filter dest_trigger o these o try SMT2_Util.dest_symb_list)
- |> (fn [] => false | bss => forall eq_list bss)
-
- fun proper_quant inside f t =
- (case t of
- Const (@{const_name All}, _) $ Abs (_, _, u) => proper_quant true f u
- | Const (@{const_name Ex}, _) $ Abs (_, _, u) => proper_quant true f u
- | @{const trigger} $ p $ u =>
- (if inside then f p else false) andalso proper_quant false f u
- | Abs (_, _, u) => proper_quant false f u
- | u1 $ u2 => proper_quant false f u1 andalso proper_quant false f u2
- | _ => true)
-
- fun check_trigger_error ctxt t =
- error ("SMT triggers must only occur under quantifier and multipatterns " ^
- "must have the same kind: " ^ Syntax.string_of_term ctxt t)
-
- fun check_trigger_conv ctxt ct =
- if proper_quant false proper_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct
- else check_trigger_error ctxt (Thm.term_of ct)
-
-
- (*** infer simple triggers ***)
-
- fun dest_cond_eq ct =
- (case Thm.term_of ct of
- Const (@{const_name HOL.eq}, _) $ _ $ _ => Thm.dest_binop ct
- | @{const HOL.implies} $ _ $ _ => dest_cond_eq (Thm.dest_arg ct)
- | _ => raise CTERM ("no equation", [ct]))
-
- fun get_constrs thy (Type (n, _)) = these (Datatype_Data.get_constrs thy n)
- | get_constrs _ _ = []
-
- fun is_constr thy (n, T) =
- let fun match (m, U) = m = n andalso Sign.typ_instance thy (T, U)
- in can (the o find_first match o get_constrs thy o Term.body_type) T end
-
- fun is_constr_pat thy t =
- (case Term.strip_comb t of
- (Free _, []) => true
- | (Const c, ts) => is_constr thy c andalso forall (is_constr_pat thy) ts
- | _ => false)
-
- fun is_simp_lhs ctxt t =
- (case Term.strip_comb t of
- (Const c, ts as _ :: _) =>
- not (SMT2_Builtin.is_builtin_fun_ext ctxt c ts) andalso
- forall (is_constr_pat (Proof_Context.theory_of ctxt)) ts
- | _ => false)
-
- fun has_all_vars vs t =
- subset (op aconv) (vs, map Free (Term.add_frees t []))
-
- fun minimal_pats vs ct =
- if has_all_vars vs (Thm.term_of ct) then
- (case Thm.term_of ct of
- _ $ _ =>
- (case pairself (minimal_pats vs) (Thm.dest_comb ct) of
- ([], []) => [[ct]]
- | (ctss, ctss') => union (eq_set (op aconvc)) ctss ctss')
- | _ => [])
- else []
-
- fun proper_mpat _ _ _ [] = false
- | proper_mpat thy gen u cts =
- let
- val tps = (op ~~) (`gen (map Thm.term_of cts))
- fun some_match u = tps |> exists (fn (t', t) =>
- Pattern.matches thy (t', u) andalso not (t aconv u))
- in not (Term.exists_subterm some_match u) end
-
- val pat = SMT2_Util.mk_const_pat @{theory} @{const_name pat} SMT2_Util.destT1
- fun mk_pat ct = Thm.apply (SMT2_Util.instT' ct pat) ct
-
- fun mk_clist T =
- pairself (Thm.cterm_of @{theory}) (SMT2_Util.symb_cons_const T, SMT2_Util.symb_nil_const T)
- fun mk_list (ccons, cnil) f cts = fold_rev (Thm.mk_binop ccons o f) cts cnil
- val mk_pat_list = mk_list (mk_clist @{typ pattern})
- val mk_mpat_list = mk_list (mk_clist @{typ "pattern symb_list"})
- fun mk_trigger ctss = mk_mpat_list (mk_pat_list mk_pat) ctss
-
- val trigger_eq = mk_meta_eq @{lemma "p = trigger t p" by (simp add: trigger_def)}
-
- fun insert_trigger_conv [] ct = Conv.all_conv ct
- | insert_trigger_conv ctss ct =
- let val (ctr, cp) = Thm.dest_binop (Thm.rhs_of trigger_eq) ||> rpair ct
- in Thm.instantiate ([], [cp, (ctr, mk_trigger ctss)]) trigger_eq end
-
- fun infer_trigger_eq_conv outer_ctxt (ctxt, cvs) ct =
- let
- val (lhs, rhs) = dest_cond_eq ct
-
- val vs = map Thm.term_of cvs
- val thy = Proof_Context.theory_of ctxt
-
- fun get_mpats ct =
- if is_simp_lhs ctxt (Thm.term_of ct) then minimal_pats vs ct
- else []
- val gen = Variable.export_terms ctxt outer_ctxt
- val filter_mpats = filter (proper_mpat thy gen (Thm.term_of rhs))
-
- in insert_trigger_conv (filter_mpats (get_mpats lhs)) ct end
-
- fun has_trigger (@{const trigger} $ _ $ _) = true
- | has_trigger _ = false
-
- fun try_trigger_conv cv ct =
- if SMT2_Util.under_quant has_trigger (SMT2_Util.term_of ct) then Conv.all_conv ct
- else Conv.try_conv cv ct
-
- fun infer_trigger_conv ctxt =
- if Config.get ctxt SMT2_Config.infer_triggers then
- try_trigger_conv (SMT2_Util.under_quant_conv (infer_trigger_eq_conv ctxt) ctxt)
- else Conv.all_conv
-in
-
-fun trigger_conv ctxt =
- SMT2_Util.prop_conv (check_trigger_conv ctxt then_conv infer_trigger_conv ctxt)
-
-val setup_trigger =
- fold SMT2_Builtin.add_builtin_fun_ext''
- [@{const_name pat}, @{const_name nopat}, @{const_name trigger}]
-
-end
-
-
-(** combined general normalizations **)
-
-fun gen_normalize1_conv ctxt =
- atomize_conv ctxt then_conv
- unfold_special_quants_conv ctxt then_conv
- Thm.beta_conversion true then_conv
- trigger_conv ctxt
-
-fun gen_normalize1 ctxt =
- instantiate_elim #>
- norm_def #>
- Conv.fconv_rule (Thm.beta_conversion true then_conv Thm.eta_conversion) #>
- Drule.forall_intr_vars #>
- Conv.fconv_rule (gen_normalize1_conv ctxt) #>
- (* Z3 4.3.1 silently normalizes "P --> Q --> R" to "P & Q --> R" *)
- Raw_Simplifier.rewrite_rule ctxt @{thms HOL.imp_conjL[symmetric, THEN eq_reflection]}
-
-fun gen_norm1_safe ctxt (i, thm) =
- (case try (gen_normalize1 ctxt) thm of
- SOME thm' => SOME (i, thm')
- | NONE => (drop_fact_warning ctxt thm; NONE))
-
-fun gen_normalize ctxt iwthms = map_filter (gen_norm1_safe ctxt) iwthms
-
-
-(* unfolding of definitions and theory-specific rewritings *)
-
-fun expand_head_conv cv ct =
- (case Thm.term_of ct of
- _ $ _ =>
- Conv.fun_conv (expand_head_conv cv) then_conv
- Conv.try_conv (Thm.beta_conversion false)
- | _ => cv) ct
-
-
-(** rewrite bool case expressions as if expressions **)
-
-val case_bool_entry = (@{const_name "bool.case_bool"}, @{thm case_bool_if})
-
-local
- fun is_case_bool (Const (@{const_name "bool.case_bool"}, _)) = true
- | is_case_bool _ = false
-
- fun unfold_conv _ =
- SMT2_Util.if_true_conv (is_case_bool o Term.head_of)
- (expand_head_conv (Conv.rewr_conv @{thm case_bool_if}))
-in
-
-fun rewrite_case_bool_conv ctxt =
- SMT2_Util.if_exists_conv is_case_bool (Conv.top_conv unfold_conv ctxt)
-
-val setup_case_bool = SMT2_Builtin.add_builtin_fun_ext'' @{const_name "bool.case_bool"}
-
-end
-
-
-(** unfold abs, min and max **)
-
-val abs_min_max_table = [
- (@{const_name min}, @{thm min_def_raw}),
- (@{const_name max}, @{thm max_def_raw}),
- (@{const_name abs}, @{thm abs_if_raw})]
-
-local
- fun abs_min_max ctxt (Const (n, Type (@{type_name fun}, [T, _]))) =
- (case AList.lookup (op =) abs_min_max_table n of
- NONE => NONE
- | SOME thm => if SMT2_Builtin.is_builtin_typ_ext ctxt T then SOME thm else NONE)
- | abs_min_max _ _ = NONE
-
- fun unfold_amm_conv ctxt ct =
- (case abs_min_max ctxt (Term.head_of (Thm.term_of ct)) of
- SOME thm => expand_head_conv (Conv.rewr_conv thm)
- | NONE => Conv.all_conv) ct
-in
-
-fun unfold_abs_min_max_conv ctxt =
- SMT2_Util.if_exists_conv (is_some o abs_min_max ctxt) (Conv.top_conv unfold_amm_conv ctxt)
-
-val setup_abs_min_max = fold (SMT2_Builtin.add_builtin_fun_ext'' o fst) abs_min_max_table
-
-end
-
-
-(** normalize numerals **)
-
-local
- (*
- rewrite Numeral1 into 1
- rewrite - 0 into 0
- *)
-
- fun is_irregular_number (Const (@{const_name numeral}, _) $ Const (@{const_name num.One}, _)) =
- true
- | is_irregular_number (Const (@{const_name uminus}, _) $ Const (@{const_name Groups.zero}, _)) =
- true
- | is_irregular_number _ = false
-
- fun is_strange_number ctxt t = is_irregular_number t andalso SMT2_Builtin.is_builtin_num ctxt t
-
- val proper_num_ss =
- simpset_of (put_simpset HOL_ss @{context} addsimps @{thms Num.numeral_One minus_zero})
-
- fun norm_num_conv ctxt =
- SMT2_Util.if_conv (is_strange_number ctxt) (Simplifier.rewrite (put_simpset proper_num_ss ctxt))
- Conv.no_conv
-in
-
-fun normalize_numerals_conv ctxt =
- SMT2_Util.if_exists_conv (is_strange_number ctxt) (Conv.top_sweep_conv norm_num_conv ctxt)
-
-end
-
-
-(** combined unfoldings and rewritings **)
-
-fun unfold_conv ctxt =
- rewrite_case_bool_conv ctxt then_conv
- unfold_abs_min_max_conv ctxt then_conv
- Thm.beta_conversion true
-
-fun unfold_polymorph ctxt = map (apsnd (Conv.fconv_rule (unfold_conv ctxt)))
-fun unfold_monomorph ctxt = map (apsnd (Conv.fconv_rule (normalize_numerals_conv ctxt)))
-
-
-(* overall normalization *)
-
-fun burrow_ids f ithms =
- let
- val (is, thms) = split_list ithms
- val (thms', extra_thms) = f thms
- in (is ~~ thms') @ map (pair ~1) extra_thms end
-
-type extra_norm = Proof.context -> thm list * thm list -> thm list * thm list
-
-structure Extra_Norms = Generic_Data
-(
- type T = extra_norm SMT2_Util.dict
- val empty = []
- val extend = I
- fun merge data = SMT2_Util.dict_merge fst data
-)
-
-fun add_extra_norm (cs, norm) = Extra_Norms.map (SMT2_Util.dict_update (cs, norm))
-
-fun apply_extra_norms ctxt ithms =
- let
- val cs = SMT2_Config.solver_class_of ctxt
- val es = SMT2_Util.dict_lookup (Extra_Norms.get (Context.Proof ctxt)) cs
- in burrow_ids (fold (fn e => e ctxt) es o rpair []) ithms end
-
-local
- val ignored = member (op =) [@{const_name All}, @{const_name Ex},
- @{const_name Let}, @{const_name If}, @{const_name HOL.eq}]
-
- val schematic_consts_of =
- let
- fun collect (@{const trigger} $ p $ t) = collect_trigger p #> collect t
- | collect (t $ u) = collect t #> collect u
- | collect (Abs (_, _, t)) = collect t
- | collect (t as Const (n, _)) =
- if not (ignored n) then Monomorph.add_schematic_consts_of t else I
- | collect _ = I
- and collect_trigger t =
- let val dest = these o try SMT2_Util.dest_symb_list
- in fold (fold collect_pat o dest) (dest t) end
- and collect_pat (Const (@{const_name pat}, _) $ t) = collect t
- | collect_pat (Const (@{const_name nopat}, _) $ t) = collect t
- | collect_pat _ = I
- in (fn t => collect t Symtab.empty) end
-in
-
-fun monomorph ctxt xthms =
- let val (xs, thms) = split_list xthms
- in
- map (pair 1) thms
- |> Monomorph.monomorph schematic_consts_of ctxt
- |> maps (uncurry (map o pair)) o map2 pair xs o map (map snd)
- end
-
-end
-
-fun normalize ctxt wthms =
- wthms
- |> map_index I
- |> gen_normalize ctxt
- |> unfold_polymorph ctxt
- |> monomorph ctxt
- |> unfold_monomorph ctxt
- |> apply_extra_norms ctxt
-
-val _ = Theory.setup (Context.theory_map (
- setup_atomize #>
- setup_unfolded_quants #>
- setup_trigger #>
- setup_case_bool #>
- setup_abs_min_max))
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_real.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,121 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_real.ML
- Author: Sascha Boehme, TU Muenchen
-
-SMT setup for reals.
-*)
-
-structure SMT2_Real: sig end =
-struct
-
-
-(* SMT-LIB logic *)
-
-fun smtlib_logic ts =
- if exists (Term.exists_type (Term.exists_subtype (equal @{typ real}))) ts
- then SOME "AUFLIRA"
- else NONE
-
-
-(* SMT-LIB and Z3 built-ins *)
-
-local
- fun real_num _ i = SOME (string_of_int i ^ ".0")
-
- fun is_linear [t] = SMT2_Util.is_number t
- | is_linear [t, u] = SMT2_Util.is_number t orelse SMT2_Util.is_number u
- | is_linear _ = false
-
- fun mk_times ts = Term.list_comb (@{const times (real)}, ts)
-
- fun times _ _ ts = if is_linear ts then SOME ("*", 2, ts, mk_times) else NONE
-in
-
-val setup_builtins =
- SMT2_Builtin.add_builtin_typ SMTLIB2_Interface.smtlib2C
- (@{typ real}, K (SOME "Real"), real_num) #>
- fold (SMT2_Builtin.add_builtin_fun' SMTLIB2_Interface.smtlib2C) [
- (@{const less (real)}, "<"),
- (@{const less_eq (real)}, "<="),
- (@{const uminus (real)}, "-"),
- (@{const plus (real)}, "+"),
- (@{const minus (real)}, "-") ] #>
- SMT2_Builtin.add_builtin_fun SMTLIB2_Interface.smtlib2C
- (Term.dest_Const @{const times (real)}, times) #>
- SMT2_Builtin.add_builtin_fun' Z3_New_Interface.smtlib2_z3C
- (@{const times (real)}, "*") #>
- SMT2_Builtin.add_builtin_fun' Z3_New_Interface.smtlib2_z3C
- (@{const divide (real)}, "/")
-
-end
-
-
-(* Z3 constructors *)
-
-local
- fun z3_mk_builtin_typ (Z3_New_Interface.Sym ("Real", _)) = SOME @{typ real}
- | z3_mk_builtin_typ (Z3_New_Interface.Sym ("real", _)) = SOME @{typ real}
- (*FIXME: delete*)
- | z3_mk_builtin_typ _ = NONE
-
- fun z3_mk_builtin_num _ i T =
- if T = @{typ real} then SOME (Numeral.mk_cnumber @{ctyp real} i)
- else NONE
-
- fun mk_nary _ cu [] = cu
- | mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
-
- val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (real)})
- val add = Thm.cterm_of @{theory} @{const plus (real)}
- val real0 = Numeral.mk_cnumber @{ctyp real} 0
- val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (real)})
- val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (real)})
- val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const divide (real)})
- val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (real)})
- val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (real)})
-
- fun z3_mk_builtin_fun (Z3_New_Interface.Sym ("-", _)) [ct] = SOME (mk_uminus ct)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym ("+", _)) cts =
- SOME (mk_nary add real0 cts)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym ("-", _)) [ct, cu] =
- SOME (mk_sub ct cu)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym ("*", _)) [ct, cu] =
- SOME (mk_mul ct cu)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym ("/", _)) [ct, cu] =
- SOME (mk_div ct cu)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym ("<", _)) [ct, cu] =
- SOME (mk_lt ct cu)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym ("<=", _)) [ct, cu] =
- SOME (mk_le ct cu)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym (">", _)) [ct, cu] =
- SOME (mk_lt cu ct)
- | z3_mk_builtin_fun (Z3_New_Interface.Sym (">=", _)) [ct, cu] =
- SOME (mk_le cu ct)
- | z3_mk_builtin_fun _ _ = NONE
-in
-
-val z3_mk_builtins = {
- mk_builtin_typ = z3_mk_builtin_typ,
- mk_builtin_num = z3_mk_builtin_num,
- mk_builtin_fun = (fn _ => fn sym => fn cts =>
- (case try (#T o Thm.rep_cterm o hd) cts of
- SOME @{typ real} => z3_mk_builtin_fun sym cts
- | _ => NONE)) }
-
-end
-
-
-(* Z3 proof replay *)
-
-val real_linarith_proc = Simplifier.simproc_global @{theory} "fast_real_arith" [
- "(m::real) < n", "(m::real) <= n", "(m::real) = n"] Lin_Arith.simproc
-
-
-(* setup *)
-
-val _ = Theory.setup (Context.theory_map (
- SMTLIB2_Interface.add_logic (10, smtlib_logic) #>
- setup_builtins #>
- Z3_New_Interface.add_mk_builtins z3_mk_builtins #>
- Z3_New_Replay_Util.add_simproc real_linarith_proc))
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_solver.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,306 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_solver.ML
- Author: Sascha Boehme, TU Muenchen
-
-SMT solvers registry and SMT tactic.
-*)
-
-signature SMT2_SOLVER =
-sig
- (*configuration*)
- datatype outcome = Unsat | Sat | Unknown
-
- type parsed_proof =
- {outcome: SMT2_Failure.failure option,
- fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list,
- atp_proof: unit -> (term, string) ATP_Proof.atp_step list}
-
- type solver_config =
- {name: string,
- class: Proof.context -> SMT2_Util.class,
- avail: unit -> bool,
- command: unit -> string list,
- options: Proof.context -> string list,
- smt_options: (string * string) list,
- default_max_relevant: int,
- outcome: string -> string list -> outcome * string list,
- parse_proof: (Proof.context -> SMT2_Translate.replay_data ->
- ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
- parsed_proof) option,
- replay: (Proof.context -> SMT2_Translate.replay_data -> string list -> thm) option}
-
- (*registry*)
- val add_solver: solver_config -> theory -> theory
- val default_max_relevant: Proof.context -> string -> int
-
- (*filter*)
- val smt2_filter: Proof.context -> thm -> ((string * ATP_Problem_Generate.stature) * thm) list ->
- int -> Time.time -> parsed_proof
-
- (*tactic*)
- val smt2_tac: Proof.context -> thm list -> int -> tactic
- val smt2_tac': Proof.context -> thm list -> int -> tactic
-end;
-
-structure SMT2_Solver: SMT2_SOLVER =
-struct
-
-(* interface to external solvers *)
-
-local
-
-fun make_command command options problem_path proof_path =
- "(exec 2>&1;" :: map File.shell_quote (command () @ options) @
- [File.shell_path problem_path, ")", ">", File.shell_path proof_path]
- |> space_implode " "
-
-fun with_trace ctxt msg f x =
- let val _ = SMT2_Config.trace_msg ctxt (fn () => msg) ()
- in f x end
-
-fun run ctxt name mk_cmd input =
- (case SMT2_Config.certificates_of ctxt of
- NONE =>
- if not (SMT2_Config.is_available ctxt name) then
- error ("The SMT solver " ^ quote name ^ " is not installed")
- else if Config.get ctxt SMT2_Config.debug_files = "" then
- with_trace ctxt ("Invoking SMT solver " ^ quote name ^ " ...") (Cache_IO.run mk_cmd) input
- else
- let
- val base_path = Path.explode (Config.get ctxt SMT2_Config.debug_files)
- val in_path = Path.ext "smt2_in" base_path
- val out_path = Path.ext "smt2_out" base_path
- in Cache_IO.raw_run mk_cmd input in_path out_path end
- | SOME certs =>
- (case Cache_IO.lookup certs input of
- (NONE, key) =>
- if Config.get ctxt SMT2_Config.read_only_certificates then
- error ("Bad certificate cache: missing certificate")
- else
- Cache_IO.run_and_cache certs key mk_cmd input
- | (SOME output, _) =>
- with_trace ctxt ("Using cached certificate from " ^
- File.shell_path (Cache_IO.cache_path_of certs) ^ " ...") I output))
-
-(* Z3 returns 1 if "get-model" or "get-model" fails *)
-val normal_return_codes = [0, 1]
-
-fun run_solver ctxt name mk_cmd input =
- let
- fun pretty tag lines = Pretty.string_of (Pretty.big_list tag (map Pretty.str lines))
-
- val _ = SMT2_Config.trace_msg ctxt (pretty "Problem:" o split_lines) input
-
- val {redirected_output = res, output = err, return_code} =
- SMT2_Config.with_timeout ctxt (run ctxt name mk_cmd) input
- val _ = SMT2_Config.trace_msg ctxt (pretty "Solver:") err
-
- val output = fst (take_suffix (equal "") res)
- val _ = SMT2_Config.trace_msg ctxt (pretty "Result:") output
-
- val _ = member (op =) normal_return_codes return_code orelse
- raise SMT2_Failure.SMT (SMT2_Failure.Abnormal_Termination return_code)
- in output end
-
-fun trace_assms ctxt =
- SMT2_Config.trace_msg ctxt (Pretty.string_of o
- Pretty.big_list "Assertions:" o map (Display.pretty_thm ctxt o snd))
-
-fun trace_replay_data ({context = ctxt, typs, terms, ...} : SMT2_Translate.replay_data) =
- let
- fun pretty_eq n p = Pretty.block [Pretty.str n, Pretty.str " = ", p]
- fun p_typ (n, T) = pretty_eq n (Syntax.pretty_typ ctxt T)
- fun p_term (n, t) = pretty_eq n (Syntax.pretty_term ctxt t)
- in
- SMT2_Config.trace_msg ctxt (fn () =>
- Pretty.string_of (Pretty.big_list "Names:" [
- Pretty.big_list "sorts:" (map p_typ (Symtab.dest typs)),
- Pretty.big_list "functions:" (map p_term (Symtab.dest terms))])) ()
- end
-
-in
-
-fun invoke name command smt_options ithms ctxt =
- let
- val options = SMT2_Config.solver_options_of ctxt
- val comments = [space_implode " " options]
-
- val (str, replay_data as {context = ctxt', ...}) =
- ithms
- |> tap (trace_assms ctxt)
- |> SMT2_Translate.translate ctxt smt_options comments
- ||> tap trace_replay_data
- in (run_solver ctxt' name (make_command command options) str, replay_data) end
-
-end
-
-
-(* configuration *)
-
-datatype outcome = Unsat | Sat | Unknown
-
-type parsed_proof =
- {outcome: SMT2_Failure.failure option,
- fact_ids: (int * ((string * ATP_Problem_Generate.stature) * thm)) list,
- atp_proof: unit -> (term, string) ATP_Proof.atp_step list}
-
-type solver_config =
- {name: string,
- class: Proof.context -> SMT2_Util.class,
- avail: unit -> bool,
- command: unit -> string list,
- options: Proof.context -> string list,
- smt_options: (string * string) list,
- default_max_relevant: int,
- outcome: string -> string list -> outcome * string list,
- parse_proof: (Proof.context -> SMT2_Translate.replay_data ->
- ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
- parsed_proof) option,
- replay: (Proof.context -> SMT2_Translate.replay_data -> string list -> thm) option}
-
-
-(* check well-sortedness *)
-
-val has_topsort = Term.exists_type (Term.exists_subtype (fn
- TFree (_, []) => true
- | TVar (_, []) => true
- | _ => false))
-
-(* top sorts cause problems with atomization *)
-fun check_topsort ctxt thm =
- if has_topsort (Thm.prop_of thm) then (SMT2_Normalize.drop_fact_warning ctxt thm; TrueI) else thm
-
-
-(* registry *)
-
-type solver_info = {
- command: unit -> string list,
- smt_options: (string * string) list,
- default_max_relevant: int,
- parse_proof: Proof.context -> SMT2_Translate.replay_data ->
- ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
- parsed_proof,
- replay: Proof.context -> SMT2_Translate.replay_data -> string list -> thm}
-
-structure Solvers = Generic_Data
-(
- type T = solver_info Symtab.table
- val empty = Symtab.empty
- val extend = I
- fun merge data = Symtab.merge (K true) data
-)
-
-local
- fun parse_proof outcome parse_proof0 outer_ctxt replay_data xfacts prems concl output =
- (case outcome output of
- (Unsat, lines) =>
- (case parse_proof0 of
- SOME pp => pp outer_ctxt replay_data xfacts prems concl lines
- | NONE => {outcome = NONE, fact_ids = [], atp_proof = K []})
- | (result, _) => raise SMT2_Failure.SMT (SMT2_Failure.Counterexample (result = Sat)))
-
- fun replay outcome replay0 oracle outer_ctxt
- (replay_data as {context = ctxt, ...} : SMT2_Translate.replay_data) output =
- (case outcome output of
- (Unsat, lines) =>
- if not (Config.get ctxt SMT2_Config.oracle) andalso is_some replay0
- then the replay0 outer_ctxt replay_data lines
- else oracle ()
- | (result, _) => raise SMT2_Failure.SMT (SMT2_Failure.Counterexample (result = Sat)))
-
- val cfalse = Thm.cterm_of @{theory} @{prop False}
-in
-
-fun add_solver ({name, class, avail, command, options, smt_options, default_max_relevant, outcome,
- parse_proof = parse_proof0, replay = replay0} : solver_config) =
- let
- fun solver oracle = {
- command = command,
- smt_options = smt_options,
- default_max_relevant = default_max_relevant,
- parse_proof = parse_proof (outcome name) parse_proof0,
- replay = replay (outcome name) replay0 oracle}
-
- val info = {name = name, class = class, avail = avail, options = options}
- in
- Thm.add_oracle (Binding.name name, K cfalse) #-> (fn (_, oracle) =>
- Context.theory_map (Solvers.map (Symtab.update_new (name, solver oracle)))) #>
- Context.theory_map (SMT2_Config.add_solver info)
- end
-
-end
-
-fun get_info ctxt name = the (Symtab.lookup (Solvers.get (Context.Proof ctxt)) name)
-
-fun name_and_info_of ctxt =
- let val name = SMT2_Config.solver_of ctxt
- in (name, get_info ctxt name) end
-
-val default_max_relevant = #default_max_relevant oo get_info
-
-fun apply_solver_and_replay ctxt thms0 =
- let
- val thms = map (check_topsort ctxt) thms0
- val (name, {command, smt_options, replay, ...}) = name_and_info_of ctxt
- val (output, replay_data) =
- invoke name command smt_options (SMT2_Normalize.normalize ctxt thms) ctxt
- in replay ctxt replay_data output end
-
-
-(* filter *)
-
-fun smt2_filter ctxt0 goal xfacts i time_limit =
- let
- val ctxt = ctxt0 |> Config.put SMT2_Config.timeout (Time.toReal time_limit)
-
- val ({context = ctxt, prems, concl, ...}, _) = Subgoal.focus ctxt i goal
- fun negate ct = Thm.dest_comb ct ||> Thm.apply @{cterm Not} |-> Thm.apply
- val cprop =
- (case try negate (Thm.rhs_of (SMT2_Normalize.atomize_conv ctxt concl)) of
- SOME ct => ct
- | NONE => raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure "goal is not a HOL term"))
-
- val conjecture = Thm.assume cprop
- val facts = map snd xfacts
- val thms = conjecture :: prems @ facts
- val thms' = map (check_topsort ctxt) thms
-
- val (name, {command, smt_options, parse_proof, ...}) = name_and_info_of ctxt
- val (output, replay_data) =
- invoke name command smt_options (SMT2_Normalize.normalize ctxt thms') ctxt
- in
- parse_proof ctxt replay_data xfacts (map Thm.prop_of prems) (Thm.term_of concl) output
- end
- handle SMT2_Failure.SMT fail => {outcome = SOME fail, fact_ids = [], atp_proof = K []}
-
-
-(* SMT tactic *)
-
-local
- fun str_of ctxt fail =
- "Solver " ^ SMT2_Config.solver_of ctxt ^ ": " ^ SMT2_Failure.string_of_failure fail
-
- fun safe_solve ctxt facts = SOME (apply_solver_and_replay ctxt facts)
- handle
- SMT2_Failure.SMT (fail as SMT2_Failure.Counterexample _) =>
- (SMT2_Config.verbose_msg ctxt (str_of ctxt) fail; NONE)
- | SMT2_Failure.SMT (fail as SMT2_Failure.Time_Out) =>
- error ("SMT: Solver " ^ quote (SMT2_Config.solver_of ctxt) ^ ": " ^
- SMT2_Failure.string_of_failure fail ^ " (setting the " ^
- "configuration option " ^ quote (Config.name_of SMT2_Config.timeout) ^ " might help)")
- | SMT2_Failure.SMT fail => error (str_of ctxt fail)
-
- fun resolve (SOME thm) = rtac thm 1
- | resolve NONE = no_tac
-
- fun tac prove ctxt rules =
- CONVERSION (SMT2_Normalize.atomize_conv ctxt)
- THEN' rtac @{thm ccontr}
- THEN' SUBPROOF (fn {context = ctxt, prems, ...} => resolve (prove ctxt (rules @ prems))) ctxt
-in
-
-val smt2_tac = tac safe_solve
-val smt2_tac' = tac (SOME oo apply_solver_and_replay)
-
-end
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_systems.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,189 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_systems.ML
- Author: Sascha Boehme, TU Muenchen
-
-Setup SMT solvers.
-*)
-
-signature SMT2_SYSTEMS =
-sig
- datatype z3_non_commercial =
- Z3_Non_Commercial_Unknown |
- Z3_Non_Commercial_Accepted |
- Z3_Non_Commercial_Declined
- val z3_non_commercial: unit -> z3_non_commercial
- val z3_extensions: bool Config.T
-end;
-
-structure SMT2_Systems: SMT2_SYSTEMS =
-struct
-
-(* helper functions *)
-
-fun make_avail name () = getenv (name ^ "_SOLVER") <> ""
-
-fun make_command name () = [getenv (name ^ "_SOLVER")]
-
-fun outcome_of unsat sat unknown solver_name line =
- if String.isPrefix unsat line then SMT2_Solver.Unsat
- else if String.isPrefix sat line then SMT2_Solver.Sat
- else if String.isPrefix unknown line then SMT2_Solver.Unknown
- else raise SMT2_Failure.SMT (SMT2_Failure.Other_Failure ("Solver " ^ quote solver_name ^
- " failed -- enable tracing using the " ^ quote (Config.name_of SMT2_Config.trace) ^
- " option for details"))
-
-fun on_first_line test_outcome solver_name lines =
- let
- val split_first = (fn [] => ("", []) | l :: ls => (l, ls))
- val (l, ls) = split_first (snd (take_prefix (curry (op =) "") lines))
- in (test_outcome solver_name l, ls) end
-
-fun on_first_non_unsupported_line test_outcome solver_name lines =
- on_first_line test_outcome solver_name (filter (curry (op <>) "unsupported") lines)
-
-(* CVC3 *)
-
-local
- fun cvc3_options ctxt = [
- "-seed", string_of_int (Config.get ctxt SMT2_Config.random_seed),
- "-lang", "smt2",
- "-timeout", string_of_int (Real.ceil (Config.get ctxt SMT2_Config.timeout))]
-in
-
-val cvc3: SMT2_Solver.solver_config = {
- name = "cvc3",
- class = K SMTLIB2_Interface.smtlib2C,
- avail = make_avail "CVC3",
- command = make_command "CVC3",
- options = cvc3_options,
- smt_options = [],
- default_max_relevant = 400 (* FUDGE *),
- outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
- parse_proof = NONE,
- replay = NONE }
-
-end
-
-
-(* CVC4 *)
-
-local
- fun cvc4_options ctxt = [
- "--random-seed=" ^ string_of_int (Config.get ctxt SMT2_Config.random_seed),
- "--lang=smt2",
- "--tlimit", string_of_int (Real.ceil (1000.0 * Config.get ctxt SMT2_Config.timeout))]
-in
-
-val cvc4: SMT2_Solver.solver_config = {
- name = "cvc4",
- class = K SMTLIB2_Interface.smtlib2C,
- avail = make_avail "CVC4",
- command = make_command "CVC4",
- options = cvc4_options,
- smt_options = [],
- default_max_relevant = 400 (* FUDGE *),
- outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
- parse_proof = NONE,
- replay = NONE }
-
-end
-
-(* veriT *)
-
-val veriT: SMT2_Solver.solver_config = {
- name = "veriT",
- class = K SMTLIB2_Interface.smtlib2C,
- avail = make_avail "VERIT",
- command = make_command "VERIT",
- options = (fn ctxt => [
- "--proof-version=1",
- "--proof=-",
- "--proof-prune",
- "--proof-merge",
- "--disable-print-success",
- "--disable-banner",
- "--max-time=" ^ string_of_int (Real.ceil (Config.get ctxt SMT2_Config.timeout))]),
- smt_options = [],
- default_max_relevant = 120 (* FUDGE *),
- outcome = on_first_non_unsupported_line (outcome_of "unsat" "sat"
- "warning : proof_done: status is still open"),
- parse_proof = SOME VeriT_Proof_Parse.parse_proof,
- replay = NONE }
-
-(* Z3 *)
-
-datatype z3_non_commercial =
- Z3_Non_Commercial_Unknown |
- Z3_Non_Commercial_Accepted |
- Z3_Non_Commercial_Declined
-
-local
- val accepted = member (op =) ["yes", "Yes", "YES"]
- val declined = member (op =) ["no", "No", "NO"]
-in
-
-fun z3_non_commercial () =
- let
- val flag1 = Options.default_string @{system_option z3_non_commercial}
- val flag2 = getenv "Z3_NON_COMMERCIAL"
- in
- if accepted flag1 then Z3_Non_Commercial_Accepted
- else if declined flag1 then Z3_Non_Commercial_Declined
- else if accepted flag2 then Z3_Non_Commercial_Accepted
- else if declined flag2 then Z3_Non_Commercial_Declined
- else Z3_Non_Commercial_Unknown
- end
-
-fun if_z3_non_commercial f =
- (case z3_non_commercial () of
- Z3_Non_Commercial_Accepted => f ()
- | Z3_Non_Commercial_Declined =>
- error (Pretty.string_of (Pretty.para
- "The SMT solver Z3 may be used only for non-commercial applications."))
- | Z3_Non_Commercial_Unknown =>
- error (Pretty.string_of (Pretty.para
- ("The SMT solver Z3 is not activated. To activate it, set the Isabelle \
- \system option \"z3_non_commercial\" to \"yes\" (e.g. via \
- \the Isabelle/jEdit menu Plugin Options / Isabelle / General)."))))
-
-end
-
-val z3_extensions = Attrib.setup_config_bool @{binding z3_new_extensions} (K false)
-
-local
- fun z3_make_command name () = if_z3_non_commercial (make_command name)
-
- fun z3_options ctxt =
- ["smt.random_seed=" ^ string_of_int (Config.get ctxt SMT2_Config.random_seed),
- "smt.refine_inj_axioms=false",
- "-T:" ^ string_of_int (Real.ceil (Config.get ctxt SMT2_Config.timeout)),
- "-smt2"]
-
- fun select_class ctxt =
- if Config.get ctxt z3_extensions then Z3_New_Interface.smtlib2_z3C
- else SMTLIB2_Interface.smtlib2C
-in
-
-val z3: SMT2_Solver.solver_config = {
- name = "z3",
- class = select_class,
- avail = make_avail "Z3_NEW",
- command = z3_make_command "Z3_NEW",
- options = z3_options,
- smt_options = [(":produce-proofs", "true")],
- default_max_relevant = 350 (* FUDGE *),
- outcome = on_first_line (outcome_of "unsat" "sat" "unknown"),
- parse_proof = SOME Z3_New_Replay.parse_proof,
- replay = SOME Z3_New_Replay.replay }
-
-end
-
-
-(* overall setup *)
-
-val _ = Theory.setup (
- SMT2_Solver.add_solver cvc3 #>
- SMT2_Solver.add_solver cvc4 #>
- SMT2_Solver.add_solver veriT #>
- SMT2_Solver.add_solver z3)
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_translate.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,522 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_translate.ML
- Author: Sascha Boehme, TU Muenchen
-
-Translate theorems into an SMT intermediate format and serialize them.
-*)
-
-signature SMT2_TRANSLATE =
-sig
- (*intermediate term structure*)
- datatype squant = SForall | SExists
- datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
- datatype sterm =
- SVar of int |
- SApp of string * sterm list |
- SLet of string * sterm * sterm |
- SQua of squant * string list * sterm spattern list * sterm
-
- (*translation configuration*)
- type sign = {
- logic: string,
- sorts: string list,
- dtyps: (string * (string * (string * string) list) list) list list,
- funcs: (string * (string list * string)) list }
- type config = {
- logic: term list -> string,
- has_datatypes: bool,
- serialize: (string * string) list -> string list -> sign -> sterm list -> string }
- type replay_data = {
- context: Proof.context,
- typs: typ Symtab.table,
- terms: term Symtab.table,
- ll_defs: term list,
- rewrite_rules: thm list,
- assms: (int * thm) list }
-
- (*translation*)
- val add_config: SMT2_Util.class * (Proof.context -> config) -> Context.generic -> Context.generic
- val translate: Proof.context -> (string * string) list -> string list -> (int * thm) list ->
- string * replay_data
-end;
-
-structure SMT2_Translate: SMT2_TRANSLATE =
-struct
-
-
-(* intermediate term structure *)
-
-datatype squant = SForall | SExists
-
-datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
-
-datatype sterm =
- SVar of int |
- SApp of string * sterm list |
- SLet of string * sterm * sterm |
- SQua of squant * string list * sterm spattern list * sterm
-
-
-(* translation configuration *)
-
-type sign = {
- logic: string,
- sorts: string list,
- dtyps: (string * (string * (string * string) list) list) list list,
- funcs: (string * (string list * string)) list }
-
-type config = {
- logic: term list -> string,
- has_datatypes: bool,
- serialize: (string * string) list -> string list -> sign -> sterm list -> string }
-
-type replay_data = {
- context: Proof.context,
- typs: typ Symtab.table,
- terms: term Symtab.table,
- ll_defs: term list,
- rewrite_rules: thm list,
- assms: (int * thm) list }
-
-
-(* translation context *)
-
-fun add_components_of_typ (Type (s, Ts)) =
- cons (Long_Name.base_name s) #> fold_rev add_components_of_typ Ts
- | add_components_of_typ (TFree (s, _)) = cons (perhaps (try (unprefix "'")) s)
- | add_components_of_typ _ = I;
-
-fun suggested_name_of_typ T = space_implode "_" (add_components_of_typ T []);
-
-fun suggested_name_of_term (Const (s, _)) = Long_Name.base_name s
- | suggested_name_of_term (Free (s, _)) = s
- | suggested_name_of_term _ = Name.uu
-
-val empty_tr_context = (Name.context, Typtab.empty, Termtab.empty)
-val safe_suffix = "$"
-
-fun add_typ T proper (cx as (names, typs, terms)) =
- (case Typtab.lookup typs T of
- SOME (name, _) => (name, cx)
- | NONE =>
- let
- val sugg = Name.desymbolize (SOME true) (suggested_name_of_typ T) ^ safe_suffix
- val (name, names') = Name.variant sugg names
- val typs' = Typtab.update (T, (name, proper)) typs
- in (name, (names', typs', terms)) end)
-
-fun add_fun t sort (cx as (names, typs, terms)) =
- (case Termtab.lookup terms t of
- SOME (name, _) => (name, cx)
- | NONE =>
- let
- val sugg = Name.desymbolize (SOME false) (suggested_name_of_term t) ^ safe_suffix
- val (name, names') = Name.variant sugg names
- val terms' = Termtab.update (t, (name, sort)) terms
- in (name, (names', typs, terms')) end)
-
-fun sign_of logic dtyps (_, typs, terms) = {
- logic = logic,
- sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
- dtyps = dtyps,
- funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
-
-fun replay_data_of ctxt ll_defs rules assms (_, typs, terms) =
- let
- fun add_typ (T, (n, _)) = Symtab.update (n, T)
- val typs' = Typtab.fold add_typ typs Symtab.empty
-
- fun add_fun (t, (n, _)) = Symtab.update (n, t)
- val terms' = Termtab.fold add_fun terms Symtab.empty
- in
- {context = ctxt, typs = typs', terms = terms', ll_defs = ll_defs, rewrite_rules = rules,
- assms = assms}
- end
-
-
-(* preprocessing *)
-
-(** datatype declarations **)
-
-fun collect_datatypes_and_records (tr_context, ctxt) ts =
- let
- val (declss, ctxt') = fold (Term.fold_types SMT2_Datatypes.add_decls) ts ([], ctxt)
-
- fun is_decl_typ T = exists (exists (equal T o fst)) declss
-
- fun add_typ' T proper =
- (case SMT2_Builtin.dest_builtin_typ ctxt' T of
- SOME n => pair n
- | NONE => add_typ T proper)
-
- fun tr_select sel =
- let val T = Term.range_type (Term.fastype_of sel)
- in add_fun sel NONE ##>> add_typ' T (not (is_decl_typ T)) end
- fun tr_constr (constr, selects) =
- add_fun constr NONE ##>> fold_map tr_select selects
- fun tr_typ (T, cases) = add_typ' T false ##>> fold_map tr_constr cases
- val (declss', tr_context') = fold_map (fold_map tr_typ) declss tr_context
-
- fun add (constr, selects) =
- Termtab.update (constr, length selects) #>
- fold (Termtab.update o rpair 1) selects
- val funcs = fold (fold (fold add o snd)) declss Termtab.empty
- in ((funcs, declss', tr_context', ctxt'), ts) end
- (* FIXME: also return necessary datatype and record theorems *)
-
-
-(** eta-expand quantifiers, let expressions and built-ins *)
-
-local
- fun eta f T t = Abs (Name.uu, T, f (Term.incr_boundvars 1 t $ Bound 0))
-
- fun exp f T = eta f (Term.domain_type (Term.domain_type T))
-
- fun exp2 T q =
- let val U = Term.domain_type T
- in Abs (Name.uu, U, q $ eta I (Term.domain_type U) (Bound 0)) end
-
- fun expf k i T t =
- let val Ts = drop i (fst (SMT2_Util.dest_funT k T))
- in
- Term.incr_boundvars (length Ts) t
- |> fold_rev (fn i => fn u => u $ Bound i) (0 upto length Ts - 1)
- |> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts
- end
-in
-
-fun eta_expand ctxt funcs =
- let
- fun exp_func t T ts =
- (case Termtab.lookup funcs t of
- SOME k => Term.list_comb (t, ts) |> k <> length ts ? expf k (length ts) T
- | NONE => Term.list_comb (t, ts))
-
- fun expand ((q as Const (@{const_name All}, _)) $ Abs a) = q $ abs_expand a
- | expand ((q as Const (@{const_name All}, T)) $ t) = q $ exp expand T t
- | expand (q as Const (@{const_name All}, T)) = exp2 T q
- | expand ((q as Const (@{const_name Ex}, _)) $ Abs a) = q $ abs_expand a
- | expand ((q as Const (@{const_name Ex}, T)) $ t) = q $ exp expand T t
- | expand (q as Const (@{const_name Ex}, T)) = exp2 T q
- | expand (Const (@{const_name Let}, _) $ t $ u) = expand (Term.betapply (u, t))
- | expand (Const (@{const_name Let}, T) $ t) =
- let val U = Term.domain_type (Term.range_type T)
- in Abs (Name.uu, U, Bound 0 $ Term.incr_boundvars 1 t) end
- | expand (Const (@{const_name Let}, T)) =
- let val U = Term.domain_type (Term.range_type T)
- in Abs (Name.uu, Term.domain_type T, Abs (Name.uu, U, Bound 0 $ Bound 1)) end
- | expand t =
- (case Term.strip_comb t of
- (u as Const (c as (_, T)), ts) =>
- (case SMT2_Builtin.dest_builtin ctxt c ts of
- SOME (_, k, us, mk) =>
- if k = length us then mk (map expand us)
- else if k < length us then chop k (map expand us) |>> mk |> Term.list_comb
- else expf k (length ts) T (mk (map expand us))
- | NONE => exp_func u T (map expand ts))
- | (u as Free (_, T), ts) => exp_func u T (map expand ts)
- | (Abs a, ts) => Term.list_comb (abs_expand a, map expand ts)
- | (u, ts) => Term.list_comb (u, map expand ts))
-
- and abs_expand (n, T, t) = Abs (n, T, expand t)
-
- in map expand end
-
-end
-
-
-(** introduce explicit applications **)
-
-local
- (*
- Make application explicit for functions with varying number of arguments.
- *)
-
- fun add t i = apfst (Termtab.map_default (t, i) (Integer.min i))
- fun add_type T = apsnd (Typtab.update (T, ()))
-
- fun min_arities t =
- (case Term.strip_comb t of
- (u as Const _, ts) => add u (length ts) #> fold min_arities ts
- | (u as Free _, ts) => add u (length ts) #> fold min_arities ts
- | (Abs (_, T, u), ts) => (can dest_funT T ? add_type T) #> min_arities u #> fold min_arities ts
- | (_, ts) => fold min_arities ts)
-
- fun minimize types t i =
- let
- fun find_min j [] _ = j
- | find_min j (U :: Us) T =
- if Typtab.defined types T then j else find_min (j + 1) Us (U --> T)
-
- val (Ts, T) = Term.strip_type (Term.type_of t)
- in find_min 0 (take i (rev Ts)) T end
-
- fun app u (t, T) = (Const (@{const_name fun_app}, T --> T) $ t $ u, Term.range_type T)
-
- fun apply i t T ts =
- let
- val (ts1, ts2) = chop i ts
- val (_, U) = SMT2_Util.dest_funT i T
- in fst (fold app ts2 (Term.list_comb (t, ts1), U)) end
-in
-
-fun intro_explicit_application ctxt funcs ts =
- let
- val (arities, types) = fold min_arities ts (Termtab.empty, Typtab.empty)
- val arities' = Termtab.map (minimize types) arities (* FIXME: highly suspicious *)
-
- fun app_func t T ts =
- if is_some (Termtab.lookup funcs t) then Term.list_comb (t, ts)
- else apply (the (Termtab.lookup arities' t)) t T ts
-
- fun in_list T f t = SMT2_Util.mk_symb_list T (map f (SMT2_Util.dest_symb_list t))
-
- fun traverse Ts t =
- (case Term.strip_comb t of
- (q as Const (@{const_name All}, _), [Abs (x, T, u)]) =>
- q $ Abs (x, T, in_trigger (T :: Ts) u)
- | (q as Const (@{const_name Ex}, _), [Abs (x, T, u)]) =>
- q $ Abs (x, T, in_trigger (T :: Ts) u)
- | (q as Const (@{const_name Let}, _), [u1, u2 as Abs _]) =>
- q $ traverse Ts u1 $ traverse Ts u2
- | (u as Const (c as (_, T)), ts) =>
- (case SMT2_Builtin.dest_builtin ctxt c ts of
- SOME (_, k, us, mk) =>
- let
- val (ts1, ts2) = chop k (map (traverse Ts) us)
- val U = Term.strip_type T |>> snd o chop k |> (op --->)
- in apply 0 (mk ts1) U ts2 end
- | NONE => app_func u T (map (traverse Ts) ts))
- | (u as Free (_, T), ts) => app_func u T (map (traverse Ts) ts)
- | (u as Bound i, ts) => apply 0 u (nth Ts i) (map (traverse Ts) ts)
- | (Abs (n, T, u), ts) => traverses Ts (Abs (n, T, traverse (T::Ts) u)) ts
- | (u, ts) => traverses Ts u ts)
- and in_trigger Ts ((c as @{const trigger}) $ p $ t) = c $ in_pats Ts p $ traverse Ts t
- | in_trigger Ts t = traverse Ts t
- and in_pats Ts ps =
- in_list @{typ "pattern symb_list"} (in_list @{typ pattern} (in_pat Ts)) ps
- and in_pat Ts ((p as Const (@{const_name pat}, _)) $ t) = p $ traverse Ts t
- | in_pat Ts ((p as Const (@{const_name nopat}, _)) $ t) = p $ traverse Ts t
- | in_pat _ t = raise TERM ("bad pattern", [t])
- and traverses Ts t ts = Term.list_comb (t, map (traverse Ts) ts)
- in map (traverse []) ts end
-
-val fun_app_eq = mk_meta_eq @{thm fun_app_def}
-
-end
-
-
-(** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
-
-local
- val is_quant = member (op =) [@{const_name All}, @{const_name Ex}]
-
- val fol_rules = [
- Let_def,
- @{lemma "P = True == P" by (rule eq_reflection) simp},
- @{lemma "if P then True else False == P" by (rule eq_reflection) simp}]
-
- exception BAD_PATTERN of unit
-
- fun wrap_in_if pat t =
- if pat then raise BAD_PATTERN () else @{const If (bool)} $ t $ @{const True} $ @{const False}
-
- fun is_builtin_conn_or_pred ctxt c ts =
- is_some (SMT2_Builtin.dest_builtin_conn ctxt c ts) orelse
- is_some (SMT2_Builtin.dest_builtin_pred ctxt c ts)
-in
-
-fun folify ctxt =
- let
- fun in_list T f t = SMT2_Util.mk_symb_list T (map_filter f (SMT2_Util.dest_symb_list t))
-
- fun in_term pat t =
- (case Term.strip_comb t of
- (@{const True}, []) => t
- | (@{const False}, []) => t
- | (u as Const (@{const_name If}, _), [t1, t2, t3]) =>
- if pat then raise BAD_PATTERN () else u $ in_form t1 $ in_term pat t2 $ in_term pat t3
- | (Const (c as (n, _)), ts) =>
- if is_builtin_conn_or_pred ctxt c ts then wrap_in_if pat (in_form t)
- else if is_quant n then wrap_in_if pat (in_form t)
- else Term.list_comb (Const c, map (in_term pat) ts)
- | (Free c, ts) => Term.list_comb (Free c, map (in_term pat) ts)
- | _ => t)
-
- and in_pat ((p as Const (@{const_name pat}, _)) $ t) =
- p $ in_term true t
- | in_pat ((p as Const (@{const_name nopat}, _)) $ t) =
- p $ in_term true t
- | in_pat t = raise TERM ("bad pattern", [t])
-
- and in_pats ps =
- in_list @{typ "pattern symb_list"} (SOME o in_list @{typ pattern} (try in_pat)) ps
-
- and in_trigger ((c as @{const trigger}) $ p $ t) = c $ in_pats p $ in_form t
- | in_trigger t = in_form t
-
- and in_form t =
- (case Term.strip_comb t of
- (q as Const (qn, _), [Abs (n, T, u)]) =>
- if is_quant qn then q $ Abs (n, T, in_trigger u)
- else in_term false t
- | (Const c, ts) =>
- (case SMT2_Builtin.dest_builtin_conn ctxt c ts of
- SOME (_, _, us, mk) => mk (map in_form us)
- | NONE =>
- (case SMT2_Builtin.dest_builtin_pred ctxt c ts of
- SOME (_, _, us, mk) => mk (map (in_term false) us)
- | NONE => in_term false t))
- | _ => in_term false t)
- in
- map in_form #>
- pair (fol_rules, I)
- end
-
-end
-
-
-(* translation into intermediate format *)
-
-(** utility functions **)
-
-val quantifier = (fn
- @{const_name All} => SOME SForall
- | @{const_name Ex} => SOME SExists
- | _ => NONE)
-
-fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
- if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
- | group_quant _ Ts t = (Ts, t)
-
-fun dest_pat (Const (@{const_name pat}, _) $ t) = (t, true)
- | dest_pat (Const (@{const_name nopat}, _) $ t) = (t, false)
- | dest_pat t = raise TERM ("bad pattern", [t])
-
-fun dest_pats [] = I
- | dest_pats ts =
- (case map dest_pat ts |> split_list ||> distinct (op =) of
- (ps, [true]) => cons (SPat ps)
- | (ps, [false]) => cons (SNoPat ps)
- | _ => raise TERM ("bad multi-pattern", ts))
-
-fun dest_trigger (@{const trigger} $ tl $ t) =
- (rev (fold (dest_pats o SMT2_Util.dest_symb_list) (SMT2_Util.dest_symb_list tl) []), t)
- | dest_trigger t = ([], t)
-
-fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
- let
- val (Ts, u) = group_quant qn [T] t
- val (ps, p) = dest_trigger u
- in (q, rev Ts, ps, p) end)
-
-fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
- | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
-
-
-(** translation from Isabelle terms into SMT intermediate terms **)
-
-fun intermediate logic dtyps builtin ctxt ts trx =
- let
- fun transT (T as TFree _) = add_typ T true
- | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
- | transT (T as Type _) =
- (case SMT2_Builtin.dest_builtin_typ ctxt T of
- SOME n => pair n
- | NONE => add_typ T true)
-
- fun app n ts = SApp (n, ts)
-
- fun trans t =
- (case Term.strip_comb t of
- (Const (qn, _), [Abs (_, T, t1)]) =>
- (case dest_quant qn T t1 of
- SOME (q, Ts, ps, b) =>
- fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
- trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', b'))
- | NONE => raise TERM ("unsupported quantifier", [t]))
- | (Const (@{const_name Let}, _), [t1, Abs (_, T, t2)]) =>
- transT T ##>> trans t1 ##>> trans t2 #>> (fn ((U, u1), u2) => SLet (U, u1, u2))
- | (u as Const (c as (_, T)), ts) =>
- (case builtin ctxt c ts of
- SOME (n, _, us, _) => fold_map trans us #>> app n
- | NONE => transs u T ts)
- | (u as Free (_, T), ts) => transs u T ts
- | (Bound i, []) => pair (SVar i)
- | _ => raise TERM ("bad SMT term", [t]))
-
- and transs t T ts =
- let val (Us, U) = SMT2_Util.dest_funT (length ts) T
- in
- fold_map transT Us ##>> transT U #-> (fn Up =>
- add_fun t (SOME Up) ##>> fold_map trans ts #>> SApp)
- end
-
- val (us, trx') = fold_map trans ts trx
- in ((sign_of (logic ts) dtyps trx', us), trx') end
-
-
-(* translation *)
-
-structure Configs = Generic_Data
-(
- type T = (Proof.context -> config) SMT2_Util.dict
- val empty = []
- val extend = I
- fun merge data = SMT2_Util.dict_merge fst data
-)
-
-fun add_config (cs, cfg) = Configs.map (SMT2_Util.dict_update (cs, cfg))
-
-fun get_config ctxt =
- let val cs = SMT2_Config.solver_class_of ctxt
- in
- (case SMT2_Util.dict_get (Configs.get (Context.Proof ctxt)) cs of
- SOME cfg => cfg ctxt
- | NONE => error ("SMT: no translation configuration found " ^
- "for solver class " ^ quote (SMT2_Util.string_of_class cs)))
- end
-
-fun translate ctxt smt_options comments ithms =
- let
- val {logic, has_datatypes, serialize} = get_config ctxt
-
- fun no_dtyps (tr_context, ctxt) ts =
- ((Termtab.empty, [], tr_context, ctxt), ts)
-
- val ts1 = map (Envir.beta_eta_contract o SMT2_Util.prop_of o snd) ithms
-
- val ((funcs, dtyps, tr_context, ctxt1), ts2) =
- ((empty_tr_context, ctxt), ts1)
- |-> (if has_datatypes then collect_datatypes_and_records else no_dtyps)
-
- fun is_binder (Const (@{const_name Let}, _) $ _) = true
- | is_binder t = Lambda_Lifting.is_quantifier t
-
- fun mk_trigger ((q as Const (@{const_name All}, _)) $ Abs (n, T, t)) =
- q $ Abs (n, T, mk_trigger t)
- | mk_trigger (eq as (Const (@{const_name HOL.eq}, T) $ lhs $ _)) =
- Term.domain_type T --> @{typ pattern}
- |> (fn T => Const (@{const_name pat}, T) $ lhs)
- |> SMT2_Util.mk_symb_list @{typ pattern} o single
- |> SMT2_Util.mk_symb_list @{typ "pattern symb_list"} o single
- |> (fn t => @{const trigger} $ t $ eq)
- | mk_trigger t = t
-
- val (ctxt2, (ts3, ll_defs)) =
- ts2
- |> eta_expand ctxt1 funcs
- |> rpair ctxt1
- |-> Lambda_Lifting.lift_lambdas NONE is_binder
- |-> (fn (ts', ll_defs) => fn ctxt' =>
- (ctxt', (intro_explicit_application ctxt' funcs (map mk_trigger ll_defs @ ts'), ll_defs)))
-
- val ((rewrite_rules, builtin), ts4) = folify ctxt2 ts3
- |>> apfst (cons fun_app_eq)
- in
- (ts4, tr_context)
- |-> intermediate logic dtyps (builtin SMT2_Builtin.dest_builtin) ctxt2
- |>> uncurry (serialize smt_options comments)
- ||> replay_data_of ctxt2 ll_defs rewrite_rules ithms
- end
-
-end;
--- a/src/HOL/Tools/SMT2/smt2_util.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,246 +0,0 @@
-(* Title: HOL/Tools/SMT2/smt2_util.ML
- Author: Sascha Boehme, TU Muenchen
-
-General utility functions.
-*)
-
-signature SMT2_UTIL =
-sig
- (*basic combinators*)
- val repeat: ('a -> 'a option) -> 'a -> 'a
- val repeat_yield: ('a -> 'b -> ('a * 'b) option) -> 'a -> 'b -> 'a * 'b
-
- (*class dictionaries*)
- type class = string list
- val basicC: class
- val string_of_class: class -> string
- type 'a dict = (class * 'a) Ord_List.T
- val dict_map_default: class * 'a -> ('a -> 'a) -> 'a dict -> 'a dict
- val dict_update: class * 'a -> 'a dict -> 'a dict
- val dict_merge: ('a * 'a -> 'a) -> 'a dict * 'a dict -> 'a dict
- val dict_lookup: 'a dict -> class -> 'a list
- val dict_get: 'a dict -> class -> 'a option
-
- (*types*)
- val dest_funT: int -> typ -> typ list * typ
-
- (*terms*)
- val dest_conj: term -> term * term
- val dest_disj: term -> term * term
- val under_quant: (term -> 'a) -> term -> 'a
- val is_number: term -> bool
-
- (*symbolic lists*)
- val symb_nil_const: typ -> term
- val symb_cons_const: typ -> term
- val mk_symb_list: typ -> term list -> term
- val dest_symb_list: term -> term list
-
- (*patterns and instantiations*)
- val mk_const_pat: theory -> string -> (ctyp -> 'a) -> 'a * cterm
- val destT1: ctyp -> ctyp
- val destT2: ctyp -> ctyp
- val instTs: ctyp list -> ctyp list * cterm -> cterm
- val instT: ctyp -> ctyp * cterm -> cterm
- val instT': cterm -> ctyp * cterm -> cterm
-
- (*certified terms*)
- val certify: Proof.context -> term -> cterm
- val typ_of: cterm -> typ
- val dest_cabs: cterm -> Proof.context -> cterm * Proof.context
- val dest_all_cabs: cterm -> Proof.context -> cterm * Proof.context
- val dest_cbinder: cterm -> Proof.context -> cterm * Proof.context
- val dest_all_cbinders: cterm -> Proof.context -> cterm * Proof.context
- val mk_cprop: cterm -> cterm
- val dest_cprop: cterm -> cterm
- val mk_cequals: cterm -> cterm -> cterm
- val term_of: cterm -> term
- val prop_of: thm -> term
-
- (*conversions*)
- val if_conv: (term -> bool) -> conv -> conv -> conv
- val if_true_conv: (term -> bool) -> conv -> conv
- val if_exists_conv: (term -> bool) -> conv -> conv
- val binders_conv: (Proof.context -> conv) -> Proof.context -> conv
- val under_quant_conv: (Proof.context * cterm list -> conv) ->
- Proof.context -> conv
- val prop_conv: conv -> conv
-end;
-
-structure SMT2_Util: SMT2_UTIL =
-struct
-
-(* basic combinators *)
-
-fun repeat f =
- let fun rep x = (case f x of SOME y => rep y | NONE => x)
- in rep end
-
-fun repeat_yield f =
- let fun rep x y = (case f x y of SOME (x', y') => rep x' y' | NONE => (x, y))
- in rep end
-
-
-(* class dictionaries *)
-
-type class = string list
-
-val basicC = []
-
-fun string_of_class [] = "basic"
- | string_of_class cs = "basic." ^ space_implode "." cs
-
-type 'a dict = (class * 'a) Ord_List.T
-
-fun class_ord ((cs1, _), (cs2, _)) =
- rev_order (list_ord fast_string_ord (cs1, cs2))
-
-fun dict_insert (cs, x) d =
- if AList.defined (op =) d cs then d
- else Ord_List.insert class_ord (cs, x) d
-
-fun dict_map_default (cs, x) f =
- dict_insert (cs, x) #> AList.map_entry (op =) cs f
-
-fun dict_update (e as (_, x)) = dict_map_default e (K x)
-
-fun dict_merge val_merge = sort class_ord o AList.join (op =) (K val_merge)
-
-fun dict_lookup d cs =
- let fun match (cs', x) = if is_prefix (op =) cs' cs then SOME x else NONE
- in map_filter match d end
-
-fun dict_get d cs =
- (case AList.lookup (op =) d cs of
- NONE => (case cs of [] => NONE | _ => dict_get d (take (length cs - 1) cs))
- | SOME x => SOME x)
-
-
-(* types *)
-
-val dest_funT =
- let
- fun dest Ts 0 T = (rev Ts, T)
- | dest Ts i (Type ("fun", [T, U])) = dest (T::Ts) (i-1) U
- | dest _ _ T = raise TYPE ("not a function type", [T], [])
- in dest [] end
-
-
-(* terms *)
-
-fun dest_conj (@{const HOL.conj} $ t $ u) = (t, u)
- | dest_conj t = raise TERM ("not a conjunction", [t])
-
-fun dest_disj (@{const HOL.disj} $ t $ u) = (t, u)
- | dest_disj t = raise TERM ("not a disjunction", [t])
-
-fun under_quant f t =
- (case t of
- Const (@{const_name All}, _) $ Abs (_, _, u) => under_quant f u
- | Const (@{const_name Ex}, _) $ Abs (_, _, u) => under_quant f u
- | _ => f t)
-
-val is_number =
- let
- fun is_num env (Const (@{const_name Let}, _) $ t $ Abs (_, _, u)) = is_num (t :: env) u
- | is_num env (Bound i) = i < length env andalso is_num env (nth env i)
- | is_num _ t = can HOLogic.dest_number t
- in is_num [] end
-
-
-(* symbolic lists *)
-
-fun symb_listT T = Type (@{type_name symb_list}, [T])
-
-fun symb_nil_const T = Const (@{const_name Symb_Nil}, symb_listT T)
-
-fun symb_cons_const T =
- let val listT = symb_listT T in Const (@{const_name Symb_Cons}, T --> listT --> listT) end
-
-fun mk_symb_list T ts =
- fold_rev (fn t => fn u => symb_cons_const T $ t $ u) ts (symb_nil_const T)
-
-fun dest_symb_list (Const (@{const_name Symb_Nil}, _)) = []
- | dest_symb_list (Const (@{const_name Symb_Cons}, _) $ t $ u) = t :: dest_symb_list u
-
-
-(* patterns and instantiations *)
-
-fun mk_const_pat thy name destT =
- let val cpat = Thm.cterm_of thy (Const (name, Sign.the_const_type thy name))
- in (destT (Thm.ctyp_of_term cpat), cpat) end
-
-val destT1 = hd o Thm.dest_ctyp
-val destT2 = hd o tl o Thm.dest_ctyp
-
-fun instTs cUs (cTs, ct) = Thm.instantiate_cterm (cTs ~~ cUs, []) ct
-fun instT cU (cT, ct) = instTs [cU] ([cT], ct)
-fun instT' ct = instT (Thm.ctyp_of_term ct)
-
-
-(* certified terms *)
-
-fun certify ctxt = Thm.cterm_of (Proof_Context.theory_of ctxt)
-
-fun typ_of ct = #T (Thm.rep_cterm ct)
-
-fun dest_cabs ct ctxt =
- (case Thm.term_of ct of
- Abs _ =>
- let val (n, ctxt') = yield_singleton Variable.variant_fixes Name.uu ctxt
- in (snd (Thm.dest_abs (SOME n) ct), ctxt') end
- | _ => raise CTERM ("no abstraction", [ct]))
-
-val dest_all_cabs = repeat_yield (try o dest_cabs)
-
-fun dest_cbinder ct ctxt =
- (case Thm.term_of ct of
- Const _ $ Abs _ => dest_cabs (Thm.dest_arg ct) ctxt
- | _ => raise CTERM ("not a binder", [ct]))
-
-val dest_all_cbinders = repeat_yield (try o dest_cbinder)
-
-val mk_cprop = Thm.apply (Thm.cterm_of @{theory} @{const Trueprop})
-
-fun dest_cprop ct =
- (case Thm.term_of ct of
- @{const Trueprop} $ _ => Thm.dest_arg ct
- | _ => raise CTERM ("not a property", [ct]))
-
-val equals = mk_const_pat @{theory} @{const_name Pure.eq} destT1
-fun mk_cequals ct cu = Thm.mk_binop (instT' ct equals) ct cu
-
-val dest_prop = (fn @{const Trueprop} $ t => t | t => t)
-fun term_of ct = dest_prop (Thm.term_of ct)
-fun prop_of thm = dest_prop (Thm.prop_of thm)
-
-
-(* conversions *)
-
-fun if_conv pred cv1 cv2 ct = if pred (Thm.term_of ct) then cv1 ct else cv2 ct
-
-fun if_true_conv pred cv = if_conv pred cv Conv.all_conv
-
-fun if_exists_conv pred = if_true_conv (Term.exists_subterm pred)
-
-fun binders_conv cv ctxt =
- Conv.binder_conv (binders_conv cv o snd) ctxt else_conv cv ctxt
-
-fun under_quant_conv cv ctxt =
- let
- fun quant_conv inside ctxt cvs ct =
- (case Thm.term_of ct of
- Const (@{const_name All}, _) $ Abs _ =>
- Conv.binder_conv (under_conv cvs) ctxt
- | Const (@{const_name Ex}, _) $ Abs _ =>
- Conv.binder_conv (under_conv cvs) ctxt
- | _ => if inside then cv (ctxt, cvs) else Conv.all_conv) ct
- and under_conv cvs (cv, ctxt) = quant_conv true ctxt (cv :: cvs)
- in quant_conv false ctxt [] end
-
-fun prop_conv cv ct =
- (case Thm.term_of ct of
- @{const Trueprop} $ _ => Conv.arg_conv cv ct
- | _ => raise CTERM ("not a property", [ct]))
-
-end;
--- a/src/HOL/Tools/SMT2/smtlib2.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,191 +0,0 @@
-(* Title: HOL/Tools/SMT2/smtlib2.ML
- Author: Sascha Boehme, TU Muenchen
-
-Parsing and generating SMT-LIB 2.
-*)
-
-signature SMTLIB2 =
-sig
- exception PARSE of int * string
- datatype tree =
- Num of int |
- Dec of int * int |
- Str of string |
- Sym of string |
- Key of string |
- S of tree list
- val parse: string list -> tree
- val pretty_tree: tree -> Pretty.T
- val str_of: tree -> string
-end;
-
-structure SMTLIB2: SMTLIB2 =
-struct
-
-(* data structures *)
-
-exception PARSE of int * string
-
-datatype tree =
- Num of int |
- Dec of int * int |
- Str of string |
- Sym of string |
- Key of string |
- S of tree list
-
-datatype unfinished = None | String of string | Symbol of string
-
-
-(* utilities *)
-
-fun read_raw pred l cs =
- (case take_prefix pred cs of
- ([], []) => raise PARSE (l, "empty token")
- | ([], c :: _) => raise PARSE (l, "unexpected character " ^ quote c)
- | x => x)
-
-
-(* numerals and decimals *)
-
-fun int_of cs = fst (read_int cs)
-
-fun read_num l cs =
- (case read_raw Symbol.is_ascii_digit l cs of
- (cs1, "." :: cs') =>
- let val (cs2, cs'') = read_raw Symbol.is_ascii_digit l cs'
- in (Dec (int_of cs1, int_of cs2), cs'') end
- | (cs1, cs2) => (Num (int_of cs1), cs2))
-
-
-(* binary numbers *)
-
-fun is_bin c = (c = "0" orelse c = "1")
-
-fun read_bin l cs = read_raw is_bin l cs |>> Num o fst o read_radix_int 2
-
-
-(* hex numbers *)
-
-val is_hex = member (op =) (raw_explode "0123456789abcdefABCDEF")
-
-fun within c1 c2 c = (ord c1 <= ord c andalso ord c <= ord c2)
-
-fun unhex i [] = i
- | unhex i (c :: cs) =
- if within "0" "9" c then unhex (i * 16 + (ord c - ord "0")) cs
- else if within "a" "f" c then unhex (i * 16 + (ord c - ord "a" + 10)) cs
- else if within "A" "F" c then unhex (i * 16 + (ord c - ord "A" + 10)) cs
- else raise Fail ("bad hex character " ^ quote c)
-
-fun read_hex l cs = read_raw is_hex l cs |>> Num o unhex 0
-
-
-(* symbols *)
-
-val symbol_chars = raw_explode "~!@$%^&*_+=<>.?/-"
-
-fun is_sym c =
- Symbol.is_ascii_letter c orelse
- Symbol.is_ascii_digit c orelse
- member (op =) symbol_chars c
-
-fun read_sym f l cs = read_raw is_sym l cs |>> f o implode
-
-
-(* quoted tokens *)
-
-fun read_quoted stop (escape, replacement) cs =
- let
- fun read _ [] = NONE
- | read rs (cs as (c :: cs')) =
- if is_prefix (op =) stop cs then
- SOME (implode (rev rs), drop (length stop) cs)
- else if not (null escape) andalso is_prefix (op =) escape cs then
- read (replacement :: rs) (drop (length escape) cs)
- else read (c :: rs) cs'
- in read [] cs end
-
-fun read_string cs = read_quoted ["\\", "\""] (["\\", "\\"], "\\") cs
-fun read_symbol cs = read_quoted ["|"] ([], "") cs
-
-
-(* core parser *)
-
-fun read _ [] rest tss = (rest, tss)
- | read l ("(" :: cs) None tss = read l cs None ([] :: tss)
- | read l (")" :: cs) None (ts1 :: ts2 :: tss) =
- read l cs None ((S (rev ts1) :: ts2) :: tss)
- | read l ("#" :: "x" :: cs) None (ts :: tss) =
- token read_hex l cs ts tss
- | read l ("#" :: "b" :: cs) None (ts :: tss) =
- token read_bin l cs ts tss
- | read l (":" :: cs) None (ts :: tss) =
- token (read_sym Key) l cs ts tss
- | read l ("\"" :: cs) None (ts :: tss) =
- quoted read_string String Str l "" cs ts tss
- | read l ("|" :: cs) None (ts :: tss) =
- quoted read_symbol Symbol Sym l "" cs ts tss
- | read l ((c as "!") :: cs) None (ts :: tss) =
- token (fn _ => pair (Sym c)) l cs ts tss
- | read l (c :: cs) None (ts :: tss) =
- if Symbol.is_ascii_blank c then read l cs None (ts :: tss)
- else if Symbol.is_digit c then token read_num l (c :: cs) ts tss
- else token (read_sym Sym) l (c :: cs) ts tss
- | read l cs (String s) (ts :: tss) =
- quoted read_string String Str l s cs ts tss
- | read l cs (Symbol s) (ts :: tss) =
- quoted read_symbol Symbol Sym l s cs ts tss
- | read l _ _ [] = raise PARSE (l, "bad parser state")
-
-and token f l cs ts tss =
- let val (t, cs') = f l cs
- in read l cs' None ((t :: ts) :: tss) end
-
-and quoted r f g l s cs ts tss =
- (case r cs of
- NONE => (f (s ^ implode cs), ts :: tss)
- | SOME (s', cs') => read l cs' None ((g (s ^ s') :: ts) :: tss))
-
-
-
-(* overall parser *)
-
-fun read_line l line = read l (raw_explode line)
-
-fun add_line line (l, (None, tss)) =
- if size line = 0 orelse nth_string line 0 = ";" then (l + 1, (None, tss))
- else (l + 1, read_line l line None tss)
- | add_line line (l, (unfinished, tss)) =
- (l + 1, read_line l line unfinished tss)
-
-fun finish (_, (None, [[t]])) = t
- | finish (l, _) = raise PARSE (l, "bad nesting")
-
-fun parse lines = finish (fold add_line lines (1, (None, [[]])))
-
-
-(* pretty printer *)
-
-fun pretty_tree (Num i) = Pretty.str (string_of_int i)
- | pretty_tree (Dec (i, j)) =
- Pretty.str (string_of_int i ^ "." ^ string_of_int j)
- | pretty_tree (Str s) =
- raw_explode s
- |> maps (fn "\"" => ["\\", "\""] | "\\" => ["\\", "\\"] | c => [c])
- |> implode
- |> enclose "\"" "\""
- |> Pretty.str
- | pretty_tree (Sym s) =
- if String.isPrefix "(" s (* for bit vector functions *) orelse
- forall is_sym (raw_explode s) then
- Pretty.str s
- else
- Pretty.str ("|" ^ s ^ "|")
- | pretty_tree (Key s) = Pretty.str (":" ^ s)
- | pretty_tree (S trees) =
- Pretty.enclose "(" ")" (Pretty.separate "" (map pretty_tree trees))
-
-val str_of = Pretty.str_of o pretty_tree
-
-end;
--- a/src/HOL/Tools/SMT2/smtlib2_interface.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,164 +0,0 @@
-(* Title: HOL/Tools/SMT2/smtlib2_interface.ML
- Author: Sascha Boehme, TU Muenchen
- Author: Jasmin Blanchette, TU Muenchen
-
-Interface to SMT solvers based on the SMT-LIB 2 format.
-*)
-
-signature SMTLIB2_INTERFACE =
-sig
- val smtlib2C: SMT2_Util.class
- val add_logic: int * (term list -> string option) -> Context.generic -> Context.generic
- val translate_config: Proof.context -> SMT2_Translate.config
- val assert_index_of_name: string -> int
- val assert_prefix : string
-end;
-
-structure SMTLIB2_Interface: SMTLIB2_INTERFACE =
-struct
-
-val smtlib2C = ["smtlib2"]
-
-
-(* builtins *)
-
-local
- fun int_num _ i = SOME (string_of_int i)
-
- fun is_linear [t] = SMT2_Util.is_number t
- | is_linear [t, u] = SMT2_Util.is_number t orelse SMT2_Util.is_number u
- | is_linear _ = false
-
- fun times _ _ ts =
- let val mk = Term.list_comb o pair @{const times (int)}
- in if is_linear ts then SOME ("*", 2, ts, mk) else NONE end
-in
-
-val setup_builtins =
- fold (SMT2_Builtin.add_builtin_typ smtlib2C) [
- (@{typ bool}, K (SOME "Bool"), K (K NONE)),
- (@{typ int}, K (SOME "Int"), int_num)] #>
- fold (SMT2_Builtin.add_builtin_fun' smtlib2C) [
- (@{const True}, "true"),
- (@{const False}, "false"),
- (@{const Not}, "not"),
- (@{const HOL.conj}, "and"),
- (@{const HOL.disj}, "or"),
- (@{const HOL.implies}, "=>"),
- (@{const HOL.eq ('a)}, "="),
- (@{const If ('a)}, "ite"),
- (@{const less (int)}, "<"),
- (@{const less_eq (int)}, "<="),
- (@{const uminus (int)}, "-"),
- (@{const plus (int)}, "+"),
- (@{const minus (int)}, "-")] #>
- SMT2_Builtin.add_builtin_fun smtlib2C
- (Term.dest_Const @{const times (int)}, times)
-
-end
-
-
-(* serialization *)
-
-(** logic **)
-
-fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
-
-structure Logics = Generic_Data
-(
- type T = (int * (term list -> string option)) list
- val empty = []
- val extend = I
- fun merge data = Ord_List.merge fst_int_ord data
-)
-
-fun add_logic pf = Logics.map (Ord_List.insert fst_int_ord pf)
-
-fun choose_logic ctxt ts =
- let
- fun choose [] = "AUFLIA"
- | choose ((_, f) :: fs) = (case f ts of SOME s => s | NONE => choose fs)
- in
- (case choose (Logics.get (Context.Proof ctxt)) of
- "" => "" (* for default Z3 logic, a subset of everything *)
- | logic => "(set-logic " ^ logic ^ ")\n")
- end
-
-
-(** serialization **)
-
-fun var i = "?v" ^ string_of_int i
-
-fun tree_of_sterm l (SMT2_Translate.SVar i) = SMTLIB2.Sym (var (l - i - 1))
- | tree_of_sterm _ (SMT2_Translate.SApp (n, [])) = SMTLIB2.Sym n
- | tree_of_sterm l (SMT2_Translate.SApp (n, ts)) =
- SMTLIB2.S (SMTLIB2.Sym n :: map (tree_of_sterm l) ts)
- | tree_of_sterm _ (SMT2_Translate.SLet _) =
- raise Fail "SMT-LIB: unsupported let expression"
- | tree_of_sterm l (SMT2_Translate.SQua (q, ss, pats, t)) =
- let
- val l' = l + length ss
-
- fun quant_name SMT2_Translate.SForall = "forall"
- | quant_name SMT2_Translate.SExists = "exists"
-
- fun gen_trees_of_pat keyword ps =
- [SMTLIB2.Key keyword, (case map (tree_of_sterm l') ps of [t] => t | ts => SMTLIB2.S ts)]
- fun trees_of_pat (SMT2_Translate.SPat ps) = gen_trees_of_pat "pattern" ps
- | trees_of_pat (SMT2_Translate.SNoPat ps) = gen_trees_of_pat "no-pattern" ps
- fun tree_of_pats [] t = t
- | tree_of_pats pats t = SMTLIB2.S (SMTLIB2.Sym "!" :: t :: maps trees_of_pat pats)
-
- val vs = map_index (fn (i, ty) =>
- SMTLIB2.S [SMTLIB2.Sym (var (l + i)), SMTLIB2.Sym ty]) ss
-
- val body = t
- |> tree_of_sterm l'
- |> tree_of_pats pats
- in
- SMTLIB2.S [SMTLIB2.Sym (quant_name q), SMTLIB2.S vs, body]
- end
-
-
-fun sctrarg (sel, typ) = "(" ^ sel ^ " " ^ typ ^ ")"
-fun sctr (name, args) = enclose "(" ")" (space_implode " " (name :: map sctrarg args))
-fun sdatatype (name, ctrs) = enclose "(" ")" (space_implode " " (name :: map sctr ctrs))
-
-fun string_of_fun (f, (ss, s)) = f ^ " (" ^ space_implode " " ss ^ ") " ^ s
-
-fun named_sterm s t = SMTLIB2.S [SMTLIB2.Sym "!", t, SMTLIB2.Key "named", SMTLIB2.Sym s]
-
-val assert_prefix = "a"
-
-fun assert_name_of_index i = assert_prefix ^ string_of_int i
-fun assert_index_of_name s = the_default ~1 (Int.fromString (unprefix assert_prefix s))
-
-fun serialize smt_options comments {logic, sorts, dtyps, funcs} ts =
- Buffer.empty
- |> fold (Buffer.add o enclose "; " "\n") comments
- |> fold (fn (k, v) => Buffer.add ("(set-option " ^ k ^ " " ^ v ^ ")\n")) smt_options
- |> Buffer.add logic
- |> fold (Buffer.add o enclose "(declare-sort " " 0)\n") (sort fast_string_ord sorts)
- |> (if null dtyps then I
- else Buffer.add (enclose "(declare-datatypes () (" "))\n"
- (space_implode "\n " (maps (map sdatatype) dtyps))))
- |> fold (Buffer.add o enclose "(declare-fun " ")\n" o string_of_fun)
- (sort (fast_string_ord o pairself fst) funcs)
- |> fold (fn (i, t) => Buffer.add (enclose "(assert " ")\n"
- (SMTLIB2.str_of (named_sterm (assert_name_of_index i) (tree_of_sterm 0 t)))))
- (map_index I ts)
- |> Buffer.add "(check-sat)\n(get-proof)\n"
- |> Buffer.content
-
-(* interface *)
-
-fun translate_config ctxt = {
- logic = choose_logic ctxt,
- has_datatypes = false,
- serialize = serialize}
-
-val _ = Theory.setup (Context.theory_map
- (setup_builtins #>
- SMT2_Translate.add_config (smtlib2C, translate_config)))
-
-end;
--- a/src/HOL/Tools/SMT2/smtlib2_isar.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,71 +0,0 @@
-(* Title: HOL/Tools/SMT2/smtlib2_isar.ML
- Author: Jasmin Blanchette, TU Muenchen
- Author: Mathias Fleury, ENS Rennes
-
-General tools for Isar proof reconstruction.
-*)
-
-signature SMTLIB2_ISAR =
-sig
- val unlift_term: term list -> term -> term
- val postprocess_step_conclusion: theory -> thm list -> term list -> term -> term
- val normalizing_prems : Proof.context -> term -> (string * string list) list
- val distinguish_conjecture_and_hypothesis : ''a list -> ''b -> ''b -> ''b list ->
- (''a * 'c) list -> 'c list -> 'c -> (ATP_Problem.atp_formula_role * 'c) option
- val unskolemize_names: term -> term
-end;
-
-structure SMTLIB2_Isar: SMTLIB2_ISAR =
-struct
-
-open ATP_Util
-open ATP_Problem
-open ATP_Proof_Reconstruct
-
-fun unlift_term ll_defs =
- let
- val lifted = map (ATP_Util.extract_lambda_def dest_Free o ATP_Util.hol_open_form I) ll_defs
-
- fun un_free (t as Free (s, _)) =
- (case AList.lookup (op =) lifted s of
- SOME t => un_term t
- | NONE => t)
- | un_free t = t
- and un_term t = map_aterms un_free t
- in un_term end
-
-(* It is not entirely clear why this should be necessary, especially for abstractions variables. *)
-val unskolemize_names =
- Term.map_abs_vars (perhaps (try Name.dest_skolem))
- #> Term.map_aterms (perhaps (try (fn Free (s, T) => Free (Name.dest_skolem s, T))))
-
-fun postprocess_step_conclusion thy rewrite_rules ll_defs =
- Raw_Simplifier.rewrite_term thy rewrite_rules []
- #> Object_Logic.atomize_term thy
- #> not (null ll_defs) ? unlift_term ll_defs
- #> simplify_bool
- #> unskolemize_names
- #> HOLogic.mk_Trueprop
-
-fun normalizing_prems ctxt concl0 =
- SMT2_Normalize.case_bool_entry :: SMT2_Normalize.special_quant_table @
- SMT2_Normalize.abs_min_max_table
- |> map_filter (fn (c, th) =>
- if exists_Const (curry (op =) c o fst) concl0 then
- let val s = short_thm_name ctxt th in SOME (s, [s]) end
- else
- NONE)
-
-fun distinguish_conjecture_and_hypothesis ss id conjecture_id prem_ids fact_helper_ts hyp_ts
- concl_t =
- (case ss of
- [s] => SOME (Axiom, the (AList.lookup (op =) fact_helper_ts s))
- | _ =>
- if id = conjecture_id then
- SOME (Conjecture, concl_t)
- else
- (case find_index (curry (op =) id) prem_ids of
- ~1 => NONE (* lambda-lifting definition *)
- | i => SOME (Hypothesis, nth hyp_ts i)))
-
-end;
--- a/src/HOL/Tools/SMT2/smtlib2_proof.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,298 +0,0 @@
-(* Title: HOL/Tools/SMT2/smtlib2_proof.ML
- Author: Sascha Boehme, TU Muenchen
- Author: Mathias Fleury, ENS Rennes
- Author: Jasmin Blanchette, TU Muenchen
-
-SMT-LIB-2-style proofs: parsing and abstract syntax tree.
-*)
-
-signature SMTLIB2_PROOF =
-sig
- datatype 'b shared = Tree of SMTLIB2.tree | Term of term | Proof of 'b | None
- type ('a, 'b) context
-
- val mk_context: Proof.context -> int -> 'b shared Symtab.table -> typ Symtab.table ->
- term Symtab.table -> 'a -> ('a, 'b) context
- val empty_context: Proof.context -> typ Symtab.table -> term Symtab.table -> ('a list, 'b) context
- val ctxt_of: ('a, 'b) context -> Proof.context
- val lookup_binding: ('a, 'b) context -> string -> 'b shared
- val update_binding: string * 'b shared -> ('a, 'b) context -> ('a, 'b) context
- val with_bindings: (string * 'b shared) list -> (('a, 'b) context -> 'c * ('d, 'b) context) ->
- ('a, 'b) context -> 'c * ('d, 'b) context
- val next_id: ('a, 'b) context -> int * ('a, 'b) context
- val with_fresh_names: (('a list, 'b) context ->
- term * ((string * (string * typ)) list, 'b) context) -> ('c, 'b) context -> (term * string list)
-
- (*type and term parsers*)
- type type_parser = SMTLIB2.tree * typ list -> typ option
- type term_parser = SMTLIB2.tree * term list -> term option
- val add_type_parser: type_parser -> Context.generic -> Context.generic
- val add_term_parser: term_parser -> Context.generic -> Context.generic
-
- exception SMTLIB2_PARSE of string * SMTLIB2.tree
-
- val declare_fun: string -> typ -> ((string * typ) list, 'a) context ->
- ((string * typ) list, 'a) context
- val dest_binding: SMTLIB2.tree -> string * 'a shared
- val type_of: ('a, 'b) context -> SMTLIB2.tree -> typ
- val term_of: SMTLIB2.tree -> ((string * (string * typ)) list, 'a) context ->
- term * ((string * (string * typ)) list, 'a) context
-end;
-
-structure SMTLIB2_Proof: SMTLIB2_PROOF =
-struct
-
-(* proof parser context *)
-
-datatype 'b shared = Tree of SMTLIB2.tree | Term of term | Proof of 'b | None
-
-type ('a, 'b) context = {
- ctxt: Proof.context,
- id: int,
- syms: 'b shared Symtab.table,
- typs: typ Symtab.table,
- funs: term Symtab.table,
- extra: 'a}
-
-fun mk_context ctxt id syms typs funs extra: ('a, 'b) context =
- {ctxt = ctxt, id = id, syms = syms, typs = typs, funs = funs, extra = extra}
-
-fun empty_context ctxt typs funs = mk_context ctxt 1 Symtab.empty typs funs []
-
-fun ctxt_of ({ctxt, ...}: ('a, 'b) context) = ctxt
-
-fun lookup_binding ({syms, ...}: ('a, 'b) context) =
- the_default None o Symtab.lookup syms
-
-fun map_syms f ({ctxt, id, syms, typs, funs, extra}: ('a, 'b) context) =
- mk_context ctxt id (f syms) typs funs extra
-
-fun update_binding b = map_syms (Symtab.update b)
-
-fun with_bindings bs f cx =
- let val bs' = map (lookup_binding cx o fst) bs
- in
- cx
- |> fold update_binding bs
- |> f
- ||> fold2 (fn (name, _) => update_binding o pair name) bs bs'
- end
-
-fun next_id ({ctxt, id, syms, typs, funs, extra}: ('a, 'b) context) =
- (id, mk_context ctxt (id + 1) syms typs funs extra)
-
-fun with_fresh_names f ({ctxt, id, syms, typs, funs, ...}: ('a, 'b) context) =
- let
- fun bind (_, v as (_, T)) t = Logic.all_const T $ Term.absfree v t
-
- val needs_inferT = equal Term.dummyT orf Term.is_TVar
- val needs_infer = Term.exists_type (Term.exists_subtype needs_inferT)
- fun infer_types ctxt =
- singleton (Type_Infer_Context.infer_types ctxt) #>
- singleton (Proof_Context.standard_term_check_finish ctxt)
- fun infer ctxt t = if needs_infer t then infer_types ctxt t else t
-
- val (t, {ctxt = ctxt', extra = names, ...}: ((string * (string * typ)) list, 'b) context) =
- f (mk_context ctxt id syms typs funs [])
- val t' = infer ctxt' (fold_rev bind names (HOLogic.mk_Trueprop t))
- in
- (t', map fst names)
- end
-
-fun lookup_typ ({typs, ...}: ('a, 'b) context) = Symtab.lookup typs
-fun lookup_fun ({funs, ...}: ('a, 'b) context) = Symtab.lookup funs
-
-
-(* core type and term parser *)
-
-fun core_type_parser (SMTLIB2.Sym "Bool", []) = SOME @{typ HOL.bool}
- | core_type_parser (SMTLIB2.Sym "Int", []) = SOME @{typ Int.int}
- | core_type_parser _ = NONE
-
-fun mk_unary n t =
- let val T = fastype_of t
- in Const (n, T --> T) $ t end
-
-fun mk_binary' n T U t1 t2 = Const (n, [T, T] ---> U) $ t1 $ t2
-
-fun mk_binary n t1 t2 =
- let val T = fastype_of t1
- in mk_binary' n T T t1 t2 end
-
-fun mk_rassoc f t ts =
- let val us = rev (t :: ts)
- in fold f (tl us) (hd us) end
-
-fun mk_lassoc f t ts = fold (fn u1 => fn u2 => f u2 u1) ts t
-
-fun mk_lassoc' n = mk_lassoc (mk_binary n)
-
-fun mk_binary_pred n S t1 t2 =
- let
- val T1 = fastype_of t1
- val T2 = fastype_of t2
- val T =
- if T1 <> Term.dummyT then T1
- else if T2 <> Term.dummyT then T2
- else TVar (("?a", serial ()), S)
- in mk_binary' n T @{typ HOL.bool} t1 t2 end
-
-fun mk_less t1 t2 = mk_binary_pred @{const_name ord_class.less} @{sort linorder} t1 t2
-fun mk_less_eq t1 t2 = mk_binary_pred @{const_name ord_class.less_eq} @{sort linorder} t1 t2
-
-fun core_term_parser (SMTLIB2.Sym "true", _) = SOME @{const HOL.True}
- | core_term_parser (SMTLIB2.Sym "false", _) = SOME @{const HOL.False}
- | core_term_parser (SMTLIB2.Sym "not", [t]) = SOME (HOLogic.mk_not t)
- | core_term_parser (SMTLIB2.Sym "and", t :: ts) = SOME (mk_rassoc (curry HOLogic.mk_conj) t ts)
- | core_term_parser (SMTLIB2.Sym "or", t :: ts) = SOME (mk_rassoc (curry HOLogic.mk_disj) t ts)
- | core_term_parser (SMTLIB2.Sym "=>", [t1, t2]) = SOME (HOLogic.mk_imp (t1, t2))
- | core_term_parser (SMTLIB2.Sym "implies", [t1, t2]) = SOME (HOLogic.mk_imp (t1, t2))
- | core_term_parser (SMTLIB2.Sym "=", [t1, t2]) = SOME (HOLogic.mk_eq (t1, t2))
- | core_term_parser (SMTLIB2.Sym "~", [t1, t2]) = SOME (HOLogic.mk_eq (t1, t2))
- | core_term_parser (SMTLIB2.Sym "ite", [t1, t2, t3]) =
- let
- val T = fastype_of t2
- val c = Const (@{const_name HOL.If}, [@{typ HOL.bool}, T, T] ---> T)
- in SOME (c $ t1 $ t2 $ t3) end
- | core_term_parser (SMTLIB2.Num i, []) = SOME (HOLogic.mk_number @{typ Int.int} i)
- | core_term_parser (SMTLIB2.Sym "-", [t]) = SOME (mk_unary @{const_name uminus_class.uminus} t)
- | core_term_parser (SMTLIB2.Sym "~", [t]) = SOME (mk_unary @{const_name uminus_class.uminus} t)
- | core_term_parser (SMTLIB2.Sym "+", t :: ts) =
- SOME (mk_lassoc' @{const_name plus_class.plus} t ts)
- | core_term_parser (SMTLIB2.Sym "-", t :: ts) =
- SOME (mk_lassoc' @{const_name minus_class.minus} t ts)
- | core_term_parser (SMTLIB2.Sym "*", t :: ts) =
- SOME (mk_lassoc' @{const_name times_class.times} t ts)
- | core_term_parser (SMTLIB2.Sym "div", [t1, t2]) = SOME (mk_binary @{const_name z3div} t1 t2)
- | core_term_parser (SMTLIB2.Sym "mod", [t1, t2]) = SOME (mk_binary @{const_name z3mod} t1 t2)
- | core_term_parser (SMTLIB2.Sym "<", [t1, t2]) = SOME (mk_less t1 t2)
- | core_term_parser (SMTLIB2.Sym ">", [t1, t2]) = SOME (mk_less t2 t1)
- | core_term_parser (SMTLIB2.Sym "<=", [t1, t2]) = SOME (mk_less_eq t1 t2)
- | core_term_parser (SMTLIB2.Sym ">=", [t1, t2]) = SOME (mk_less_eq t2 t1)
- | core_term_parser _ = NONE
-
-
-(* custom type and term parsers *)
-
-type type_parser = SMTLIB2.tree * typ list -> typ option
-
-type term_parser = SMTLIB2.tree * term list -> term option
-
-fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
-
-structure Parsers = Generic_Data
-(
- type T = (int * type_parser) list * (int * term_parser) list
- val empty : T = ([(serial (), core_type_parser)], [(serial (), core_term_parser)])
- val extend = I
- fun merge ((tys1, ts1), (tys2, ts2)) =
- (Ord_List.merge id_ord (tys1, tys2), Ord_List.merge id_ord (ts1, ts2))
-)
-
-fun add_type_parser type_parser =
- Parsers.map (apfst (Ord_List.insert id_ord (serial (), type_parser)))
-
-fun add_term_parser term_parser =
- Parsers.map (apsnd (Ord_List.insert id_ord (serial (), term_parser)))
-
-fun get_type_parsers ctxt = map snd (fst (Parsers.get (Context.Proof ctxt)))
-fun get_term_parsers ctxt = map snd (snd (Parsers.get (Context.Proof ctxt)))
-
-fun apply_parsers parsers x =
- let
- fun apply [] = NONE
- | apply (parser :: parsers) =
- (case parser x of
- SOME y => SOME y
- | NONE => apply parsers)
- in apply parsers end
-
-
-(* type and term parsing *)
-
-exception SMTLIB2_PARSE of string * SMTLIB2.tree
-
-val desymbolize = Name.desymbolize (SOME false) o perhaps (try (unprefix "?"))
-
-fun fresh_fun add name n T ({ctxt, id, syms, typs, funs, extra}: ('a, 'b) context) =
- let
- val (n', ctxt') = yield_singleton Variable.variant_fixes n ctxt
- val t = Free (n', T)
- val funs' = Symtab.update (name, t) funs
- in (t, mk_context ctxt' id syms typs funs' (add (n', T) extra)) end
-
-fun declare_fun name = snd oo fresh_fun cons name (desymbolize name)
-fun declare_free name = fresh_fun (cons o pair name) name (desymbolize name)
-
-fun parse_type cx ty Ts =
- (case apply_parsers (get_type_parsers (ctxt_of cx)) (ty, Ts) of
- SOME T => T
- | NONE =>
- (case ty of
- SMTLIB2.Sym name =>
- (case lookup_typ cx name of
- SOME T => T
- | NONE => raise SMTLIB2_PARSE ("unknown SMT type", ty))
- | _ => raise SMTLIB2_PARSE ("bad SMT type format", ty)))
-
-fun parse_term t ts cx =
- (case apply_parsers (get_term_parsers (ctxt_of cx)) (t, ts) of
- SOME u => (u, cx)
- | NONE =>
- (case t of
- SMTLIB2.Sym name =>
- (case lookup_fun cx name of
- SOME u => (Term.list_comb (u, ts), cx)
- | NONE =>
- if null ts then declare_free name Term.dummyT cx
- else raise SMTLIB2_PARSE ("bad SMT term", t))
- | _ => raise SMTLIB2_PARSE ("bad SMT term format", t)))
-
-fun type_of cx ty =
- (case try (parse_type cx ty) [] of
- SOME T => T
- | NONE =>
- (case ty of
- SMTLIB2.S (ty' :: tys) => parse_type cx ty' (map (type_of cx) tys)
- | _ => raise SMTLIB2_PARSE ("bad SMT type", ty)))
-
-fun dest_var cx (SMTLIB2.S [SMTLIB2.Sym name, ty]) = (name, (desymbolize name, type_of cx ty))
- | dest_var _ v = raise SMTLIB2_PARSE ("bad SMT quantifier variable format", v)
-
-fun dest_body (SMTLIB2.S (SMTLIB2.Sym "!" :: body :: _)) = dest_body body
- | dest_body body = body
-
-fun dest_binding (SMTLIB2.S [SMTLIB2.Sym name, t]) = (name, Tree t)
- | dest_binding b = raise SMTLIB2_PARSE ("bad SMT let binding format", b)
-
-fun term_of t cx =
- (case t of
- SMTLIB2.S [SMTLIB2.Sym "forall", SMTLIB2.S vars, body] => quant HOLogic.mk_all vars body cx
- | SMTLIB2.S [SMTLIB2.Sym "exists", SMTLIB2.S vars, body] => quant HOLogic.mk_exists vars body cx
- | SMTLIB2.S [SMTLIB2.Sym "let", SMTLIB2.S bindings, body] =>
- with_bindings (map dest_binding bindings) (term_of body) cx
- | SMTLIB2.S (SMTLIB2.Sym "!" :: t :: _) => term_of t cx
- | SMTLIB2.S (f :: args) =>
- cx
- |> fold_map term_of args
- |-> parse_term f
- | SMTLIB2.Sym name =>
- (case lookup_binding cx name of
- Tree u =>
- cx
- |> term_of u
- |-> (fn u' => pair u' o update_binding (name, Term u'))
- | Term u => (u, cx)
- | None => parse_term t [] cx
- | _ => raise SMTLIB2_PARSE ("bad SMT term format", t))
- | _ => parse_term t [] cx)
-
-and quant q vars body cx =
- let val vs = map (dest_var cx) vars
- in
- cx
- |> with_bindings (map (apsnd (Term o Free)) vs) (term_of (dest_body body))
- |>> fold_rev (fn (_, (n, T)) => fn t => q (n, T, t)) vs
- end
-
-end;
--- a/src/HOL/Tools/SMT2/verit_isar.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,59 +0,0 @@
-(* Title: HOL/Tools/SMT2/verit_isar.ML
- Author: Mathias Fleury, TU Muenchen
- Author: Jasmin Blanchette, TU Muenchen
-
-VeriT proofs as generic ATP proofs for Isar proof reconstruction.
-*)
-
-signature VERIT_ISAR =
-sig
- type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
- val atp_proof_of_veriT_proof: Proof.context -> term list -> thm list -> term list -> term ->
- (string * term) list -> int list -> int -> (int * string) list -> VeriT_Proof.veriT_step list ->
- (term, string) ATP_Proof.atp_step list
-end;
-
-structure VeriT_Isar: VERIT_ISAR =
-struct
-
-open ATP_Util
-open ATP_Problem
-open ATP_Proof
-open ATP_Proof_Reconstruct
-open SMTLIB2_Isar
-open VeriT_Proof
-
-fun atp_proof_of_veriT_proof ctxt ll_defs rewrite_rules hyp_ts concl_t fact_helper_ts prem_ids
- conjecture_id fact_helper_ids proof =
- let
- val thy = Proof_Context.theory_of ctxt
- fun steps_of (VeriT_Proof.VeriT_Step {id, rule, prems, concl, ...}) =
- let
- val concl' = postprocess_step_conclusion thy rewrite_rules ll_defs concl
- fun standard_step role = ((id, []), role, concl', rule, map (fn id => (id, [])) prems)
- in
- if rule = veriT_input_rule then
- let val ss = the_list (AList.lookup (op =) fact_helper_ids (the (Int.fromString id))) in
- (case distinguish_conjecture_and_hypothesis ss (the (Int.fromString id))
- conjecture_id prem_ids fact_helper_ts hyp_ts concl_t of
- NONE => []
- | SOME (role0, concl00) =>
- let
- val name0 = (id ^ "a", ss)
- val concl0 = unskolemize_names concl00
- in
- [(name0, role0, concl0, rule, []),
- ((id, []), Plain, concl', veriT_rewrite_rule,
- name0 :: normalizing_prems ctxt concl0)]
- end)
- end
- else if rule = veriT_tmp_ite_elim_rule then
- [standard_step Lemma]
- else
- [standard_step Plain]
- end
- in
- maps steps_of proof
- end
-
-end;
--- a/src/HOL/Tools/SMT2/verit_proof.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,334 +0,0 @@
-(* Title: HOL/Tools/SMT2/verit_proof.ML
- Author: Mathias Fleury, ENS Rennes
- Author: Sascha Boehme, TU Muenchen
-
-VeriT proofs: parsing and abstract syntax tree.
-*)
-
-signature VERIT_PROOF =
-sig
- (*proofs*)
- datatype veriT_step = VeriT_Step of {
- id: string,
- rule: string,
- prems: string list,
- concl: term,
- fixes: string list}
-
- (*proof parser*)
- val parse: typ Symtab.table -> term Symtab.table -> string list ->
- Proof.context -> veriT_step list * Proof.context
-
- val veriT_step_prefix : string
- val veriT_input_rule: string
- val veriT_la_generic_rule : string
- val veriT_rewrite_rule : string
- val veriT_simp_arith_rule : string
- val veriT_tmp_ite_elim_rule : string
- val veriT_tmp_skolemize_rule : string
-end;
-
-structure VeriT_Proof: VERIT_PROOF =
-struct
-
-open SMTLIB2_Proof
-
-datatype veriT_node = VeriT_Node of {
- id: string,
- rule: string,
- prems: string list,
- concl: term,
- bounds: string list}
-
-fun mk_node id rule prems concl bounds =
- VeriT_Node {id = id, rule = rule, prems = prems, concl = concl, bounds = bounds}
-
-datatype veriT_step = VeriT_Step of {
- id: string,
- rule: string,
- prems: string list,
- concl: term,
- fixes: string list}
-
-fun mk_step id rule prems concl fixes =
- VeriT_Step {id = id, rule = rule, prems = prems, concl = concl, fixes = fixes}
-
-val veriT_step_prefix = ".c"
-val veriT_alpha_conv_rule = "tmp_alphaconv"
-val veriT_input_rule = "input"
-val veriT_la_generic_rule = "la_generic"
-val veriT_rewrite_rule = "__rewrite" (* arbitrary *)
-val veriT_simp_arith_rule = "simp_arith"
-val veriT_tmp_ite_elim_rule = "tmp_ite_elim"
-val veriT_tmp_skolemize_rule = "tmp_skolemize"
-
-(* proof parser *)
-
-fun node_of p cx =
- ([], cx)
- ||>> `(with_fresh_names (term_of p))
- |>> snd
-
-(*in order to get Z3-style quantification*)
-fun repair_quantification (SMTLIB2.S (SMTLIB2.Sym "forall" :: l)) =
- let val (quantified_vars, t) = split_last (map repair_quantification l)
- in
- SMTLIB2.S (SMTLIB2.Sym "forall" :: SMTLIB2.S quantified_vars :: t :: [])
- end
- | repair_quantification (SMTLIB2.S (SMTLIB2.Sym "exists" :: l)) =
- let val (quantified_vars, t) = split_last (map repair_quantification l)
- in
- SMTLIB2.S (SMTLIB2.Sym "exists" :: SMTLIB2.S quantified_vars :: t :: [])
- end
- | repair_quantification (SMTLIB2.S l) = SMTLIB2.S (map repair_quantification l)
- | repair_quantification x = x
-
-fun replace_bound_var_by_free_var (q $ Abs (var, ty, u)) free_var =
- (case List.find (fn v => String.isPrefix v var) free_var of
- NONE => q $ Abs (var, ty, replace_bound_var_by_free_var u free_var)
- | SOME _ => replace_bound_var_by_free_var (Term.subst_bound (Free (var, ty), u)) free_var)
- | replace_bound_var_by_free_var (u $ v) free_vars = replace_bound_var_by_free_var u free_vars $
- replace_bound_var_by_free_var v free_vars
- | replace_bound_var_by_free_var u _ = u
-
-fun find_type_in_formula (Abs(v, ty, u)) var_name =
- if String.isPrefix var_name v then SOME ty else find_type_in_formula u var_name
- | find_type_in_formula (u $ v) var_name =
- (case find_type_in_formula u var_name of
- NONE => find_type_in_formula v var_name
- | a => a)
- | find_type_in_formula _ _ = NONE
-
-fun add_bound_variables_to_ctxt cx bounds concl =
- fold (fn a => fn b => update_binding a b)
- (map (fn s => ((s, Term (Free (s, the_default dummyT (find_type_in_formula concl s))))))
- bounds) cx
-
-fun update_step_and_cx (st as VeriT_Node {id, rule, prems, concl, bounds}) cx =
- if rule = veriT_tmp_ite_elim_rule then
- (mk_node id rule prems concl bounds, add_bound_variables_to_ctxt cx bounds concl)
- else if rule = veriT_tmp_skolemize_rule then
- let
- val concl' = replace_bound_var_by_free_var concl bounds
- in
- (mk_node id rule prems concl' [], add_bound_variables_to_ctxt cx bounds concl)
- end
- else
- (st, cx)
-
-(*FIXME: using a reference would be better to know th numbers of the steps to add*)
-fun fix_subproof_steps ((((id_of_father_step, rule), prems), subproof), ((step_concl, bounds),
- cx)) =
- let
- fun mk_prop_of_term concl = (fastype_of concl = @{typ "bool"} ?
- curry (op $) @{term "Trueprop"}) concl
- fun inline_assumption assumption assumption_id (st as VeriT_Node {id, rule, prems, concl,
- bounds}) =
- if List.find (curry (op =) assumption_id) prems <> NONE then
- let
- val prems' = filter_out (curry (op =) assumption_id) prems
- in
- mk_node id rule (filter_out (curry (op =) assumption_id) prems')
- (Const (@{const_name "Pure.imp"}, @{typ "prop"} --> @{typ "prop"} --> @{typ "prop"})
- $ mk_prop_of_term assumption $ mk_prop_of_term concl) bounds
- end
- else
- st
- fun find_input_steps_and_inline [] last_step = ([], last_step)
- | find_input_steps_and_inline (VeriT_Node {id = id', rule, prems, concl, bounds} :: steps)
- last_step =
- if rule = veriT_input_rule then
- find_input_steps_and_inline (map (inline_assumption concl id') steps) last_step
- else
- apfst (cons (mk_node (id_of_father_step ^ id') rule prems concl bounds))
- (find_input_steps_and_inline steps (id_of_father_step ^ id'))
- val (subproof', last_step_id) = find_input_steps_and_inline subproof ""
- val prems' =
- if last_step_id = "" then prems
- else
- (case prems of
- NONE => SOME [last_step_id]
- | SOME l => SOME (last_step_id :: l))
- in
- (subproof', (((((id_of_father_step, rule), prems'), step_concl), bounds), cx))
- end
-
-(*
-(set id rule :clauses(...) :args(..) :conclusion (...)).
-or
-(set id subproof (set ...) :conclusion (...)).
-*)
-
-fun parse_proof_step cx =
- let
- fun rotate_pair (a, (b, c)) = ((a, b), c)
- fun get_id (SMTLIB2.S [SMTLIB2.Sym "set", SMTLIB2.Sym id, SMTLIB2.S l]) = (id, l)
- | get_id t = raise Fail ("unrecognized VeriT Proof" ^ PolyML.makestring t)
- fun parse_rule (SMTLIB2.Sym rule :: l) = (rule, l)
- fun parse_source (SMTLIB2.Key "clauses" :: SMTLIB2.S source ::l) =
- (SOME (map (fn (SMTLIB2.Sym id) => id) source), l)
- | parse_source l = (NONE, l)
- fun parse_subproof cx id_of_father_step ((subproof_step as SMTLIB2.S (SMTLIB2.Sym "set" :: _)) :: l) =
- let val (subproof_steps, cx') = parse_proof_step cx subproof_step in
- apfst (apfst (curry (op @) subproof_steps)) (parse_subproof cx' id_of_father_step l)
- end
- | parse_subproof cx _ l = (([], cx), l)
- fun skip_args (SMTLIB2.Key "args" :: SMTLIB2.S _ :: l) = l
- | skip_args l = l
- fun parse_conclusion (SMTLIB2.Key "conclusion" :: SMTLIB2.S concl :: []) = concl
- fun make_or_from_clausification l =
- foldl1 (fn ((concl1, bounds1), (concl2, bounds2)) =>
- (HOLogic.mk_disj (perhaps (try HOLogic.dest_Trueprop) concl1,
- perhaps (try HOLogic.dest_Trueprop) concl2), bounds1 @ bounds2)) l
- fun to_node (((((id, rule), prems), concl), bounds), cx) = (mk_node id rule
- (the_default [] prems) concl bounds, cx)
- in
- get_id
- ##> parse_rule
- #> rotate_pair
- ##> parse_source
- #> rotate_pair
- ##> skip_args
- #> (fn (((id, rule), prems), sub) => (((id, rule), prems), parse_subproof cx id sub))
- #> rotate_pair
- ##> parse_conclusion
- ##> map repair_quantification
- #> (fn ((((id, rule), prems), (subproof, cx)), terms) =>
- (((((id, rule), prems), subproof), fold_map (fn t => fn cx => node_of t cx) terms cx)))
- ##> apfst (fn [] => (@{const False}, []) | concls => make_or_from_clausification concls)
- #> fix_subproof_steps
- ##> to_node
- #> (fn (subproof, (step, cx)) => (subproof @ [step], cx))
- #-> fold_map update_step_and_cx
- end
-
-(*subproofs are written on multiple lines: SMTLIB can not parse then, because parentheses are
-unbalanced on each line*)
-fun seperate_into_steps lines =
- let
- fun count ("(" :: l) n = count l (n+1)
- | count (")" :: l) n = count l (n-1)
- | count (_ :: l) n = count l n
- | count [] n = n
- fun seperate (line :: l) actual_lines m =
- let val n = count (raw_explode line) 0 in
- if m + n = 0 then
- [actual_lines ^ line] :: seperate l "" 0
- else seperate l (actual_lines ^ line) (m + n)
- end
- | seperate [] _ 0 = []
- in
- seperate lines "" 0
- end
-
- (* VeriT adds @ before every variable. *)
-fun remove_all_at (SMTLIB2.Sym v :: l) = SMTLIB2.Sym (perhaps (try (unprefix "@")) v) :: remove_all_at l
- | remove_all_at (SMTLIB2.S l :: l') = SMTLIB2.S (remove_all_at l) :: remove_all_at l'
- | remove_all_at (SMTLIB2.Key v :: l) = SMTLIB2.Key v :: remove_all_at l
- | remove_all_at (v :: l) = v :: remove_all_at l
- | remove_all_at [] = []
-
-fun find_in_which_step_defined var (VeriT_Node {id, bounds, ...} :: l) =
- (case List.find (fn v => String.isPrefix v var) bounds of
- NONE => find_in_which_step_defined var l
- | SOME _ => id)
- | find_in_which_step_defined var _ = raise Fail ("undefined " ^ var)
-
-(*Yes every case is possible: the introduced var is not on a special size of the equality sign.*)
-fun find_ite_var_in_term (Const ("HOL.If", _) $ _ $
- (Const (@{const_name "HOL.eq"}, _) $ Free (var1, _) $ Free (var2, _) ) $
- (Const (@{const_name "HOL.eq"}, _) $ Free (var3, _) $ Free (var4, _) )) =
- let
- fun get_number_of_ite_transformed_var var =
- perhaps (try (unprefix "ite")) var
- |> Int.fromString
- fun is_equal_and_has_correct_substring var var' var'' =
- if var = var' andalso String.isPrefix "ite" var then SOME var'
- else if var = var'' andalso String.isPrefix "ite" var then SOME var'' else NONE
- val var1_introduced_var = is_equal_and_has_correct_substring var1 var3 var4
- val var2_introduced_var = is_equal_and_has_correct_substring var3 var1 var2
- in
- (case (var1_introduced_var, var2_introduced_var) of
- (SOME a, SOME b) =>
- (*ill-generated case, might be possible when applying the rule to max a a. Only if the
- variable have been introduced before. Probably an impossible edge case*)
- (case (get_number_of_ite_transformed_var a, get_number_of_ite_transformed_var b) of
- (SOME a, SOME b) => if a < b then var2_introduced_var else var1_introduced_var
- (*Otherwise, it is a name clase between a parameter name and the introduced variable.
- Or the name convention has been changed.*)
- | (NONE, SOME _) => var2_introduced_var
- | (SOME _, NONE) => var2_introduced_var)
- | (_, SOME _) => var2_introduced_var
- | (SOME _, _) => var1_introduced_var)
- end
- | find_ite_var_in_term (Const (@{const_name "If"}, _) $ _ $
- (Const (@{const_name "HOL.eq"}, _) $ Free (var, _) $ _ ) $
- (Const (@{const_name "HOL.eq"}, _) $ Free (var', _) $ _ )) =
- if var = var' then SOME var else NONE
- | find_ite_var_in_term (Const (@{const_name "If"}, _) $ _ $
- (Const (@{const_name "HOL.eq"}, _) $ _ $ Free (var, _)) $
- (Const (@{const_name "HOL.eq"}, _) $ _ $ Free (var', _))) =
- if var = var' then SOME var else NONE
- | find_ite_var_in_term (p $ q) =
- (case find_ite_var_in_term p of
- NONE => find_ite_var_in_term q
- | x => x)
- | find_ite_var_in_term (Abs (_, _, body)) = find_ite_var_in_term body
- | find_ite_var_in_term _ = NONE
-
-fun correct_veriT_step steps (st as VeriT_Node {id, rule, prems, concl, bounds}) =
- if rule = veriT_tmp_ite_elim_rule then
- if bounds = [] then
- (*if the introduced var has already been defined, adding the definition as a dependency*)
- let
- val new_prems =
- (case find_ite_var_in_term concl of
- NONE => prems
- | SOME var => find_in_which_step_defined var steps :: prems)
- in
- VeriT_Node {id = id, rule = rule, prems = new_prems, concl = concl, bounds = bounds}
- end
- else
- (*some new variables are created*)
- let
- val concl' = replace_bound_var_by_free_var concl bounds
- in
- mk_node id rule prems concl' []
- end
- else
- st
-
-fun remove_alpha_conversion _ [] = []
- | remove_alpha_conversion replace_table (VeriT_Node {id, rule, prems, concl, bounds} :: steps) =
- let
- fun correct_dependency prems =
- map (fn x => perhaps (Symtab.lookup replace_table) x) prems
- fun find_predecessor prem = perhaps (Symtab.lookup replace_table) prem
- in
- if rule = veriT_alpha_conv_rule then
- remove_alpha_conversion (Symtab.update (id, find_predecessor (hd prems))
- replace_table) steps
- else
- VeriT_Node {id = id, rule = rule, prems = correct_dependency prems,
- concl = concl, bounds = bounds} :: remove_alpha_conversion replace_table steps
- end
-
-fun correct_veriT_steps steps =
- steps
- |> map (correct_veriT_step steps)
- |> remove_alpha_conversion Symtab.empty
-
-fun parse typs funs lines ctxt =
- let
- val smtlib2_lines_without_at =
- remove_all_at (map SMTLIB2.parse (seperate_into_steps lines))
- val (u, env) = apfst flat (fold_map (fn l => fn cx => parse_proof_step cx l)
- smtlib2_lines_without_at (empty_context ctxt typs funs))
- val t = correct_veriT_steps u
- fun node_to_step (VeriT_Node {id, rule, prems, concl, bounds, ...}) =
- mk_step id rule prems concl bounds
- in
- (map node_to_step t, ctxt_of env)
- end
-
-end;
--- a/src/HOL/Tools/SMT2/verit_proof_parse.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,104 +0,0 @@
-(* Title: HOL/Tools/SMT2/verit_proof_parse.ML
- Author: Mathias Fleury, TU Muenchen
- Author: Jasmin Blanchette, TU Muenchen
-
-VeriT proof parsing.
-*)
-
-signature VERIT_PROOF_PARSE =
-sig
- type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
- val parse_proof: Proof.context -> SMT2_Translate.replay_data ->
- ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
- SMT2_Solver.parsed_proof
-end;
-
-structure VeriT_Proof_Parse: VERIT_PROOF_PARSE =
-struct
-
-open ATP_Util
-open ATP_Problem
-open ATP_Proof
-open ATP_Proof_Reconstruct
-open VeriT_Isar
-open VeriT_Proof
-
-fun find_and_add_missing_dependances steps assms ll_offset =
- let
- fun prems_to_theorem_number [] id repl = (([], []), (id, repl))
- | prems_to_theorem_number (x :: ths) id replaced =
- (case Int.fromString (perhaps (try (unprefix SMTLIB2_Interface.assert_prefix)) x) of
- NONE =>
- let
- val ((prems, iidths), (id', replaced')) = prems_to_theorem_number ths id replaced
- in
- ((x :: prems, iidths), (id', replaced'))
- end
- | SOME th =>
- (case Option.map snd (List.find (fst #> curry (op =) x) replaced) of
- NONE =>
- let
- val id' = if th = ll_offset then 0 else id - ll_offset (* 0: for the conjecture*)
- val ((prems, iidths), (id'', replaced')) =
- prems_to_theorem_number ths (if th <> ll_offset then id + 1 else id)
- ((x, string_of_int id') :: replaced)
- in
- ((string_of_int id' :: prems, (th, (id', th - ll_offset)) :: iidths),
- (id'', replaced'))
- end
- | SOME x =>
- let
- val ((prems, iidths), (id', replaced')) = prems_to_theorem_number ths id replaced
- in ((x :: prems, iidths), (id', replaced')) end))
- fun update_step (VeriT_Proof.VeriT_Step {prems, id = id0, rule = rule0,
- concl = concl0, fixes = fixes0}) (id, replaced) =
- let val ((prems', iidths), (id', replaced)) = prems_to_theorem_number prems id replaced
- in
- ((VeriT_Proof.VeriT_Step {id = id0, rule = rule0, prems = prems', concl = concl0,
- fixes = fixes0}, iidths), (id', replaced))
- end
- in
- fold_map update_step steps (1, [])
- |> fst
- |> `(map snd)
- ||> (map fst)
- |>> flat
- |>> map (fn (_, (id, tm_id)) => let val (i, tm) = nth assms tm_id in (i, (id, tm)) end)
- end
-
-fun add_missing_steps iidths =
- let
- fun add_single_step (_, (id, th)) = VeriT_Proof.VeriT_Step {id = string_of_int id,
- rule = veriT_input_rule, prems = [], concl = prop_of th, fixes = []}
- in map add_single_step iidths end
-
-fun parse_proof _
- ({context = ctxt, typs, terms, ll_defs, rewrite_rules, assms} : SMT2_Translate.replay_data)
- xfacts prems concl output =
- let
- val (steps, _) = VeriT_Proof.parse typs terms output ctxt
- val (iidths, steps'') = find_and_add_missing_dependances steps assms (length ll_defs)
- val steps' = add_missing_steps iidths @ steps''
- fun id_of_index i = the_default ~1 (Option.map fst (AList.lookup (op =) iidths i))
-
- val prems_i = 1
- val facts_i = prems_i + length prems
- val conjecture_i = 0
- val ll_offset = id_of_index conjecture_i
- val prem_ids = map id_of_index (prems_i upto facts_i - 1)
- val helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths
-
- val fact_ids = map_filter (fn (i, (id, _)) =>
- (try (apsnd (nth xfacts)) (id, i - facts_i))) iidths
- val fact_helper_ts =
- map (fn (_, th) => (ATP_Util.short_thm_name ctxt th, prop_of th)) helper_ids @
- map (fn (_, ((s, _), th)) => (s, prop_of th)) fact_ids
- val fact_helper_ids =
- map (apsnd (ATP_Util.short_thm_name ctxt)) helper_ids @ map (apsnd (fst o fst)) fact_ids
- in
- {outcome = NONE, fact_ids = fact_ids,
- atp_proof = fn () => atp_proof_of_veriT_proof ctxt ll_defs rewrite_rules prems concl
- fact_helper_ts prem_ids ll_offset fact_helper_ids steps'}
- end
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_interface.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,192 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_interface.ML
- Author: Sascha Boehme, TU Muenchen
-
-Interface to Z3 based on a relaxed version of SMT-LIB.
-*)
-
-signature Z3_NEW_INTERFACE =
-sig
- val smtlib2_z3C: SMT2_Util.class
-
- datatype sym = Sym of string * sym list
- type mk_builtins = {
- mk_builtin_typ: sym -> typ option,
- mk_builtin_num: theory -> int -> typ -> cterm option,
- mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
- val add_mk_builtins: mk_builtins -> Context.generic -> Context.generic
- val mk_builtin_typ: Proof.context -> sym -> typ option
- val mk_builtin_num: Proof.context -> int -> typ -> cterm option
- val mk_builtin_fun: Proof.context -> sym -> cterm list -> cterm option
-
- val is_builtin_theory_term: Proof.context -> term -> bool
-end;
-
-structure Z3_New_Interface: Z3_NEW_INTERFACE =
-struct
-
-val smtlib2_z3C = SMTLIB2_Interface.smtlib2C @ ["z3"]
-
-
-(* interface *)
-
-local
- fun translate_config ctxt =
- {logic = K "", has_datatypes = true,
- serialize = #serialize (SMTLIB2_Interface.translate_config ctxt)}
-
- fun is_div_mod @{const div (int)} = true
- | is_div_mod @{const mod (int)} = true
- | is_div_mod _ = false
-
- val have_int_div_mod = exists (Term.exists_subterm is_div_mod o Thm.prop_of)
-
- fun add_div_mod _ (thms, extra_thms) =
- if have_int_div_mod thms orelse have_int_div_mod extra_thms then
- (thms, @{thms div_as_z3div mod_as_z3mod} @ extra_thms)
- else (thms, extra_thms)
-
- val setup_builtins =
- SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const times (int)}, "*") #>
- SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const z3div}, "div") #>
- SMT2_Builtin.add_builtin_fun' smtlib2_z3C (@{const z3mod}, "mod")
-in
-
-val _ = Theory.setup (Context.theory_map (
- setup_builtins #>
- SMT2_Normalize.add_extra_norm (smtlib2_z3C, add_div_mod) #>
- SMT2_Translate.add_config (smtlib2_z3C, translate_config)))
-
-end
-
-
-(* constructors *)
-
-datatype sym = Sym of string * sym list
-
-
-(** additional constructors **)
-
-type mk_builtins = {
- mk_builtin_typ: sym -> typ option,
- mk_builtin_num: theory -> int -> typ -> cterm option,
- mk_builtin_fun: theory -> sym -> cterm list -> cterm option }
-
-fun chained _ [] = NONE
- | chained f (b :: bs) = (case f b of SOME y => SOME y | NONE => chained f bs)
-
-fun chained_mk_builtin_typ bs sym =
- chained (fn {mk_builtin_typ=mk, ...} : mk_builtins => mk sym) bs
-
-fun chained_mk_builtin_num ctxt bs i T =
- let val thy = Proof_Context.theory_of ctxt
- in chained (fn {mk_builtin_num=mk, ...} : mk_builtins => mk thy i T) bs end
-
-fun chained_mk_builtin_fun ctxt bs s cts =
- let val thy = Proof_Context.theory_of ctxt
- in chained (fn {mk_builtin_fun=mk, ...} : mk_builtins => mk thy s cts) bs end
-
-fun fst_int_ord ((i1, _), (i2, _)) = int_ord (i1, i2)
-
-structure Mk_Builtins = Generic_Data
-(
- type T = (int * mk_builtins) list
- val empty = []
- val extend = I
- fun merge data = Ord_List.merge fst_int_ord data
-)
-
-fun add_mk_builtins mk = Mk_Builtins.map (Ord_List.insert fst_int_ord (serial (), mk))
-
-fun get_mk_builtins ctxt = map snd (Mk_Builtins.get (Context.Proof ctxt))
-
-
-(** basic and additional constructors **)
-
-fun mk_builtin_typ _ (Sym ("Bool", _)) = SOME @{typ bool}
- | mk_builtin_typ _ (Sym ("Int", _)) = SOME @{typ int}
- | mk_builtin_typ _ (Sym ("bool", _)) = SOME @{typ bool} (*FIXME: legacy*)
- | mk_builtin_typ _ (Sym ("int", _)) = SOME @{typ int} (*FIXME: legacy*)
- | mk_builtin_typ ctxt sym = chained_mk_builtin_typ (get_mk_builtins ctxt) sym
-
-fun mk_builtin_num _ i @{typ int} = SOME (Numeral.mk_cnumber @{ctyp int} i)
- | mk_builtin_num ctxt i T =
- chained_mk_builtin_num ctxt (get_mk_builtins ctxt) i T
-
-val mk_true = Thm.cterm_of @{theory} (@{const Not} $ @{const False})
-val mk_false = Thm.cterm_of @{theory} @{const False}
-val mk_not = Thm.apply (Thm.cterm_of @{theory} @{const Not})
-val mk_implies = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.implies})
-val mk_iff = Thm.mk_binop (Thm.cterm_of @{theory} @{const HOL.eq (bool)})
-val conj = Thm.cterm_of @{theory} @{const HOL.conj}
-val disj = Thm.cterm_of @{theory} @{const HOL.disj}
-
-fun mk_nary _ cu [] = cu
- | mk_nary ct _ cts = uncurry (fold_rev (Thm.mk_binop ct)) (split_last cts)
-
-val eq = SMT2_Util.mk_const_pat @{theory} @{const_name HOL.eq} SMT2_Util.destT1
-fun mk_eq ct cu = Thm.mk_binop (SMT2_Util.instT' ct eq) ct cu
-
-val if_term =
- SMT2_Util.mk_const_pat @{theory} @{const_name If} (SMT2_Util.destT1 o SMT2_Util.destT2)
-fun mk_if cc ct = Thm.mk_binop (Thm.apply (SMT2_Util.instT' ct if_term) cc) ct
-
-val access = SMT2_Util.mk_const_pat @{theory} @{const_name fun_app} SMT2_Util.destT1
-fun mk_access array = Thm.apply (SMT2_Util.instT' array access) array
-
-val update =
- SMT2_Util.mk_const_pat @{theory} @{const_name fun_upd} (Thm.dest_ctyp o SMT2_Util.destT1)
-fun mk_update array index value =
- let val cTs = Thm.dest_ctyp (Thm.ctyp_of_term array)
- in Thm.apply (Thm.mk_binop (SMT2_Util.instTs cTs update) array index) value end
-
-val mk_uminus = Thm.apply (Thm.cterm_of @{theory} @{const uminus (int)})
-val add = Thm.cterm_of @{theory} @{const plus (int)}
-val int0 = Numeral.mk_cnumber @{ctyp int} 0
-val mk_sub = Thm.mk_binop (Thm.cterm_of @{theory} @{const minus (int)})
-val mk_mul = Thm.mk_binop (Thm.cterm_of @{theory} @{const times (int)})
-val mk_div = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3div})
-val mk_mod = Thm.mk_binop (Thm.cterm_of @{theory} @{const z3mod})
-val mk_lt = Thm.mk_binop (Thm.cterm_of @{theory} @{const less (int)})
-val mk_le = Thm.mk_binop (Thm.cterm_of @{theory} @{const less_eq (int)})
-
-fun mk_builtin_fun ctxt sym cts =
- (case (sym, cts) of
- (Sym ("true", _), []) => SOME mk_true
- | (Sym ("false", _), []) => SOME mk_false
- | (Sym ("not", _), [ct]) => SOME (mk_not ct)
- | (Sym ("and", _), _) => SOME (mk_nary conj mk_true cts)
- | (Sym ("or", _), _) => SOME (mk_nary disj mk_false cts)
- | (Sym ("implies", _), [ct, cu]) => SOME (mk_implies ct cu)
- | (Sym ("iff", _), [ct, cu]) => SOME (mk_iff ct cu)
- | (Sym ("~", _), [ct, cu]) => SOME (mk_iff ct cu)
- | (Sym ("xor", _), [ct, cu]) => SOME (mk_not (mk_iff ct cu))
- | (Sym ("if", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3)
- | (Sym ("ite", _), [ct1, ct2, ct3]) => SOME (mk_if ct1 ct2 ct3) (* FIXME: remove *)
- | (Sym ("=", _), [ct, cu]) => SOME (mk_eq ct cu)
- | (Sym ("select", _), [ca, ck]) => SOME (Thm.apply (mk_access ca) ck)
- | (Sym ("store", _), [ca, ck, cv]) => SOME (mk_update ca ck cv)
- | _ =>
- (case (sym, try (#T o Thm.rep_cterm o hd) cts, cts) of
- (Sym ("+", _), SOME @{typ int}, _) => SOME (mk_nary add int0 cts)
- | (Sym ("-", _), SOME @{typ int}, [ct]) => SOME (mk_uminus ct)
- | (Sym ("-", _), SOME @{typ int}, [ct, cu]) => SOME (mk_sub ct cu)
- | (Sym ("*", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mul ct cu)
- | (Sym ("div", _), SOME @{typ int}, [ct, cu]) => SOME (mk_div ct cu)
- | (Sym ("mod", _), SOME @{typ int}, [ct, cu]) => SOME (mk_mod ct cu)
- | (Sym ("<", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt ct cu)
- | (Sym ("<=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le ct cu)
- | (Sym (">", _), SOME @{typ int}, [ct, cu]) => SOME (mk_lt cu ct)
- | (Sym (">=", _), SOME @{typ int}, [ct, cu]) => SOME (mk_le cu ct)
- | _ => chained_mk_builtin_fun ctxt (get_mk_builtins ctxt) sym cts))
-
-
-(* abstraction *)
-
-fun is_builtin_theory_term ctxt t =
- if SMT2_Builtin.is_builtin_num ctxt t then true
- else
- (case Term.strip_comb t of
- (Const c, ts) => SMT2_Builtin.is_builtin_fun ctxt c ts
- | _ => false)
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_isar.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,123 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_isar.ML
- Author: Jasmin Blanchette, TU Muenchen
-
-Z3 proofs as generic ATP proofs for Isar proof reconstruction.
-*)
-
-signature Z3_NEW_ISAR =
-sig
- val atp_proof_of_z3_proof: Proof.context -> term list -> thm list -> term list -> term ->
- (string * term) list -> int list -> int -> (int * string) list -> Z3_New_Proof.z3_step list ->
- (term, string) ATP_Proof.atp_step list
-end;
-
-structure Z3_New_Isar: Z3_NEW_ISAR =
-struct
-
-open ATP_Util
-open ATP_Problem
-open ATP_Proof
-open ATP_Proof_Reconstruct
-open SMTLIB2_Isar
-
-val z3_apply_def_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Apply_Def
-val z3_hypothesis_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Hypothesis
-val z3_intro_def_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Intro_Def
-val z3_lemma_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Lemma
-
-fun inline_z3_defs _ [] = []
- | inline_z3_defs defs ((name, role, t, rule, deps) :: lines) =
- if rule = z3_intro_def_rule then
- let val def = t |> HOLogic.dest_Trueprop |> HOLogic.dest_eq |> swap in
- inline_z3_defs (insert (op =) def defs)
- (map (replace_dependencies_in_line (name, [])) lines)
- end
- else if rule = z3_apply_def_rule then
- inline_z3_defs defs (map (replace_dependencies_in_line (name, [])) lines)
- else
- (name, role, Term.subst_atomic defs t, rule, deps) :: inline_z3_defs defs lines
-
-fun add_z3_hypotheses [] = I
- | add_z3_hypotheses hyps =
- HOLogic.dest_Trueprop
- #> curry s_imp (Library.foldr1 s_conj (map HOLogic.dest_Trueprop hyps))
- #> HOLogic.mk_Trueprop
-
-fun inline_z3_hypotheses _ _ [] = []
- | inline_z3_hypotheses hyp_names hyps ((name, role, t, rule, deps) :: lines) =
- if rule = z3_hypothesis_rule then
- inline_z3_hypotheses (name :: hyp_names) (AList.map_default (op =) (t, []) (cons name) hyps)
- lines
- else
- let val deps' = subtract (op =) hyp_names deps in
- if rule = z3_lemma_rule then
- (name, role, t, rule, deps') :: inline_z3_hypotheses hyp_names hyps lines
- else
- let
- val add_hyps = filter_out (null o inter (op =) deps o snd) hyps
- val t' = add_z3_hypotheses (map fst add_hyps) t
- val deps' = subtract (op =) hyp_names deps
- val hyps' = fold (AList.update (op =) o apsnd (insert (op =) name)) add_hyps hyps
- in
- (name, role, t', rule, deps') :: inline_z3_hypotheses hyp_names hyps' lines
- end
- end
-
-fun dest_alls (Const (@{const_name Pure.all}, _) $ Abs (abs as (_, T, _))) =
- let val (s', t') = Term.dest_abs abs in
- dest_alls t' |>> cons (s', T)
- end
- | dest_alls t = ([], t)
-
-val reorder_foralls =
- dest_alls
- #>> sort_wrt fst
- #-> fold_rev (Logic.all o Free);
-
-fun atp_proof_of_z3_proof ctxt ll_defs rewrite_rules hyp_ts concl_t fact_helper_ts prem_ids
- conjecture_id fact_helper_ids proof =
- let
- val thy = Proof_Context.theory_of ctxt
-
- fun steps_of (Z3_New_Proof.Z3_Step {id, rule, prems, concl, ...}) =
- let
- val sid = string_of_int id
-
- val concl' = concl
- |> reorder_foralls (* crucial for skolemization steps *)
- |> postprocess_step_conclusion thy rewrite_rules ll_defs
- fun standard_step role =
- ((sid, []), role, concl', Z3_New_Proof.string_of_rule rule,
- map (fn id => (string_of_int id, [])) prems)
- in
- (case rule of
- Z3_New_Proof.Asserted =>
- let val ss = the_list (AList.lookup (op =) fact_helper_ids id) in
- (case distinguish_conjecture_and_hypothesis ss id conjecture_id prem_ids fact_helper_ts
- hyp_ts concl_t of
- NONE => []
- | SOME (role0, concl00) =>
- let
- val name0 = (sid ^ "a", ss)
- val concl0 = unskolemize_names concl00
- in
- (if role0 = Axiom then []
- else [(name0, role0, concl0, Z3_New_Proof.string_of_rule rule, [])]) @
- [((sid, []), Plain, concl', Z3_New_Proof.string_of_rule Z3_New_Proof.Rewrite,
- name0 :: normalizing_prems ctxt concl0)]
- end)
- end
- | Z3_New_Proof.Rewrite => [standard_step Lemma]
- | Z3_New_Proof.Rewrite_Star => [standard_step Lemma]
- | Z3_New_Proof.Skolemize => [standard_step Lemma]
- | Z3_New_Proof.Th_Lemma _ => [standard_step Lemma]
- | _ => [standard_step Plain])
- end
- in
- proof
- |> maps steps_of
- |> inline_z3_defs []
- |> inline_z3_hypotheses [] []
- end
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_proof.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,303 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_proof.ML
- Author: Sascha Boehme, TU Muenchen
-
-Z3 proofs: parsing and abstract syntax tree.
-*)
-
-signature Z3_NEW_PROOF =
-sig
- (*proof rules*)
- datatype z3_rule =
- True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity | Symmetry | Transitivity |
- Transitivity_Star | Monotonicity | Quant_Intro | Distributivity | And_Elim | Not_Or_Elim |
- Rewrite | Rewrite_Star | Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
- Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
- Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star |
- Cnf_Star | Skolemize | Modus_Ponens_Oeq | Th_Lemma of string
-
- val is_assumption: z3_rule -> bool
- val string_of_rule: z3_rule -> string
-
- (*proofs*)
- datatype z3_step = Z3_Step of {
- id: int,
- rule: z3_rule,
- prems: int list,
- concl: term,
- fixes: string list,
- is_fix_step: bool}
-
- (*proof parser*)
- val parse: typ Symtab.table -> term Symtab.table -> string list ->
- Proof.context -> z3_step list * Proof.context
-end;
-
-structure Z3_New_Proof: Z3_NEW_PROOF =
-struct
-
-open SMTLIB2_Proof
-
-
-(* proof rules *)
-
-datatype z3_rule =
- True_Axiom | Asserted | Goal | Modus_Ponens | Reflexivity | Symmetry | Transitivity |
- Transitivity_Star | Monotonicity | Quant_Intro | Distributivity | And_Elim | Not_Or_Elim |
- Rewrite | Rewrite_Star | Pull_Quant | Pull_Quant_Star | Push_Quant | Elim_Unused_Vars |
- Dest_Eq_Res | Quant_Inst | Hypothesis | Lemma | Unit_Resolution | Iff_True | Iff_False |
- Commutativity | Def_Axiom | Intro_Def | Apply_Def | Iff_Oeq | Nnf_Pos | Nnf_Neg | Nnf_Star |
- Cnf_Star | Skolemize | Modus_Ponens_Oeq | Th_Lemma of string
- (* some proof rules include further information that is currently dropped by the parser *)
-
-val rule_names = Symtab.make [
- ("true-axiom", True_Axiom),
- ("asserted", Asserted),
- ("goal", Goal),
- ("mp", Modus_Ponens),
- ("refl", Reflexivity),
- ("symm", Symmetry),
- ("trans", Transitivity),
- ("trans*", Transitivity_Star),
- ("monotonicity", Monotonicity),
- ("quant-intro", Quant_Intro),
- ("distributivity", Distributivity),
- ("and-elim", And_Elim),
- ("not-or-elim", Not_Or_Elim),
- ("rewrite", Rewrite),
- ("rewrite*", Rewrite_Star),
- ("pull-quant", Pull_Quant),
- ("pull-quant*", Pull_Quant_Star),
- ("push-quant", Push_Quant),
- ("elim-unused", Elim_Unused_Vars),
- ("der", Dest_Eq_Res),
- ("quant-inst", Quant_Inst),
- ("hypothesis", Hypothesis),
- ("lemma", Lemma),
- ("unit-resolution", Unit_Resolution),
- ("iff-true", Iff_True),
- ("iff-false", Iff_False),
- ("commutativity", Commutativity),
- ("def-axiom", Def_Axiom),
- ("intro-def", Intro_Def),
- ("apply-def", Apply_Def),
- ("iff~", Iff_Oeq),
- ("nnf-pos", Nnf_Pos),
- ("nnf-neg", Nnf_Neg),
- ("nnf*", Nnf_Star),
- ("cnf*", Cnf_Star),
- ("sk", Skolemize),
- ("mp~", Modus_Ponens_Oeq)]
-
-fun is_assumption Asserted = true
- | is_assumption Goal = true
- | is_assumption Hypothesis = true
- | is_assumption Intro_Def = true
- | is_assumption Skolemize = true
- | is_assumption _ = false
-
-fun rule_of_string name =
- (case Symtab.lookup rule_names name of
- SOME rule => rule
- | NONE => error ("unknown Z3 proof rule " ^ quote name))
-
-fun string_of_rule (Th_Lemma kind) = "th-lemma" ^ (if kind = "" then "" else " " ^ kind)
- | string_of_rule r =
- let fun eq_rule (s, r') = if r = r' then SOME s else NONE
- in the (Symtab.get_first eq_rule rule_names) end
-
-
-(* proofs *)
-
-datatype z3_node = Z3_Node of {
- id: int,
- rule: z3_rule,
- prems: z3_node list,
- concl: term,
- bounds: string list}
-
-fun mk_node id rule prems concl bounds =
- Z3_Node {id = id, rule = rule, prems = prems, concl = concl, bounds = bounds}
-
-datatype z3_step = Z3_Step of {
- id: int,
- rule: z3_rule,
- prems: int list,
- concl: term,
- fixes: string list,
- is_fix_step: bool}
-
-fun mk_step id rule prems concl fixes is_fix_step =
- Z3_Step {id = id, rule = rule, prems = prems, concl = concl, fixes = fixes,
- is_fix_step = is_fix_step}
-
-
-(* proof parser *)
-
-fun rule_of (SMTLIB2.Sym name) = rule_of_string name
- | rule_of (SMTLIB2.S (SMTLIB2.Sym "_" :: SMTLIB2.Sym name :: args)) =
- (case (name, args) of
- ("th-lemma", SMTLIB2.Sym kind :: _) => Th_Lemma kind
- | _ => rule_of_string name)
- | rule_of r = raise SMTLIB2_PARSE ("bad Z3 proof rule format", r)
-
-fun node_of p cx =
- (case p of
- SMTLIB2.Sym name =>
- (case lookup_binding cx name of
- Proof node => (node, cx)
- | Tree p' =>
- cx
- |> node_of p'
- |-> (fn node => pair node o update_binding (name, Proof node))
- | _ => raise SMTLIB2_PARSE ("bad Z3 proof format", p))
- | SMTLIB2.S [SMTLIB2.Sym "let", SMTLIB2.S bindings, p] =>
- with_bindings (map dest_binding bindings) (node_of p) cx
- | SMTLIB2.S (name :: parts) =>
- let
- val (ps, p) = split_last parts
- val r = rule_of name
- in
- cx
- |> fold_map node_of ps
- ||>> `(with_fresh_names (term_of p))
- ||>> next_id
- |>> (fn ((prems, (t, ns)), id) => mk_node id r prems t ns)
- end
- | _ => raise SMTLIB2_PARSE ("bad Z3 proof format", p))
-
-fun dest_name (SMTLIB2.Sym name) = name
- | dest_name t = raise SMTLIB2_PARSE ("bad name", t)
-
-fun dest_seq (SMTLIB2.S ts) = ts
- | dest_seq t = raise SMTLIB2_PARSE ("bad Z3 proof format", t)
-
-fun parse' (SMTLIB2.S (SMTLIB2.Sym "set-logic" :: _) :: ts) cx = parse' ts cx
- | parse' (SMTLIB2.S [SMTLIB2.Sym "declare-fun", n, tys, ty] :: ts) cx =
- let
- val name = dest_name n
- val Ts = map (type_of cx) (dest_seq tys)
- val T = type_of cx ty
- in parse' ts (declare_fun name (Ts ---> T) cx) end
- | parse' (SMTLIB2.S [SMTLIB2.Sym "proof", p] :: _) cx = node_of p cx
- | parse' ts _ = raise SMTLIB2_PARSE ("bad Z3 proof declarations", SMTLIB2.S ts)
-
-fun parse_proof typs funs lines ctxt =
- let
- val ts = dest_seq (SMTLIB2.parse lines)
- val (node, cx) = parse' ts (empty_context ctxt typs funs)
- in (node, ctxt_of cx) end
- handle SMTLIB2.PARSE (l, msg) => error ("parsing error at line " ^ string_of_int l ^ ": " ^ msg)
- | SMTLIB2_PARSE (msg, t) => error (msg ^ ": " ^ SMTLIB2.str_of t)
-
-
-(* handling of bound variables *)
-
-fun subst_of tyenv =
- let fun add (ix, (S, T)) = cons (TVar (ix, S), T)
- in Vartab.fold add tyenv [] end
-
-fun substTs_same subst =
- let val applyT = Same.function (AList.lookup (op =) subst)
- in Term_Subst.map_atypsT_same applyT end
-
-fun subst_types ctxt env bounds t =
- let
- val match = Sign.typ_match (Proof_Context.theory_of ctxt)
-
- val t' = singleton (Variable.polymorphic ctxt) t
- val patTs = map snd (Term.strip_qnt_vars @{const_name Pure.all} t')
- val objTs = map (the o Symtab.lookup env) bounds
- val subst = subst_of (fold match (patTs ~~ objTs) Vartab.empty)
- in Same.commit (Term_Subst.map_types_same (substTs_same subst)) t' end
-
-fun eq_quant (@{const_name HOL.All}, _) (@{const_name HOL.All}, _) = true
- | eq_quant (@{const_name HOL.Ex}, _) (@{const_name HOL.Ex}, _) = true
- | eq_quant _ _ = false
-
-fun opp_quant (@{const_name HOL.All}, _) (@{const_name HOL.Ex}, _) = true
- | opp_quant (@{const_name HOL.Ex}, _) (@{const_name HOL.All}, _) = true
- | opp_quant _ _ = false
-
-fun with_quant pred i (Const q1 $ Abs (_, T1, t1), Const q2 $ Abs (_, T2, t2)) =
- if pred q1 q2 andalso T1 = T2 then
- let val t = Var (("", i), T1)
- in SOME (pairself Term.subst_bound ((t, t1), (t, t2))) end
- else NONE
- | with_quant _ _ _ = NONE
-
-fun dest_quant_pair i (@{term HOL.Not} $ t1, t2) =
- Option.map (apfst HOLogic.mk_not) (with_quant opp_quant i (t1, t2))
- | dest_quant_pair i (t1, t2) = with_quant eq_quant i (t1, t2)
-
-fun dest_quant i t =
- (case dest_quant_pair i (HOLogic.dest_eq (HOLogic.dest_Trueprop t)) of
- SOME (t1, t2) => HOLogic.mk_Trueprop (HOLogic.mk_eq (t1, t2))
- | NONE => raise TERM ("lift_quant", [t]))
-
-fun match_types ctxt pat obj =
- (Vartab.empty, Vartab.empty)
- |> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, obj)
-
-fun strip_match ctxt pat i obj =
- (case try (match_types ctxt pat) obj of
- SOME (tyenv, _) => subst_of tyenv
- | NONE => strip_match ctxt pat (i + 1) (dest_quant i obj))
-
-fun dest_all i (Const (@{const_name Pure.all}, _) $ (a as Abs (_, T, _))) =
- dest_all (i + 1) (Term.betapply (a, Var (("", i), T)))
- | dest_all i t = (i, t)
-
-fun dest_alls t = dest_all (Term.maxidx_of_term t + 1) t
-
-fun match_rule ctxt env (Z3_Node {bounds = bs', concl = t', ...}) bs t =
- let
- val t'' = singleton (Variable.polymorphic ctxt) t'
- val (i, obj) = dest_alls (subst_types ctxt env bs t)
- in
- (case try (strip_match ctxt (snd (dest_alls t'')) i) obj of
- NONE => NONE
- | SOME subst =>
- let
- val applyT = Same.commit (substTs_same subst)
- val patTs = map snd (Term.strip_qnt_vars @{const_name Pure.all} t'')
- in SOME (Symtab.make (bs' ~~ map applyT patTs)) end)
- end
-
-
-(* linearizing proofs and resolving types of bound variables *)
-
-fun has_step (tab, _) = Inttab.defined tab
-
-fun add_step id rule bounds concl is_fix_step ids (tab, sts) =
- let val step = mk_step id rule ids concl bounds is_fix_step
- in (id, (Inttab.update (id, ()) tab, step :: sts)) end
-
-fun is_fix_rule rule prems =
- member (op =) [Quant_Intro, Nnf_Pos, Nnf_Neg] rule andalso length prems = 1
-
-fun lin_proof ctxt env (Z3_Node {id, rule, prems, concl, bounds}) steps =
- if has_step steps id then (id, steps)
- else
- let
- val t = subst_types ctxt env bounds concl
- val add = add_step id rule bounds t
- fun rec_apply e b = fold_map (lin_proof ctxt e) prems #-> add b
- in
- if is_fix_rule rule prems then
- (case match_rule ctxt env (hd prems) bounds t of
- NONE => rec_apply env false steps
- | SOME env' => rec_apply env' true steps)
- else rec_apply env false steps
- end
-
-fun linearize ctxt node =
- rev (snd (snd (lin_proof ctxt Symtab.empty node (Inttab.empty, []))))
-
-
-(* overall proof parser *)
-
-fun parse typs funs lines ctxt =
- let val (node, ctxt') = parse_proof typs funs lines ctxt
- in (linearize ctxt' node, ctxt') end
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_real.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,32 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_real.ML
- Author: Sascha Boehme, TU Muenchen
-
-Z3 setup for reals.
-*)
-
-structure Z3_New_Real: sig end =
-struct
-
-fun real_type_parser (SMTLIB2.Sym "Real", []) = SOME @{typ Real.real}
- | real_type_parser _ = NONE
-
-fun real_term_parser (SMTLIB2.Dec (i, 0), []) = SOME (HOLogic.mk_number @{typ Real.real} i)
- | real_term_parser (SMTLIB2.Sym "/", [t1, t2]) =
- SOME (@{term "inverse_class.divide :: real => _"} $ t1 $ t2)
- | real_term_parser (SMTLIB2.Sym "to_real", [t]) = SOME (@{term "Real.real :: int => _"} $ t)
- | real_term_parser _ = NONE
-
-fun abstract abs t =
- (case t of
- (c as @{term "inverse_class.divide :: real => _"}) $ t1 $ t2 =>
- abs t1 ##>> abs t2 #>> (fn (u1, u2) => SOME (c $ u1 $ u2))
- | (c as @{term "Real.real :: int => _"}) $ t =>
- abs t #>> (fn u => SOME (c $ u))
- | _ => pair NONE)
-
-val _ = Theory.setup (Context.theory_map (
- SMTLIB2_Proof.add_type_parser real_type_parser #>
- SMTLIB2_Proof.add_term_parser real_term_parser #>
- Z3_New_Replay_Methods.add_arith_abstracter abstract))
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_replay.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,219 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_replay.ML
- Author: Sascha Boehme, TU Muenchen
- Author: Jasmin Blanchette, TU Muenchen
-
-Z3 proof parsing and replay.
-*)
-
-signature Z3_NEW_REPLAY =
-sig
- val parse_proof: Proof.context -> SMT2_Translate.replay_data ->
- ((string * ATP_Problem_Generate.stature) * thm) list -> term list -> term -> string list ->
- SMT2_Solver.parsed_proof
- val replay: Proof.context -> SMT2_Translate.replay_data -> string list -> thm
-end;
-
-structure Z3_New_Replay: Z3_NEW_REPLAY =
-struct
-
-fun params_of t = Term.strip_qnt_vars @{const_name Pure.all} t
-
-fun varify ctxt thm =
- let
- val maxidx = Thm.maxidx_of thm + 1
- val vs = params_of (Thm.prop_of thm)
- val vars = map_index (fn (i, (n, T)) => Var ((n, i + maxidx), T)) vs
- in Drule.forall_elim_list (map (SMT2_Util.certify ctxt) vars) thm end
-
-fun add_paramTs names t =
- fold2 (fn n => fn (_, T) => AList.update (op =) (n, T)) names (params_of t)
-
-fun new_fixes ctxt nTs =
- let
- val (ns, ctxt') = Variable.variant_fixes (replicate (length nTs) "") ctxt
- fun mk (n, T) n' = (n, SMT2_Util.certify ctxt' (Free (n', T)))
- in (ctxt', Symtab.make (map2 mk nTs ns)) end
-
-fun forall_elim_term ct (Const (@{const_name Pure.all}, _) $ (a as Abs _)) =
- Term.betapply (a, Thm.term_of ct)
- | forall_elim_term _ qt = raise TERM ("forall_elim'", [qt])
-
-fun apply_fixes elim env = fold (elim o the o Symtab.lookup env)
-
-val apply_fixes_prem = uncurry o apply_fixes Thm.forall_elim
-val apply_fixes_concl = apply_fixes forall_elim_term
-
-fun export_fixes env names = Drule.forall_intr_list (map (the o Symtab.lookup env) names)
-
-fun under_fixes f ctxt (prems, nthms) names concl =
- let
- val thms1 = map (varify ctxt) prems
- val (ctxt', env) =
- add_paramTs names concl []
- |> fold (uncurry add_paramTs o apsnd Thm.prop_of) nthms
- |> new_fixes ctxt
- val thms2 = map (apply_fixes_prem env) nthms
- val t = apply_fixes_concl env names concl
- in export_fixes env names (f ctxt' (thms1 @ thms2) t) end
-
-fun replay_thm ctxt assumed nthms
- (Z3_New_Proof.Z3_Step {id, rule, concl, fixes, is_fix_step, ...}) =
- if Z3_New_Proof.is_assumption rule then
- (case Inttab.lookup assumed id of
- SOME (_, thm) => thm
- | NONE => Thm.assume (SMT2_Util.certify ctxt concl))
- else
- under_fixes (Z3_New_Replay_Methods.method_for rule) ctxt
- (if is_fix_step then (map snd nthms, []) else ([], nthms)) fixes concl
-
-fun replay_step ctxt assumed (step as Z3_New_Proof.Z3_Step {id, prems, fixes, ...}) proofs =
- let val nthms = map (the o Inttab.lookup proofs) prems
- in Inttab.update (id, (fixes, replay_thm ctxt assumed nthms step)) proofs end
-
-local
- val remove_trigger = mk_meta_eq @{thm trigger_def}
- val remove_fun_app = mk_meta_eq @{thm fun_app_def}
-
- fun rewrite_conv _ [] = Conv.all_conv
- | rewrite_conv ctxt eqs = Simplifier.full_rewrite (empty_simpset ctxt addsimps eqs)
-
- val prep_rules = [@{thm Let_def}, remove_trigger, remove_fun_app,
- Z3_New_Replay_Literals.rewrite_true]
-
- fun rewrite _ [] = I
- | rewrite ctxt eqs = Conv.fconv_rule (rewrite_conv ctxt eqs)
-
- fun lookup_assm assms_net ct =
- Z3_New_Replay_Util.net_instances assms_net ct
- |> map (fn ithm as (_, thm) => (ithm, Thm.cprop_of thm aconvc ct))
-in
-
-fun add_asserted outer_ctxt rewrite_rules assms steps ctxt =
- let
- val eqs = map (rewrite ctxt [Z3_New_Replay_Literals.rewrite_true]) rewrite_rules
- val eqs' = union Thm.eq_thm eqs prep_rules
-
- val assms_net =
- assms
- |> map (apsnd (rewrite ctxt eqs'))
- |> map (apsnd (Conv.fconv_rule Thm.eta_conversion))
- |> Z3_New_Replay_Util.thm_net_of snd
-
- fun revert_conv ctxt = rewrite_conv ctxt eqs' then_conv Thm.eta_conversion
-
- fun assume thm ctxt =
- let
- val ct = Thm.cprem_of thm 1
- val (thm', ctxt') = yield_singleton Assumption.add_assumes ct ctxt
- in (thm' RS thm, ctxt') end
-
- fun add1 id fixes thm1 ((i, th), exact) ((iidths, thms), (ctxt, ptab)) =
- let
- val (thm, ctxt') = if exact then (Thm.implies_elim thm1 th, ctxt) else assume thm1 ctxt
- val thms' = if exact then thms else th :: thms
- in (((i, (id, th)) :: iidths, thms'), (ctxt', Inttab.update (id, (fixes, thm)) ptab)) end
-
- fun add (Z3_New_Proof.Z3_Step {id, rule, concl, fixes, ...})
- (cx as ((iidths, thms), (ctxt, ptab))) =
- if Z3_New_Proof.is_assumption rule andalso rule <> Z3_New_Proof.Hypothesis then
- let
- val ct = SMT2_Util.certify ctxt concl
- val thm1 = Thm.trivial ct |> Conv.fconv_rule (Conv.arg1_conv (revert_conv outer_ctxt))
- val thm2 = singleton (Variable.export ctxt outer_ctxt) thm1
- in
- (case lookup_assm assms_net (Thm.cprem_of thm2 1) of
- [] =>
- let val (thm, ctxt') = assume thm1 ctxt
- in ((iidths, thms), (ctxt', Inttab.update (id, (fixes, thm)) ptab)) end
- | ithms => fold (add1 id fixes thm1) ithms cx)
- end
- else
- cx
- in fold add steps (([], []), (ctxt, Inttab.empty)) end
-
-end
-
-(* |- (EX x. P x) = P c |- ~ (ALL x. P x) = ~ P c *)
-local
- val sk_rules = @{lemma
- "c = (SOME x. P x) ==> (EX x. P x) = P c"
- "c = (SOME x. ~ P x) ==> (~ (ALL x. P x)) = (~ P c)"
- by (metis someI_ex)+}
-in
-
-fun discharge_sk_tac i st =
- (rtac @{thm trans} i
- THEN resolve_tac sk_rules i
- THEN (rtac @{thm refl} ORELSE' discharge_sk_tac) (i+1)
- THEN rtac @{thm refl} i) st
-
-end
-
-fun make_discharge_rules rules = rules @ [@{thm allI}, @{thm refl},
- @{thm reflexive}, Z3_New_Replay_Literals.true_thm]
-
-val intro_def_rules = @{lemma
- "(~ P | P) & (P | ~ P)"
- "(P | ~ P) & (~ P | P)"
- by fast+}
-
-fun discharge_assms_tac rules =
- REPEAT (HEADGOAL (resolve_tac (intro_def_rules @ rules) ORELSE' SOLVED' discharge_sk_tac))
-
-fun discharge_assms ctxt rules thm =
- (if Thm.nprems_of thm = 0 then
- thm
- else
- (case Seq.pull (discharge_assms_tac rules thm) of
- SOME (thm', _) => thm'
- | NONE => raise THM ("failed to discharge premise", 1, [thm])))
- |> Goal.norm_result ctxt
-
-fun discharge rules outer_ctxt inner_ctxt =
- singleton (Proof_Context.export inner_ctxt outer_ctxt)
- #> discharge_assms outer_ctxt (make_discharge_rules rules)
-
-fun parse_proof outer_ctxt
- ({context = ctxt, typs, terms, ll_defs, rewrite_rules, assms} : SMT2_Translate.replay_data)
- xfacts prems concl output =
- let
- val (steps, ctxt2) = Z3_New_Proof.parse typs terms output ctxt
- val ((iidths, _), _) = add_asserted outer_ctxt rewrite_rules assms steps ctxt2
-
- fun id_of_index i = the_default ~1 (Option.map fst (AList.lookup (op =) iidths i))
-
- val conjecture_i = 0
- val prems_i = 1
- val facts_i = prems_i + length prems
-
- val conjecture_id = id_of_index conjecture_i
- val prem_ids = map id_of_index (prems_i upto facts_i - 1)
- val helper_ids = map_filter (try (fn (~1, idth) => idth)) iidths
- val fact_ids = map_filter (fn (i, (id, _)) => try (apsnd (nth xfacts)) (id, i - facts_i)) iidths
- val fact_helper_ts =
- map (fn (_, th) => (ATP_Util.short_thm_name ctxt th, prop_of th)) helper_ids @
- map (fn (_, ((s, _), th)) => (s, prop_of th)) fact_ids
- val fact_helper_ids =
- map (apsnd (ATP_Util.short_thm_name ctxt)) helper_ids @ map (apsnd (fst o fst)) fact_ids
- in
- {outcome = NONE, fact_ids = fact_ids,
- atp_proof = fn () => Z3_New_Isar.atp_proof_of_z3_proof ctxt ll_defs rewrite_rules prems concl
- fact_helper_ts prem_ids conjecture_id fact_helper_ids steps}
- end
-
-fun replay outer_ctxt
- ({context = ctxt, typs, terms, rewrite_rules, assms, ...} : SMT2_Translate.replay_data) output =
- let
- val (steps, ctxt2) = Z3_New_Proof.parse typs terms output ctxt
- val ((_, rules), (ctxt3, assumed)) = add_asserted outer_ctxt rewrite_rules assms steps ctxt2
- val ctxt4 =
- ctxt3
- |> put_simpset (Z3_New_Replay_Util.make_simpset ctxt3 [])
- |> Config.put SAT.solver (Config.get ctxt3 SMT2_Config.sat_solver)
- val proofs = fold (replay_step ctxt4 assumed) steps assumed
- val (_, Z3_New_Proof.Z3_Step {id, ...}) = split_last steps
- in
- Inttab.lookup proofs id |> the |> snd |> discharge rules outer_ctxt ctxt4
- end
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_replay_literals.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,351 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_replay_literals.ML
- Author: Sascha Boehme, TU Muenchen
-
-Proof tools related to conjunctions and disjunctions.
-*)
-
-signature Z3_NEW_REPLAY_LITERALS =
-sig
- (*literal table*)
- type littab = thm Termtab.table
- val make_littab: thm list -> littab
- val insert_lit: thm -> littab -> littab
- val delete_lit: thm -> littab -> littab
- val lookup_lit: littab -> term -> thm option
- val get_first_lit: (term -> bool) -> littab -> thm option
-
- (*rules*)
- val true_thm: thm
- val rewrite_true: thm
-
- (*properties*)
- val is_conj: term -> bool
- val is_disj: term -> bool
- val exists_lit: bool -> (term -> bool) -> term -> bool
- val negate: cterm -> cterm
-
- (*proof tools*)
- val explode: bool -> bool -> bool -> term list -> thm -> thm list
- val join: bool -> littab -> term -> thm
- val prove_conj_disj_eq: cterm -> thm
-end;
-
-structure Z3_New_Replay_Literals: Z3_NEW_REPLAY_LITERALS =
-struct
-
-(* literal table *)
-
-type littab = thm Termtab.table
-
-fun make_littab thms = fold (Termtab.update o `SMT2_Util.prop_of) thms Termtab.empty
-
-fun insert_lit thm = Termtab.update (`SMT2_Util.prop_of thm)
-fun delete_lit thm = Termtab.delete (SMT2_Util.prop_of thm)
-fun lookup_lit lits = Termtab.lookup lits
-fun get_first_lit f =
- Termtab.get_first (fn (t, thm) => if f t then SOME thm else NONE)
-
-
-(* rules *)
-
-val true_thm = @{lemma "~False" by simp}
-val rewrite_true = @{lemma "True == ~ False" by simp}
-
-
-(* properties and term operations *)
-
-val is_neg = (fn @{const Not} $ _ => true | _ => false)
-fun is_neg' f = (fn @{const Not} $ t => f t | _ => false)
-val is_dneg = is_neg' is_neg
-val is_conj = (fn @{const HOL.conj} $ _ $ _ => true | _ => false)
-val is_disj = (fn @{const HOL.disj} $ _ $ _ => true | _ => false)
-
-fun dest_disj_term' f = (fn
- @{const Not} $ (@{const HOL.disj} $ t $ u) => SOME (f t, f u)
- | _ => NONE)
-
-val dest_conj_term = (fn @{const HOL.conj} $ t $ u => SOME (t, u) | _ => NONE)
-val dest_disj_term =
- dest_disj_term' (fn @{const Not} $ t => t | t => @{const Not} $ t)
-
-fun exists_lit is_conj P =
- let
- val dest = if is_conj then dest_conj_term else dest_disj_term
- fun exists t = P t orelse
- (case dest t of
- SOME (t1, t2) => exists t1 orelse exists t2
- | NONE => false)
- in exists end
-
-val negate = Thm.apply (Thm.cterm_of @{theory} @{const Not})
-
-
-(* proof tools *)
-
-(** explosion of conjunctions and disjunctions **)
-
-local
- val precomp = Z3_New_Replay_Util.precompose2
-
- fun destc ct = Thm.dest_binop (Thm.dest_arg ct)
- val dest_conj1 = precomp destc @{thm conjunct1}
- val dest_conj2 = precomp destc @{thm conjunct2}
- fun dest_conj_rules t =
- dest_conj_term t |> Option.map (K (dest_conj1, dest_conj2))
-
- fun destd f ct = f (Thm.dest_binop (Thm.dest_arg (Thm.dest_arg ct)))
- val dn1 = apfst Thm.dest_arg and dn2 = apsnd Thm.dest_arg
- val dest_disj1 = precomp (destd I) @{lemma "~(P | Q) ==> ~P" by fast}
- val dest_disj2 = precomp (destd dn1) @{lemma "~(~P | Q) ==> P" by fast}
- val dest_disj3 = precomp (destd I) @{lemma "~(P | Q) ==> ~Q" by fast}
- val dest_disj4 = precomp (destd dn2) @{lemma "~(P | ~Q) ==> Q" by fast}
-
- fun dest_disj_rules t =
- (case dest_disj_term' is_neg t of
- SOME (true, true) => SOME (dest_disj2, dest_disj4)
- | SOME (true, false) => SOME (dest_disj2, dest_disj3)
- | SOME (false, true) => SOME (dest_disj1, dest_disj4)
- | SOME (false, false) => SOME (dest_disj1, dest_disj3)
- | NONE => NONE)
-
- fun destn ct = [Thm.dest_arg (Thm.dest_arg (Thm.dest_arg ct))]
- val dneg_rule = Z3_New_Replay_Util.precompose destn @{thm notnotD}
-in
-
-(*
- explode a term into literals and collect all rules to be able to deduce
- particular literals afterwards
-*)
-fun explode_term is_conj =
- let
- val dest = if is_conj then dest_conj_term else dest_disj_term
- val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
-
- fun add (t, rs) = Termtab.map_default (t, rs)
- (fn rs' => if length rs' < length rs then rs' else rs)
-
- fun explode1 rules t =
- (case dest t of
- SOME (t1, t2) =>
- let val (rule1, rule2) = the (dest_rules t)
- in
- explode1 (rule1 :: rules) t1 #>
- explode1 (rule2 :: rules) t2 #>
- add (t, rev rules)
- end
- | NONE => add (t, rev rules))
-
- fun explode0 (@{const Not} $ (@{const Not} $ t)) =
- Termtab.make [(t, [dneg_rule])]
- | explode0 t = explode1 [] t Termtab.empty
-
- in explode0 end
-
-(*
- extract a literal by applying previously collected rules
-*)
-fun extract_lit thm rules = fold Z3_New_Replay_Util.compose rules thm
-
-
-(*
- explode a theorem into its literals
-*)
-fun explode is_conj full keep_intermediate stop_lits =
- let
- val dest_rules = if is_conj then dest_conj_rules else dest_disj_rules
- val tab = fold (Termtab.update o rpair ()) stop_lits Termtab.empty
-
- fun explode1 thm =
- if Termtab.defined tab (SMT2_Util.prop_of thm) then cons thm
- else
- (case dest_rules (SMT2_Util.prop_of thm) of
- SOME (rule1, rule2) =>
- explode2 rule1 thm #>
- explode2 rule2 thm #>
- keep_intermediate ? cons thm
- | NONE => cons thm)
-
- and explode2 dest_rule thm =
- if full orelse
- exists_lit is_conj (Termtab.defined tab) (SMT2_Util.prop_of thm)
- then explode1 (Z3_New_Replay_Util.compose dest_rule thm)
- else cons (Z3_New_Replay_Util.compose dest_rule thm)
-
- fun explode0 thm =
- if not is_conj andalso is_dneg (SMT2_Util.prop_of thm)
- then [Z3_New_Replay_Util.compose dneg_rule thm]
- else explode1 thm []
-
- in explode0 end
-
-end
-
-
-(** joining of literals to conjunctions or disjunctions **)
-
-local
- fun on_cprem i f thm = f (Thm.cprem_of thm i)
- fun on_cprop f thm = f (Thm.cprop_of thm)
- fun precomp2 f g thm = (on_cprem 1 f thm, on_cprem 2 g thm, f, g, thm)
- fun comp2 (cv1, cv2, f, g, rule) thm1 thm2 =
- Thm.instantiate ([], [(cv1, on_cprop f thm1), (cv2, on_cprop g thm2)]) rule
- |> Z3_New_Replay_Util.discharge thm1 |> Z3_New_Replay_Util.discharge thm2
-
- fun d1 ct = Thm.dest_arg ct and d2 ct = Thm.dest_arg (Thm.dest_arg ct)
-
- val conj_rule = precomp2 d1 d1 @{thm conjI}
- fun comp_conj ((_, thm1), (_, thm2)) = comp2 conj_rule thm1 thm2
-
- val disj1 = precomp2 d2 d2 @{lemma "~P ==> ~Q ==> ~(P | Q)" by fast}
- val disj2 = precomp2 d2 d1 @{lemma "~P ==> Q ==> ~(P | ~Q)" by fast}
- val disj3 = precomp2 d1 d2 @{lemma "P ==> ~Q ==> ~(~P | Q)" by fast}
- val disj4 = precomp2 d1 d1 @{lemma "P ==> Q ==> ~(~P | ~Q)" by fast}
-
- fun comp_disj ((false, thm1), (false, thm2)) = comp2 disj1 thm1 thm2
- | comp_disj ((false, thm1), (true, thm2)) = comp2 disj2 thm1 thm2
- | comp_disj ((true, thm1), (false, thm2)) = comp2 disj3 thm1 thm2
- | comp_disj ((true, thm1), (true, thm2)) = comp2 disj4 thm1 thm2
-
- fun dest_conj (@{const HOL.conj} $ t $ u) = ((false, t), (false, u))
- | dest_conj t = raise TERM ("dest_conj", [t])
-
- val neg = (fn @{const Not} $ t => (true, t) | t => (false, @{const Not} $ t))
- fun dest_disj (@{const Not} $ (@{const HOL.disj} $ t $ u)) = (neg t, neg u)
- | dest_disj t = raise TERM ("dest_disj", [t])
-
- val precomp = Z3_New_Replay_Util.precompose
- val dnegE = precomp (single o d2 o d1) @{thm notnotD}
- val dnegI = precomp (single o d1) @{lemma "P ==> ~~P" by fast}
- fun as_dneg f t = f (@{const Not} $ (@{const Not} $ t))
-
- val precomp2 = Z3_New_Replay_Util.precompose2
- fun dni f = apsnd f o Thm.dest_binop o f o d1
- val negIffE = precomp2 (dni d1) @{lemma "~(P = (~Q)) ==> Q = P" by fast}
- val negIffI = precomp2 (dni I) @{lemma "P = Q ==> ~(Q = (~P))" by fast}
- val iff_const = @{const HOL.eq (bool)}
- fun as_negIff f (@{const HOL.eq (bool)} $ t $ u) =
- f (@{const Not} $ (iff_const $ u $ (@{const Not} $ t)))
- | as_negIff _ _ = NONE
-in
-
-fun join is_conj littab t =
- let
- val comp = if is_conj then comp_conj else comp_disj
- val dest = if is_conj then dest_conj else dest_disj
-
- val lookup = lookup_lit littab
-
- fun lookup_rule t =
- (case t of
- @{const Not} $ (@{const Not} $ t) => (Z3_New_Replay_Util.compose dnegI, lookup t)
- | @{const Not} $ (@{const HOL.eq (bool)} $ t $ (@{const Not} $ u)) =>
- (Z3_New_Replay_Util.compose negIffI, lookup (iff_const $ u $ t))
- | @{const Not} $ ((eq as Const (@{const_name HOL.eq}, _)) $ t $ u) =>
- let fun rewr lit = lit COMP @{thm not_sym}
- in (rewr, lookup (@{const Not} $ (eq $ u $ t))) end
- | _ =>
- (case as_dneg lookup t of
- NONE => (Z3_New_Replay_Util.compose negIffE, as_negIff lookup t)
- | x => (Z3_New_Replay_Util.compose dnegE, x)))
-
- fun join1 (s, t) =
- (case lookup t of
- SOME lit => (s, lit)
- | NONE =>
- (case lookup_rule t of
- (rewrite, SOME lit) => (s, rewrite lit)
- | (_, NONE) => (s, comp (pairself join1 (dest t)))))
-
- in snd (join1 (if is_conj then (false, t) else (true, t))) end
-
-end
-
-
-(** proving equality of conjunctions or disjunctions **)
-
-fun iff_intro thm1 thm2 = thm2 COMP (thm1 COMP @{thm iffI})
-
-local
- val cp1 = @{lemma "(~P) = (~Q) ==> P = Q" by simp}
- val cp2 = @{lemma "(~P) = Q ==> P = (~Q)" by fastforce}
- val cp3 = @{lemma "P = (~Q) ==> (~P) = Q" by simp}
-in
-fun contrapos1 prove (ct, cu) = prove (negate ct, negate cu) COMP cp1
-fun contrapos2 prove (ct, cu) = prove (negate ct, Thm.dest_arg cu) COMP cp2
-fun contrapos3 prove (ct, cu) = prove (Thm.dest_arg ct, negate cu) COMP cp3
-end
-
-local
- val contra_rule = @{lemma "P ==> ~P ==> False" by (rule notE)}
- fun contra_left conj thm =
- let
- val rules = explode_term conj (SMT2_Util.prop_of thm)
- fun contra_lits (t, rs) =
- (case t of
- @{const Not} $ u => Termtab.lookup rules u |> Option.map (pair rs)
- | _ => NONE)
- in
- (case Termtab.lookup rules @{const False} of
- SOME rs => extract_lit thm rs
- | NONE =>
- the (Termtab.get_first contra_lits rules)
- |> pairself (extract_lit thm)
- |> (fn (nlit, plit) => nlit COMP (plit COMP contra_rule)))
- end
-
- val falseE_v = Thm.dest_arg (Thm.dest_arg (Thm.cprop_of @{thm FalseE}))
- fun contra_right ct = Thm.instantiate ([], [(falseE_v, ct)]) @{thm FalseE}
-in
-
-fun contradict conj ct =
- iff_intro (Z3_New_Replay_Util.under_assumption (contra_left conj) ct) (contra_right ct)
-
-end
-
-local
- fun prove_eq l r (cl, cr) =
- let
- fun explode' is_conj = explode is_conj true (l <> r) []
- fun make_tab is_conj thm = make_littab (true_thm :: explode' is_conj thm)
- fun prove is_conj ct tab = join is_conj tab (Thm.term_of ct)
-
- val thm1 = Z3_New_Replay_Util.under_assumption (prove r cr o make_tab l) cl
- val thm2 = Z3_New_Replay_Util.under_assumption (prove l cl o make_tab r) cr
- in iff_intro thm1 thm2 end
-
- datatype conj_disj = CONJ | DISJ | NCON | NDIS
- fun kind_of t =
- if is_conj t then SOME CONJ
- else if is_disj t then SOME DISJ
- else if is_neg' is_conj t then SOME NCON
- else if is_neg' is_disj t then SOME NDIS
- else NONE
-in
-
-fun prove_conj_disj_eq ct =
- let val cp as (cl, cr) = Thm.dest_binop (Thm.dest_arg ct)
- in
- (case (kind_of (Thm.term_of cl), Thm.term_of cr) of
- (SOME CONJ, @{const False}) => contradict true cl
- | (SOME DISJ, @{const Not} $ @{const False}) =>
- contrapos2 (contradict false o fst) cp
- | (kl, _) =>
- (case (kl, kind_of (Thm.term_of cr)) of
- (SOME CONJ, SOME CONJ) => prove_eq true true cp
- | (SOME CONJ, SOME NDIS) => prove_eq true false cp
- | (SOME CONJ, _) => prove_eq true true cp
- | (SOME DISJ, SOME DISJ) => contrapos1 (prove_eq false false) cp
- | (SOME DISJ, SOME NCON) => contrapos2 (prove_eq false true) cp
- | (SOME DISJ, _) => contrapos1 (prove_eq false false) cp
- | (SOME NCON, SOME NCON) => contrapos1 (prove_eq true true) cp
- | (SOME NCON, SOME DISJ) => contrapos3 (prove_eq true false) cp
- | (SOME NCON, NONE) => contrapos3 (prove_eq true false) cp
- | (SOME NDIS, SOME NDIS) => prove_eq false false cp
- | (SOME NDIS, SOME CONJ) => prove_eq false true cp
- | (SOME NDIS, NONE) => prove_eq false true cp
- | _ => raise CTERM ("prove_conj_disj_eq", [ct])))
- end
-
-end
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_replay_methods.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,666 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_replay_methods.ML
- Author: Sascha Boehme, TU Muenchen
- Author: Jasmin Blanchette, TU Muenchen
-
-Proof methods for replaying Z3 proofs.
-*)
-
-signature Z3_NEW_REPLAY_METHODS =
-sig
- (*abstraction*)
- type abs_context = int * term Termtab.table
- type 'a abstracter = term -> abs_context -> 'a * abs_context
- val add_arith_abstracter: (term abstracter -> term option abstracter) ->
- Context.generic -> Context.generic
-
- (*theory lemma methods*)
- type th_lemma_method = Proof.context -> thm list -> term -> thm
- val add_th_lemma_method: string * th_lemma_method -> Context.generic ->
- Context.generic
-
- (*methods for Z3 proof rules*)
- type z3_method = Proof.context -> thm list -> term -> thm
- val true_axiom: z3_method
- val mp: z3_method
- val refl: z3_method
- val symm: z3_method
- val trans: z3_method
- val cong: z3_method
- val quant_intro: z3_method
- val distrib: z3_method
- val and_elim: z3_method
- val not_or_elim: z3_method
- val rewrite: z3_method
- val rewrite_star: z3_method
- val pull_quant: z3_method
- val push_quant: z3_method
- val elim_unused: z3_method
- val dest_eq_res: z3_method
- val quant_inst: z3_method
- val lemma: z3_method
- val unit_res: z3_method
- val iff_true: z3_method
- val iff_false: z3_method
- val comm: z3_method
- val def_axiom: z3_method
- val apply_def: z3_method
- val iff_oeq: z3_method
- val nnf_pos: z3_method
- val nnf_neg: z3_method
- val mp_oeq: z3_method
- val th_lemma: string -> z3_method
- val method_for: Z3_New_Proof.z3_rule -> z3_method
-end;
-
-structure Z3_New_Replay_Methods: Z3_NEW_REPLAY_METHODS =
-struct
-
-type z3_method = Proof.context -> thm list -> term -> thm
-
-
-(* utility functions *)
-
-fun trace ctxt f = SMT2_Config.trace_msg ctxt f ()
-
-fun pretty_thm ctxt thm = Syntax.pretty_term ctxt (Thm.concl_of thm)
-
-fun pretty_goal ctxt msg rule thms t =
- let
- val full_msg = msg ^ ": " ^ quote (Z3_New_Proof.string_of_rule rule)
- val assms =
- if null thms then []
- else [Pretty.big_list "assumptions:" (map (pretty_thm ctxt) thms)]
- val concl = Pretty.big_list "proposition:" [Syntax.pretty_term ctxt t]
- in Pretty.big_list full_msg (assms @ [concl]) end
-
-fun replay_error ctxt msg rule thms t = error (Pretty.string_of (pretty_goal ctxt msg rule thms t))
-
-fun replay_rule_error ctxt = replay_error ctxt "Failed to replay Z3 proof step"
-
-fun trace_goal ctxt rule thms t =
- trace ctxt (fn () => Pretty.string_of (pretty_goal ctxt "Goal" rule thms t))
-
-fun as_prop (t as Const (@{const_name Trueprop}, _) $ _) = t
- | as_prop t = HOLogic.mk_Trueprop t
-
-fun dest_prop (Const (@{const_name Trueprop}, _) $ t) = t
- | dest_prop t = t
-
-fun dest_thm thm = dest_prop (Thm.concl_of thm)
-
-fun certify_prop ctxt t = SMT2_Util.certify ctxt (as_prop t)
-
-fun try_provers ctxt rule [] thms t = replay_rule_error ctxt rule thms t
- | try_provers ctxt rule ((name, prover) :: named_provers) thms t =
- (case (trace ctxt (K ("Trying prover " ^ quote name)); try prover t) of
- SOME thm => thm
- | NONE => try_provers ctxt rule named_provers thms t)
-
-fun match ctxt pat t =
- (Vartab.empty, Vartab.empty)
- |> Pattern.first_order_match (Proof_Context.theory_of ctxt) (pat, t)
-
-fun gen_certify_inst sel mk cert ctxt thm t =
- let
- val inst = match ctxt (dest_thm thm) (dest_prop t)
- fun cert_inst (ix, (a, b)) = (cert (mk (ix, a)), cert b)
- in Vartab.fold (cons o cert_inst) (sel inst) [] end
-
-fun match_instantiateT ctxt t thm =
- if Term.exists_type (Term.exists_subtype Term.is_TVar) (dest_thm thm) then
- let val certT = Thm.ctyp_of (Proof_Context.theory_of ctxt)
- in Thm.instantiate (gen_certify_inst fst TVar certT ctxt thm t, []) thm end
- else thm
-
-fun match_instantiate ctxt t thm =
- let
- val cert = SMT2_Util.certify ctxt
- val thm' = match_instantiateT ctxt t thm
- in Thm.instantiate ([], gen_certify_inst snd Var cert ctxt thm' t) thm' end
-
-fun apply_rule ctxt t =
- (case Z3_New_Replay_Rules.apply ctxt (certify_prop ctxt t) of
- SOME thm => thm
- | NONE => raise Fail "apply_rule")
-
-fun discharge _ [] thm = thm
- | discharge i (rule :: rules) thm = discharge (i + Thm.nprems_of rule) rules (rule RSN (i, thm))
-
-fun by_tac ctxt thms ns ts t tac =
- Goal.prove ctxt [] (map as_prop ts) (as_prop t)
- (fn {context, prems} => HEADGOAL (tac context prems))
- |> Drule.generalize ([], ns)
- |> discharge 1 thms
-
-fun prove ctxt t tac = by_tac ctxt [] [] [] t (K o tac)
-
-fun prop_tac ctxt prems =
- Method.insert_tac prems
- THEN' SUBGOAL (fn (prop, i) =>
- if Term.size_of_term prop > 100 then SAT.satx_tac ctxt i
- else (Classical.fast_tac ctxt ORELSE' Clasimp.force_tac ctxt) i)
-
-fun quant_tac ctxt = Blast.blast_tac ctxt
-
-
-(* plug-ins *)
-
-type abs_context = int * term Termtab.table
-
-type 'a abstracter = term -> abs_context -> 'a * abs_context
-
-type th_lemma_method = Proof.context -> thm list -> term -> thm
-
-fun id_ord ((id1, _), (id2, _)) = int_ord (id1, id2)
-
-structure Plugins = Generic_Data
-(
- type T =
- (int * (term abstracter -> term option abstracter)) list *
- th_lemma_method Symtab.table
- val empty = ([], Symtab.empty)
- val extend = I
- fun merge ((abss1, ths1), (abss2, ths2)) = (
- Ord_List.merge id_ord (abss1, abss2),
- Symtab.merge (K true) (ths1, ths2))
-)
-
-fun add_arith_abstracter abs = Plugins.map (apfst (Ord_List.insert id_ord (serial (), abs)))
-fun get_arith_abstracters ctxt = map snd (fst (Plugins.get (Context.Proof ctxt)))
-
-fun add_th_lemma_method method = Plugins.map (apsnd (Symtab.update_new method))
-fun get_th_lemma_method ctxt = snd (Plugins.get (Context.Proof ctxt))
-
-
-(* abstraction *)
-
-fun prove_abstract ctxt thms t tac f =
- let
- val ((prems, concl), (_, ts)) = f (1, Termtab.empty)
- val ns = Termtab.fold (fn (_, v) => cons (fst (Term.dest_Free v))) ts []
- in
- by_tac ctxt [] ns prems concl tac
- |> match_instantiate ctxt t
- |> discharge 1 thms
- end
-
-fun prove_abstract' ctxt t tac f =
- prove_abstract ctxt [] t tac (f #>> pair [])
-
-fun lookup_term (_, terms) t = Termtab.lookup terms t
-
-fun abstract_sub t f cx =
- (case lookup_term cx t of
- SOME v => (v, cx)
- | NONE => f cx)
-
-fun mk_fresh_free t (i, terms) =
- let val v = Free ("t" ^ string_of_int i, fastype_of t)
- in (v, (i + 1, Termtab.update (t, v) terms)) end
-
-fun apply_abstracters _ [] _ cx = (NONE, cx)
- | apply_abstracters abs (abstracter :: abstracters) t cx =
- (case abstracter abs t cx of
- (NONE, _) => apply_abstracters abs abstracters t cx
- | x as (SOME _, _) => x)
-
-fun abstract_term (t as _ $ _) = abstract_sub t (mk_fresh_free t)
- | abstract_term (t as Abs _) = abstract_sub t (mk_fresh_free t)
- | abstract_term t = pair t
-
-fun abstract_bin abs f t t1 t2 = abstract_sub t (abs t1 ##>> abs t2 #>> f)
-
-fun abstract_ter abs f t t1 t2 t3 =
- abstract_sub t (abs t1 ##>> abs t2 ##>> abs t3 #>> (Parse.triple1 #> f))
-
-fun abstract_lit (@{const HOL.Not} $ t) = abstract_term t #>> HOLogic.mk_not
- | abstract_lit t = abstract_term t
-
-fun abstract_not abs (t as @{const HOL.Not} $ t1) =
- abstract_sub t (abs t1 #>> HOLogic.mk_not)
- | abstract_not _ t = abstract_lit t
-
-fun abstract_conj (t as @{const HOL.conj} $ t1 $ t2) =
- abstract_bin abstract_conj HOLogic.mk_conj t t1 t2
- | abstract_conj t = abstract_lit t
-
-fun abstract_disj (t as @{const HOL.disj} $ t1 $ t2) =
- abstract_bin abstract_disj HOLogic.mk_disj t t1 t2
- | abstract_disj t = abstract_lit t
-
-fun abstract_prop (t as (c as @{const If (bool)}) $ t1 $ t2 $ t3) =
- abstract_ter abstract_prop (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
- | abstract_prop (t as @{const HOL.disj} $ t1 $ t2) =
- abstract_bin abstract_prop HOLogic.mk_disj t t1 t2
- | abstract_prop (t as @{const HOL.conj} $ t1 $ t2) =
- abstract_bin abstract_prop HOLogic.mk_conj t t1 t2
- | abstract_prop (t as @{const HOL.implies} $ t1 $ t2) =
- abstract_bin abstract_prop HOLogic.mk_imp t t1 t2
- | abstract_prop (t as @{term "HOL.eq :: bool => _"} $ t1 $ t2) =
- abstract_bin abstract_prop HOLogic.mk_eq t t1 t2
- | abstract_prop t = abstract_not abstract_prop t
-
-fun abstract_arith ctxt u =
- let
- fun abs (t as (c as Const _) $ Abs (s, T, t')) =
- abstract_sub t (abs t' #>> (fn u' => c $ Abs (s, T, u')))
- | abs (t as (c as Const (@{const_name If}, _)) $ t1 $ t2 $ t3) =
- abstract_ter abs (fn (t1, t2, t3) => c $ t1 $ t2 $ t3) t t1 t2 t3
- | abs (t as @{const HOL.Not} $ t1) = abstract_sub t (abs t1 #>> HOLogic.mk_not)
- | abs (t as @{const HOL.disj} $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> HOLogic.mk_disj)
- | abs (t as (c as Const (@{const_name uminus_class.uminus}, _)) $ t1) =
- abstract_sub t (abs t1 #>> (fn u => c $ u))
- | abs (t as (c as Const (@{const_name plus_class.plus}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name minus_class.minus}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name times_class.times}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name z3div}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name z3mod}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name HOL.eq}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name ord_class.less}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs (t as (c as Const (@{const_name ord_class.less_eq}, _)) $ t1 $ t2) =
- abstract_sub t (abs t1 ##>> abs t2 #>> (fn (u1, u2) => c $ u1 $ u2))
- | abs t = abstract_sub t (fn cx =>
- if can HOLogic.dest_number t then (t, cx)
- else
- (case apply_abstracters abs (get_arith_abstracters ctxt) t cx of
- (SOME u, cx') => (u, cx')
- | (NONE, _) => abstract_term t cx))
- in abs u end
-
-
-(* truth axiom *)
-
-fun true_axiom _ _ _ = @{thm TrueI}
-
-
-(* modus ponens *)
-
-fun mp _ [p, p_eq_q] _ = discharge 1 [p_eq_q, p] iffD1
- | mp ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Modus_Ponens thms t
-
-val mp_oeq = mp
-
-
-(* reflexivity *)
-
-fun refl ctxt _ t = match_instantiate ctxt t @{thm refl}
-
-
-(* symmetry *)
-
-fun symm _ [thm] _ = thm RS @{thm sym}
- | symm ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Reflexivity thms t
-
-
-(* transitivity *)
-
-fun trans _ [thm1, thm2] _ = thm1 RSN (1, thm2 RSN (2, @{thm trans}))
- | trans ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Transitivity thms t
-
-
-(* congruence *)
-
-fun ctac prems i st = st |> (
- resolve_tac (@{thm refl} :: prems) i
- ORELSE (cong_tac i THEN ctac prems (i + 1) THEN ctac prems i))
-
-fun cong_basic ctxt thms t =
- let val st = Thm.trivial (certify_prop ctxt t)
- in
- (case Seq.pull (ctac thms 1 st) of
- SOME (thm, _) => thm
- | NONE => raise THM ("cong", 0, thms @ [st]))
- end
-
-val cong_dest_rules = @{lemma
- "(~ P | Q) & (P | ~ Q) ==> P = Q"
- "(P | ~ Q) & (~ P | Q) ==> P = Q"
- by fast+}
-
-fun cong_full ctxt thms t = prove ctxt t (fn ctxt' =>
- Method.insert_tac thms
- THEN' (Classical.fast_tac ctxt'
- ORELSE' dresolve_tac cong_dest_rules
- THEN' Classical.fast_tac ctxt'))
-
-fun cong ctxt thms = try_provers ctxt Z3_New_Proof.Monotonicity [
- ("basic", cong_basic ctxt thms),
- ("full", cong_full ctxt thms)] thms
-
-
-(* quantifier introduction *)
-
-val quant_intro_rules = @{lemma
- "(!!x. P x = Q x) ==> (ALL x. P x) = (ALL x. Q x)"
- "(!!x. P x = Q x) ==> (EX x. P x) = (EX x. Q x)"
- "(!!x. (~ P x) = Q x) ==> (~ (EX x. P x)) = (ALL x. Q x)"
- "(!!x. (~ P x) = Q x) ==> (~ (ALL x. P x)) = (EX x. Q x)"
- by fast+}
-
-fun quant_intro ctxt [thm] t =
- prove ctxt t (K (REPEAT_ALL_NEW (resolve_tac (thm :: quant_intro_rules))))
- | quant_intro ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Quant_Intro thms t
-
-
-(* distributivity of conjunctions and disjunctions *)
-
-(* TODO: there are no tests with this proof rule *)
-fun distrib ctxt _ t =
- prove_abstract' ctxt t prop_tac (abstract_prop (dest_prop t))
-
-
-(* elimination of conjunctions *)
-
-fun and_elim ctxt [thm] t =
- prove_abstract ctxt [thm] t prop_tac (
- abstract_lit (dest_prop t) ##>>
- abstract_conj (dest_thm thm) #>>
- apfst single o swap)
- | and_elim ctxt thms t = replay_rule_error ctxt Z3_New_Proof.And_Elim thms t
-
-
-(* elimination of negated disjunctions *)
-
-fun not_or_elim ctxt [thm] t =
- prove_abstract ctxt [thm] t prop_tac (
- abstract_lit (dest_prop t) ##>>
- abstract_not abstract_disj (dest_thm thm) #>>
- apfst single o swap)
- | not_or_elim ctxt thms t =
- replay_rule_error ctxt Z3_New_Proof.Not_Or_Elim thms t
-
-
-(* rewriting *)
-
-local
-
-fun dest_all (Const (@{const_name HOL.All}, _) $ Abs (_, T, t)) nctxt =
- let
- val (n, nctxt') = Name.variant "" nctxt
- val f = Free (n, T)
- val t' = Term.subst_bound (f, t)
- in dest_all t' nctxt' |>> cons f end
- | dest_all t _ = ([], t)
-
-fun dest_alls t =
- let
- val nctxt = Name.make_context (Term.add_free_names t [])
- val (lhs, rhs) = HOLogic.dest_eq (dest_prop t)
- val (ls, lhs') = dest_all lhs nctxt
- val (rs, rhs') = dest_all rhs nctxt
- in
- if eq_list (op aconv) (ls, rs) then SOME (ls, (HOLogic.mk_eq (lhs', rhs')))
- else NONE
- end
-
-fun forall_intr ctxt t thm =
- let val ct = Thm.cterm_of (Proof_Context.theory_of ctxt) t
- in Thm.forall_intr ct thm COMP_INCR @{thm iff_allI} end
-
-in
-
-fun focus_eq f ctxt t =
- (case dest_alls t of
- NONE => f ctxt t
- | SOME (vs, t') => fold (forall_intr ctxt) vs (f ctxt t'))
-
-end
-
-fun abstract_eq f (Const (@{const_name HOL.eq}, _) $ t1 $ t2) =
- f t1 ##>> f t2 #>> HOLogic.mk_eq
- | abstract_eq _ t = abstract_term t
-
-fun prove_prop_rewrite ctxt t =
- prove_abstract' ctxt t prop_tac (
- abstract_eq abstract_prop (dest_prop t))
-
-fun arith_rewrite_tac ctxt _ =
- TRY o Simplifier.simp_tac ctxt
- THEN_ALL_NEW (Arith_Data.arith_tac ctxt ORELSE' Clasimp.force_tac ctxt)
-
-fun prove_arith_rewrite ctxt t =
- prove_abstract' ctxt t arith_rewrite_tac (
- abstract_eq (abstract_arith ctxt) (dest_prop t))
-
-fun rewrite ctxt _ = try_provers ctxt Z3_New_Proof.Rewrite [
- ("rules", apply_rule ctxt),
- ("prop_rewrite", prove_prop_rewrite ctxt),
- ("arith_rewrite", focus_eq prove_arith_rewrite ctxt)] []
-
-fun rewrite_star ctxt = rewrite ctxt
-
-
-(* pulling quantifiers *)
-
-fun pull_quant ctxt _ t = prove ctxt t quant_tac
-
-
-(* pushing quantifiers *)
-
-fun push_quant _ _ _ = raise Fail "unsupported" (* FIXME *)
-
-
-(* elimination of unused bound variables *)
-
-val elim_all = @{lemma "P = Q ==> (ALL x. P) = Q" by fast}
-val elim_ex = @{lemma "P = Q ==> (EX x. P) = Q" by fast}
-
-fun elim_unused_tac i st = (
- match_tac [@{thm refl}]
- ORELSE' (match_tac [elim_all, elim_ex] THEN' elim_unused_tac)
- ORELSE' (
- match_tac [@{thm iff_allI}, @{thm iff_exI}]
- THEN' elim_unused_tac)) i st
-
-fun elim_unused ctxt _ t = prove ctxt t (fn _ => elim_unused_tac)
-
-
-(* destructive equality resolution *)
-
-fun dest_eq_res _ _ _ = raise Fail "dest_eq_res" (* FIXME *)
-
-
-(* quantifier instantiation *)
-
-val quant_inst_rule = @{lemma "~P x | Q ==> ~(ALL x. P x) | Q" by fast}
-
-fun quant_inst ctxt _ t = prove ctxt t (fn _ =>
- REPEAT_ALL_NEW (rtac quant_inst_rule)
- THEN' rtac @{thm excluded_middle})
-
-
-(* propositional lemma *)
-
-exception LEMMA of unit
-
-val intro_hyp_rule1 = @{lemma "(~P ==> Q) ==> P | Q" by fast}
-val intro_hyp_rule2 = @{lemma "(P ==> Q) ==> ~P | Q" by fast}
-
-fun norm_lemma thm =
- (thm COMP_INCR intro_hyp_rule1)
- handle THM _ => thm COMP_INCR intro_hyp_rule2
-
-fun negated_prop (@{const HOL.Not} $ t) = HOLogic.mk_Trueprop t
- | negated_prop t = HOLogic.mk_Trueprop (HOLogic.mk_not t)
-
-fun intro_hyps tab (t as @{const HOL.disj} $ t1 $ t2) cx =
- lookup_intro_hyps tab t (fold (intro_hyps tab) [t1, t2]) cx
- | intro_hyps tab t cx =
- lookup_intro_hyps tab t (fn _ => raise LEMMA ()) cx
-
-and lookup_intro_hyps tab t f (cx as (thm, terms)) =
- (case Termtab.lookup tab (negated_prop t) of
- NONE => f cx
- | SOME hyp => (norm_lemma (Thm.implies_intr hyp thm), t :: terms))
-
-fun lemma ctxt (thms as [thm]) t =
- (let
- val tab = Termtab.make (map (`Thm.term_of) (#hyps (Thm.crep_thm thm)))
- val (thm', terms) = intro_hyps tab (dest_prop t) (thm, [])
- in
- prove_abstract ctxt [thm'] t prop_tac (
- fold (snd oo abstract_lit) terms #>
- abstract_disj (dest_thm thm') #>> single ##>>
- abstract_disj (dest_prop t))
- end
- handle LEMMA () => replay_error ctxt "Bad proof state" Z3_New_Proof.Lemma thms t)
- | lemma ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Lemma thms t
-
-
-(* unit resolution *)
-
-fun abstract_unit (t as (@{const HOL.Not} $ (@{const HOL.disj} $ t1 $ t2))) =
- abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
- HOLogic.mk_not o HOLogic.mk_disj)
- | abstract_unit (t as (@{const HOL.disj} $ t1 $ t2)) =
- abstract_sub t (abstract_unit t1 ##>> abstract_unit t2 #>>
- HOLogic.mk_disj)
- | abstract_unit t = abstract_lit t
-
-fun unit_res ctxt thms t =
- prove_abstract ctxt thms t prop_tac (
- fold_map (abstract_unit o dest_thm) thms ##>>
- abstract_unit (dest_prop t) #>>
- (fn (prems, concl) => (prems, concl)))
-
-
-(* iff-true *)
-
-val iff_true_rule = @{lemma "P ==> P = True" by fast}
-
-fun iff_true _ [thm] _ = thm RS iff_true_rule
- | iff_true ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Iff_True thms t
-
-
-(* iff-false *)
-
-val iff_false_rule = @{lemma "~P ==> P = False" by fast}
-
-fun iff_false _ [thm] _ = thm RS iff_false_rule
- | iff_false ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Iff_False thms t
-
-
-(* commutativity *)
-
-fun comm ctxt _ t = match_instantiate ctxt t @{thm eq_commute}
-
-
-(* definitional axioms *)
-
-fun def_axiom_disj ctxt t =
- (case dest_prop t of
- @{const HOL.disj} $ u1 $ u2 =>
- prove_abstract' ctxt t prop_tac (
- abstract_prop u2 ##>> abstract_prop u1 #>> HOLogic.mk_disj o swap)
- | u => prove_abstract' ctxt t prop_tac (abstract_prop u))
-
-fun def_axiom ctxt _ = try_provers ctxt Z3_New_Proof.Def_Axiom [
- ("rules", apply_rule ctxt),
- ("disj", def_axiom_disj ctxt)] []
-
-
-(* application of definitions *)
-
-fun apply_def _ [thm] _ = thm (* TODO: cover also the missing cases *)
- | apply_def ctxt thms t = replay_rule_error ctxt Z3_New_Proof.Apply_Def thms t
-
-
-(* iff-oeq *)
-
-fun iff_oeq _ _ _ = raise Fail "iff_oeq" (* FIXME *)
-
-
-(* negation normal form *)
-
-fun nnf_prop ctxt thms t =
- prove_abstract ctxt thms t prop_tac (
- fold_map (abstract_prop o dest_thm) thms ##>>
- abstract_prop (dest_prop t))
-
-fun nnf ctxt rule thms = try_provers ctxt rule [
- ("prop", nnf_prop ctxt thms),
- ("quant", quant_intro ctxt [hd thms])] thms
-
-fun nnf_pos ctxt = nnf ctxt Z3_New_Proof.Nnf_Pos
-fun nnf_neg ctxt = nnf ctxt Z3_New_Proof.Nnf_Neg
-
-
-(* theory lemmas *)
-
-fun arith_th_lemma_tac ctxt prems =
- Method.insert_tac prems
- THEN' SELECT_GOAL (Local_Defs.unfold_tac ctxt @{thms z3div_def z3mod_def})
- THEN' Arith_Data.arith_tac ctxt
-
-fun arith_th_lemma ctxt thms t =
- prove_abstract ctxt thms t arith_th_lemma_tac (
- fold_map (abstract_arith ctxt o dest_thm) thms ##>>
- abstract_arith ctxt (dest_prop t))
-
-val _ = Theory.setup (Context.theory_map (add_th_lemma_method ("arith", arith_th_lemma)))
-
-fun th_lemma name ctxt thms =
- (case Symtab.lookup (get_th_lemma_method ctxt) name of
- SOME method => method ctxt thms
- | NONE => replay_error ctxt "Bad theory" (Z3_New_Proof.Th_Lemma name) thms)
-
-
-(* mapping of rules to methods *)
-
-fun unsupported rule ctxt = replay_error ctxt "Unsupported" rule
-fun assumed rule ctxt = replay_error ctxt "Assumed" rule
-
-fun choose Z3_New_Proof.True_Axiom = true_axiom
- | choose (r as Z3_New_Proof.Asserted) = assumed r
- | choose (r as Z3_New_Proof.Goal) = assumed r
- | choose Z3_New_Proof.Modus_Ponens = mp
- | choose Z3_New_Proof.Reflexivity = refl
- | choose Z3_New_Proof.Symmetry = symm
- | choose Z3_New_Proof.Transitivity = trans
- | choose (r as Z3_New_Proof.Transitivity_Star) = unsupported r
- | choose Z3_New_Proof.Monotonicity = cong
- | choose Z3_New_Proof.Quant_Intro = quant_intro
- | choose Z3_New_Proof.Distributivity = distrib
- | choose Z3_New_Proof.And_Elim = and_elim
- | choose Z3_New_Proof.Not_Or_Elim = not_or_elim
- | choose Z3_New_Proof.Rewrite = rewrite
- | choose Z3_New_Proof.Rewrite_Star = rewrite_star
- | choose Z3_New_Proof.Pull_Quant = pull_quant
- | choose (r as Z3_New_Proof.Pull_Quant_Star) = unsupported r
- | choose Z3_New_Proof.Push_Quant = push_quant
- | choose Z3_New_Proof.Elim_Unused_Vars = elim_unused
- | choose Z3_New_Proof.Dest_Eq_Res = dest_eq_res
- | choose Z3_New_Proof.Quant_Inst = quant_inst
- | choose (r as Z3_New_Proof.Hypothesis) = assumed r
- | choose Z3_New_Proof.Lemma = lemma
- | choose Z3_New_Proof.Unit_Resolution = unit_res
- | choose Z3_New_Proof.Iff_True = iff_true
- | choose Z3_New_Proof.Iff_False = iff_false
- | choose Z3_New_Proof.Commutativity = comm
- | choose Z3_New_Proof.Def_Axiom = def_axiom
- | choose (r as Z3_New_Proof.Intro_Def) = assumed r
- | choose Z3_New_Proof.Apply_Def = apply_def
- | choose Z3_New_Proof.Iff_Oeq = iff_oeq
- | choose Z3_New_Proof.Nnf_Pos = nnf_pos
- | choose Z3_New_Proof.Nnf_Neg = nnf_neg
- | choose (r as Z3_New_Proof.Nnf_Star) = unsupported r
- | choose (r as Z3_New_Proof.Cnf_Star) = unsupported r
- | choose (r as Z3_New_Proof.Skolemize) = assumed r
- | choose Z3_New_Proof.Modus_Ponens_Oeq = mp_oeq
- | choose (Z3_New_Proof.Th_Lemma name) = th_lemma name
-
-fun with_tracing rule method ctxt thms t =
- let val _ = trace_goal ctxt rule thms t
- in method ctxt thms t end
-
-fun method_for rule = with_tracing rule (choose rule)
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_replay_rules.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,54 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_replay_rules.ML
- Author: Sascha Boehme, TU Muenchen
-
-Custom rules for Z3 proof replay.
-*)
-
-signature Z3_NEW_REPLAY_RULES =
-sig
- val apply: Proof.context -> cterm -> thm option
-end;
-
-structure Z3_New_Replay_Rules: Z3_NEW_REPLAY_RULES =
-struct
-
-structure Data = Generic_Data
-(
- type T = thm Net.net
- val empty = Net.empty
- val extend = I
- val merge = Net.merge Thm.eq_thm
-)
-
-fun maybe_instantiate ct thm =
- try Thm.first_order_match (Thm.cprop_of thm, ct)
- |> Option.map (fn inst => Thm.instantiate inst thm)
-
-fun apply ctxt ct =
- let
- val net = Data.get (Context.Proof ctxt)
- val xthms = Net.match_term net (Thm.term_of ct)
-
- fun select ct = map_filter (maybe_instantiate ct) xthms
- fun select' ct =
- let val thm = Thm.trivial ct
- in map_filter (try (fn rule => rule COMP thm)) xthms end
-
- in try hd (case select ct of [] => select' ct | xthms' => xthms') end
-
-val prep = `Thm.prop_of
-
-fun ins thm net = Net.insert_term Thm.eq_thm (prep thm) net handle Net.INSERT => net
-fun del thm net = Net.delete_term Thm.eq_thm (prep thm) net handle Net.DELETE => net
-
-val add = Thm.declaration_attribute (Data.map o ins)
-val del = Thm.declaration_attribute (Data.map o del)
-
-val name = Binding.name "z3_new_rule"
-
-val description = "declaration of Z3 proof rules"
-
-val _ = Theory.setup (Attrib.setup name (Attrib.add_del add del) description #>
- Global_Theory.add_thms_dynamic (name, Net.content o Data.get))
-
-end;
--- a/src/HOL/Tools/SMT2/z3_new_replay_util.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,150 +0,0 @@
-(* Title: HOL/Tools/SMT2/z3_new_replay_util.ML
- Author: Sascha Boehme, TU Muenchen
-
-Helper functions required for Z3 proof replay.
-*)
-
-signature Z3_NEW_REPLAY_UTIL =
-sig
- (*theorem nets*)
- val thm_net_of: ('a -> thm) -> 'a list -> 'a Net.net
- val net_instances: (int * thm) Net.net -> cterm -> (int * thm) list
-
- (*proof combinators*)
- val under_assumption: (thm -> thm) -> cterm -> thm
- val discharge: thm -> thm -> thm
-
- (*a faster COMP*)
- type compose_data
- val precompose: (cterm -> cterm list) -> thm -> compose_data
- val precompose2: (cterm -> cterm * cterm) -> thm -> compose_data
- val compose: compose_data -> thm -> thm
-
- (*simpset*)
- val add_simproc: Simplifier.simproc -> Context.generic -> Context.generic
- val make_simpset: Proof.context -> thm list -> simpset
-end;
-
-structure Z3_New_Replay_Util: Z3_NEW_REPLAY_UTIL =
-struct
-
-(* theorem nets *)
-
-fun thm_net_of f xthms =
- let fun insert xthm = Net.insert_term (K false) (Thm.prop_of (f xthm), xthm)
- in fold insert xthms Net.empty end
-
-fun maybe_instantiate ct thm =
- try Thm.first_order_match (Thm.cprop_of thm, ct)
- |> Option.map (fn inst => Thm.instantiate inst thm)
-
-local
- fun instances_from_net match f net ct =
- let
- val lookup = if match then Net.match_term else Net.unify_term
- val xthms = lookup net (Thm.term_of ct)
- fun select ct = map_filter (f (maybe_instantiate ct)) xthms
- fun select' ct =
- let val thm = Thm.trivial ct
- in map_filter (f (try (fn rule => rule COMP thm))) xthms end
- in (case select ct of [] => select' ct | xthms' => xthms') end
-in
-
-fun net_instances net =
- instances_from_net false (fn f => fn (i, thm) => Option.map (pair i) (f thm))
- net
-
-end
-
-
-(* proof combinators *)
-
-fun under_assumption f ct =
- let val ct' = SMT2_Util.mk_cprop ct in Thm.implies_intr ct' (f (Thm.assume ct')) end
-
-fun discharge p pq = Thm.implies_elim pq p
-
-
-(* a faster COMP *)
-
-type compose_data = cterm list * (cterm -> cterm list) * thm
-
-fun list2 (x, y) = [x, y]
-
-fun precompose f rule = (f (Thm.cprem_of rule 1), f, rule)
-fun precompose2 f rule = precompose (list2 o f) rule
-
-fun compose (cvs, f, rule) thm =
- discharge thm (Thm.instantiate ([], cvs ~~ f (Thm.cprop_of thm)) rule)
-
-
-(* simpset *)
-
-local
- val antisym_le1 = mk_meta_eq @{thm order_class.antisym_conv}
- val antisym_le2 = mk_meta_eq @{thm linorder_class.antisym_conv2}
- val antisym_less1 = mk_meta_eq @{thm linorder_class.antisym_conv1}
- val antisym_less2 = mk_meta_eq @{thm linorder_class.antisym_conv3}
-
- fun eq_prop t thm = HOLogic.mk_Trueprop t aconv Thm.prop_of thm
- fun dest_binop ((c as Const _) $ t $ u) = (c, t, u)
- | dest_binop t = raise TERM ("dest_binop", [t])
-
- fun prove_antisym_le ctxt t =
- let
- val (le, r, s) = dest_binop t
- val less = Const (@{const_name less}, Term.fastype_of le)
- val prems = Simplifier.prems_of ctxt
- in
- (case find_first (eq_prop (le $ s $ r)) prems of
- NONE =>
- find_first (eq_prop (HOLogic.mk_not (less $ r $ s))) prems
- |> Option.map (fn thm => thm RS antisym_less1)
- | SOME thm => SOME (thm RS antisym_le1))
- end
- handle THM _ => NONE
-
- fun prove_antisym_less ctxt t =
- let
- val (less, r, s) = dest_binop (HOLogic.dest_not t)
- val le = Const (@{const_name less_eq}, Term.fastype_of less)
- val prems = Simplifier.prems_of ctxt
- in
- (case find_first (eq_prop (le $ r $ s)) prems of
- NONE =>
- find_first (eq_prop (HOLogic.mk_not (less $ s $ r))) prems
- |> Option.map (fn thm => thm RS antisym_less2)
- | SOME thm => SOME (thm RS antisym_le2))
- end
- handle THM _ => NONE
-
- val basic_simpset =
- simpset_of (put_simpset HOL_ss @{context}
- addsimps @{thms field_simps times_divide_eq_right times_divide_eq_left arith_special
- arith_simps rel_simps array_rules z3div_def z3mod_def}
- addsimprocs [@{simproc binary_int_div}, @{simproc binary_int_mod},
- Simplifier.simproc_global @{theory} "fast_int_arith" [
- "(m::int) < n", "(m::int) <= n", "(m::int) = n"] Lin_Arith.simproc,
- Simplifier.simproc_global @{theory} "antisym_le" ["(x::'a::order) <= y"] prove_antisym_le,
- Simplifier.simproc_global @{theory} "antisym_less" ["~ (x::'a::linorder) < y"]
- prove_antisym_less])
-
- structure Simpset = Generic_Data
- (
- type T = simpset
- val empty = basic_simpset
- val extend = I
- val merge = Simplifier.merge_ss
- )
-in
-
-fun add_simproc simproc context =
- Simpset.map (simpset_map (Context.proof_of context)
- (fn ctxt => ctxt addsimprocs [simproc])) context
-
-fun make_simpset ctxt rules =
- simpset_of (put_simpset (Simpset.get (Context.Proof ctxt)) ctxt addsimps rules)
-
-end
-
-end;
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML Thu Aug 28 00:40:38 2014 +0200
@@ -56,8 +56,8 @@
val veriT_simp_arith_rule = "simp_arith"
val veriT_tmp_ite_elim_rule = "tmp_ite_elim"
val veriT_tmp_skolemize_rule = "tmp_skolemize"
-val z3_skolemize_rule = Z3_New_Proof.string_of_rule Z3_New_Proof.Skolemize
-val z3_th_lemma_rule_prefix = Z3_New_Proof.string_of_rule (Z3_New_Proof.Th_Lemma "")
+val z3_skolemize_rule = Z3_Proof.string_of_rule Z3_Proof.Skolemize
+val z3_th_lemma_rule_prefix = Z3_Proof.string_of_rule (Z3_Proof.Th_Lemma "")
val zipperposition_cnf_rule = "cnf"
val skolemize_rules =
@@ -153,7 +153,7 @@
fun massage_methods (meths as meth :: _) =
if not try0 then [meth]
- else if smt_proofs = SOME true then SMT2_Method :: meths
+ else if smt_proofs = SOME true then SMT_Method :: meths
else meths
val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
@@ -402,7 +402,7 @@
fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =
(case play of
- Played _ => meth = SMT2_Method andalso smt_proofs <> SOME true
+ Played _ => meth = SMT_Method andalso smt_proofs <> SOME true
| Play_Timed_Out time => Time.> (time, Time.zeroTime)
| Play_Failed => true)
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_proof_methods.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_proof_methods.ML Thu Aug 28 00:40:38 2014 +0200
@@ -12,7 +12,7 @@
datatype proof_method =
Metis_Method of string option * string option |
Meson_Method |
- SMT2_Method |
+ SMT_Method |
SATx_Method |
Blast_Method |
Simp_Method |
@@ -51,7 +51,7 @@
datatype proof_method =
Metis_Method of string option * string option |
Meson_Method |
- SMT2_Method |
+ SMT_Method |
SATx_Method |
Blast_Method |
Simp_Method |
@@ -73,7 +73,7 @@
fun is_proof_method_direct (Metis_Method _) = true
| is_proof_method_direct Meson_Method = true
- | is_proof_method_direct SMT2_Method = true
+ | is_proof_method_direct SMT_Method = true
| is_proof_method_direct Simp_Method = true
| is_proof_method_direct Simp_Size_Method = true
| is_proof_method_direct _ = false
@@ -88,7 +88,7 @@
| Metis_Method (type_enc_opt, lam_trans_opt) =>
"metis (" ^ commas (map_filter I [type_enc_opt, lam_trans_opt]) ^ ")"
| Meson_Method => "meson"
- | SMT2_Method => "smt2"
+ | SMT_Method => "smt"
| SATx_Method => "satx"
| Blast_Method => "blast"
| Simp_Method => if null ss then "simp" else "simp add:"
@@ -114,9 +114,9 @@
(lam_trans_opt |> the_default default_metis_lam_trans) ctxt global_facts
end
| Meson_Method => Meson_Tactic.meson_general_tac (silence_methods ctxt) global_facts
- | SMT2_Method =>
- let val ctxt = Config.put SMT2_Config.verbose false ctxt in
- SMT2_Solver.smt2_tac ctxt global_facts
+ | SMT_Method =>
+ let val ctxt = Config.put SMT_Config.verbose false ctxt in
+ SMT_Solver.smt_tac ctxt global_facts
end
| Simp_Method => Simplifier.asm_full_simp_tac (silence_methods ctxt addsimps global_facts)
| Simp_Size_Method =>
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover.ML Thu Aug 28 00:40:38 2014 +0200
@@ -177,7 +177,7 @@
[Metis_Method (SOME full_typesN, NONE),
Metis_Method (SOME no_typesN, SOME desperate_lam_trans),
Metis_Method (SOME really_full_type_enc, SOME desperate_lam_trans)])] @
- (if smt_proofs then [[SMT2_Method]] else [])
+ (if smt_proofs then [[SMT_Method]] else [])
fun is_fact_chained ((_, (sc, _)), _) = sc = Chained
@@ -196,8 +196,7 @@
let
val thy = Proof_Context.theory_of ctxt
val (remote_provers, local_provers) =
- sort_strings (supported_atps thy) @
- sort_strings (SMT2_Config.available_solvers_of ctxt)
+ sort_strings (supported_atps thy) @ sort_strings (SMT_Config.available_solvers_of ctxt)
|> List.partition (String.isPrefix remote_prefix)
in
Output.urgent_message ("Supported provers: " ^ commas (local_provers @ remote_provers) ^ ".")
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_minimize.ML Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_minimize.ML Thu Aug 28 00:40:38 2014 +0200
@@ -41,22 +41,22 @@
open Sledgehammer_Isar
open Sledgehammer_Prover
open Sledgehammer_Prover_ATP
-open Sledgehammer_Prover_SMT2
+open Sledgehammer_Prover_SMT
fun is_prover_supported ctxt =
let val thy = Proof_Context.theory_of ctxt in
- is_atp thy orf is_smt2_prover ctxt
+ is_atp thy orf is_smt_prover ctxt
end
fun is_prover_installed ctxt =
- is_smt2_prover ctxt orf is_atp_installed (Proof_Context.theory_of ctxt)
+ is_smt_prover ctxt orf is_atp_installed (Proof_Context.theory_of ctxt)
fun default_max_facts_of_prover ctxt name =
let val thy = Proof_Context.theory_of ctxt in
if is_atp thy name then
fold (Integer.max o fst o #1 o fst o snd) (#best_slices (get_atp thy name ()) ctxt) 0
- else if is_smt2_prover ctxt name then
- SMT2_Solver.default_max_relevant ctxt name
+ else if is_smt_prover ctxt name then
+ SMT_Solver.default_max_relevant ctxt name
else
error ("No such prover: " ^ name ^ ".")
end
@@ -64,7 +64,7 @@
fun get_prover ctxt mode name =
let val thy = Proof_Context.theory_of ctxt in
if is_atp thy name then run_atp mode name
- else if is_smt2_prover ctxt name then run_smt2_solver mode name
+ else if is_smt_prover ctxt name then run_smt_solver mode name
else error ("No such prover: " ^ name ^ ".")
end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,224 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_prover_smt.ML
+ Author: Fabian Immler, TU Muenchen
+ Author: Makarius
+ Author: Jasmin Blanchette, TU Muenchen
+
+SMT solvers as Sledgehammer provers.
+*)
+
+signature SLEDGEHAMMER_PROVER_SMT =
+sig
+ type stature = ATP_Problem_Generate.stature
+ type mode = Sledgehammer_Prover.mode
+ type prover = Sledgehammer_Prover.prover
+
+ val smt_builtins : bool Config.T
+ val smt_triggers : bool Config.T
+ val smt_max_slices : int Config.T
+ val smt_slice_fact_frac : real Config.T
+ val smt_slice_time_frac : real Config.T
+ val smt_slice_min_secs : int Config.T
+
+ val is_smt_prover : Proof.context -> string -> bool
+ val run_smt_solver : mode -> string -> prover
+end;
+
+structure Sledgehammer_Prover_SMT : SLEDGEHAMMER_PROVER_SMT =
+struct
+
+open ATP_Util
+open ATP_Proof
+open ATP_Systems
+open ATP_Problem_Generate
+open ATP_Proof_Reconstruct
+open Sledgehammer_Util
+open Sledgehammer_Proof_Methods
+open Sledgehammer_Isar
+open Sledgehammer_Prover
+
+val smt_builtins = Attrib.setup_config_bool @{binding sledgehammer_smt_builtins} (K true)
+val smt_triggers = Attrib.setup_config_bool @{binding sledgehammer_smt_triggers} (K true)
+
+val is_smt_prover = member (op =) o SMT_Config.available_solvers_of
+
+(* "SMT_Failure.Abnormal_Termination" carries the solver's return code. Until these are sorted out
+ properly in the SMT module, we must interpret these here. *)
+val z3_failures =
+ [(101, OutOfResources),
+ (103, MalformedInput),
+ (110, MalformedInput),
+ (112, TimedOut)]
+val unix_failures =
+ [(138, Crashed),
+ (139, Crashed)]
+val smt_failures = z3_failures @ unix_failures
+
+fun failure_of_smt_failure (SMT_Failure.Counterexample genuine) =
+ if genuine then Unprovable else GaveUp
+ | failure_of_smt_failure SMT_Failure.Time_Out = TimedOut
+ | failure_of_smt_failure (SMT_Failure.Abnormal_Termination code) =
+ (case AList.lookup (op =) smt_failures code of
+ SOME failure => failure
+ | NONE => UnknownError ("Abnormal termination with exit code " ^ string_of_int code ^ "."))
+ | failure_of_smt_failure SMT_Failure.Out_Of_Memory = OutOfResources
+ | failure_of_smt_failure (SMT_Failure.Other_Failure s) = UnknownError s
+
+(* FUDGE *)
+val smt_max_slices = Attrib.setup_config_int @{binding sledgehammer_smt_max_slices} (K 8)
+val smt_slice_fact_frac =
+ Attrib.setup_config_real @{binding sledgehammer_smt_slice_fact_frac} (K 0.667)
+val smt_slice_time_frac =
+ Attrib.setup_config_real @{binding sledgehammer_smt_slice_time_frac} (K 0.333)
+val smt_slice_min_secs = Attrib.setup_config_int @{binding sledgehammer_smt_slice_min_secs} (K 3)
+
+val is_boring_builtin_typ =
+ not o exists_subtype (member (op =) [@{typ nat}, @{typ int}, HOLogic.realT])
+
+fun smt_filter_loop name ({debug, overlord, max_mono_iters, max_new_mono_instances, timeout, slice,
+ ...} : params) state goal i =
+ let
+ fun repair_context ctxt =
+ ctxt |> Context.proof_map (SMT_Config.select_solver name)
+ |> Config.put SMT_Config.verbose debug
+ |> (if overlord then
+ Config.put SMT_Config.debug_files
+ (overlord_file_location_of_prover name |> (fn (path, name) => path ^ "/" ^ name))
+ else
+ I)
+ |> Config.put SMT_Config.infer_triggers (Config.get ctxt smt_triggers)
+ |> not (Config.get ctxt smt_builtins)
+ ? (SMT_Builtin.filter_builtins is_boring_builtin_typ
+ #> Config.put SMT_Systems.z3_extensions false)
+ |> repair_monomorph_context max_mono_iters default_max_mono_iters max_new_mono_instances
+ default_max_new_mono_instances
+
+ val state = Proof.map_context (repair_context) state
+ val ctxt = Proof.context_of state
+ val max_slices = if slice then Config.get ctxt smt_max_slices else 1
+
+ fun do_slice timeout slice outcome0 time_so_far (factss as (fact_filter, facts) :: _) =
+ let
+ val timer = Timer.startRealTimer ()
+ val slice_timeout =
+ if slice < max_slices then
+ let val ms = Time.toMilliseconds timeout in
+ Int.min (ms, Int.max (1000 * Config.get ctxt smt_slice_min_secs,
+ Real.ceil (Config.get ctxt smt_slice_time_frac * Real.fromInt ms)))
+ |> Time.fromMilliseconds
+ end
+ else
+ timeout
+ val num_facts = length facts
+ val _ =
+ if debug then
+ quote name ^ " slice " ^ string_of_int slice ^ " with " ^ string_of_int num_facts ^
+ " fact" ^ plural_s num_facts ^ " for " ^ string_of_time slice_timeout
+ |> Output.urgent_message
+ else
+ ()
+ val birth = Timer.checkRealTimer timer
+
+ val filter_result as {outcome, ...} =
+ SMT_Solver.smt_filter ctxt goal facts i slice_timeout
+ handle exn =>
+ if Exn.is_interrupt exn orelse debug then
+ reraise exn
+ else
+ {outcome = SOME (SMT_Failure.Other_Failure (Runtime.exn_message exn)),
+ fact_ids = [], atp_proof = K []}
+
+ val death = Timer.checkRealTimer timer
+ val outcome0 = if is_none outcome0 then SOME outcome else outcome0
+ val time_so_far = Time.+ (time_so_far, Time.- (death, birth))
+ val timeout = Time.- (timeout, Timer.checkRealTimer timer)
+
+ val too_many_facts_perhaps =
+ (case outcome of
+ NONE => false
+ | SOME (SMT_Failure.Counterexample _) => false
+ | SOME SMT_Failure.Time_Out => slice_timeout <> timeout
+ | SOME (SMT_Failure.Abnormal_Termination _) => true (* kind of *)
+ | SOME SMT_Failure.Out_Of_Memory => true
+ | SOME (SMT_Failure.Other_Failure _) => true)
+ in
+ if too_many_facts_perhaps andalso slice < max_slices andalso num_facts > 0 andalso
+ Time.> (timeout, Time.zeroTime) then
+ let
+ val new_num_facts =
+ Real.ceil (Config.get ctxt smt_slice_fact_frac * Real.fromInt num_facts)
+ val factss as (new_fact_filter, _) :: _ =
+ factss
+ |> (fn (x :: xs) => xs @ [x])
+ |> app_hd (apsnd (take new_num_facts))
+ val show_filter = fact_filter <> new_fact_filter
+
+ fun num_of_facts fact_filter num_facts =
+ string_of_int num_facts ^ (if show_filter then " " ^ quote fact_filter else "") ^
+ " fact" ^ plural_s num_facts
+
+ val _ =
+ if debug then
+ quote name ^ " invoked with " ^
+ num_of_facts fact_filter num_facts ^ ": " ^
+ string_of_atp_failure (failure_of_smt_failure (the outcome)) ^
+ " Retrying with " ^ num_of_facts new_fact_filter new_num_facts ^
+ "..."
+ |> Output.urgent_message
+ else
+ ()
+ in
+ do_slice timeout (slice + 1) outcome0 time_so_far factss
+ end
+ else
+ {outcome = if is_none outcome then NONE else the outcome0, filter_result = filter_result,
+ used_from = facts, run_time = time_so_far}
+ end
+ in
+ do_slice timeout 1 NONE Time.zeroTime
+ end
+
+fun run_smt_solver mode name (params as {debug, verbose, isar_proofs, compress, try0, smt_proofs,
+ minimize, preplay_timeout, ...})
+ ({state, goal, subgoal, subgoal_count, factss, ...} : prover_problem) =
+ let
+ val thy = Proof.theory_of state
+ val ctxt = Proof.context_of state
+
+ val factss = map (apsnd (map (apsnd (Thm.transfer thy)))) factss
+
+ val {outcome, filter_result = {fact_ids, atp_proof, ...}, used_from, run_time} =
+ smt_filter_loop name params state goal subgoal factss
+ val used_named_facts = map snd fact_ids
+ val used_facts = sort_wrt fst (map fst used_named_facts)
+ val outcome = Option.map failure_of_smt_failure outcome
+
+ val (preferred_methss, message) =
+ (case outcome of
+ NONE =>
+ let
+ val preferred_methss =
+ (SMT_Method, bunches_of_proof_methods try0 (smt_proofs <> SOME false) false liftingN)
+ in
+ (preferred_methss,
+ fn preplay =>
+ let
+ val _ = if verbose then Output.urgent_message "Generating proof text..." else ()
+
+ fun isar_params () =
+ (verbose, (NONE, NONE), preplay_timeout, compress, try0, minimize, atp_proof (),
+ goal)
+
+ val one_line_params = (preplay (), proof_banner mode name, subgoal, subgoal_count)
+ val num_chained = length (#facts (Proof.goal state))
+ in
+ proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
+ one_line_params
+ end)
+ end
+ | SOME failure => ((Auto_Method (* dummy *), []), fn _ => string_of_atp_failure failure))
+ in
+ {outcome = outcome, used_facts = used_facts, used_from = used_from,
+ preferred_methss = preferred_methss, run_time = run_time, message = message}
+ end
+
+end;
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_prover_smt2.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,224 +0,0 @@
-(* Title: HOL/Tools/Sledgehammer/sledgehammer_prover_smt2.ML
- Author: Fabian Immler, TU Muenchen
- Author: Makarius
- Author: Jasmin Blanchette, TU Muenchen
-
-SMT solvers as Sledgehammer provers.
-*)
-
-signature SLEDGEHAMMER_PROVER_SMT2 =
-sig
- type stature = ATP_Problem_Generate.stature
- type mode = Sledgehammer_Prover.mode
- type prover = Sledgehammer_Prover.prover
-
- val smt2_builtins : bool Config.T
- val smt2_triggers : bool Config.T
- val smt2_max_slices : int Config.T
- val smt2_slice_fact_frac : real Config.T
- val smt2_slice_time_frac : real Config.T
- val smt2_slice_min_secs : int Config.T
-
- val is_smt2_prover : Proof.context -> string -> bool
- val run_smt2_solver : mode -> string -> prover
-end;
-
-structure Sledgehammer_Prover_SMT2 : SLEDGEHAMMER_PROVER_SMT2 =
-struct
-
-open ATP_Util
-open ATP_Proof
-open ATP_Systems
-open ATP_Problem_Generate
-open ATP_Proof_Reconstruct
-open Sledgehammer_Util
-open Sledgehammer_Proof_Methods
-open Sledgehammer_Isar
-open Sledgehammer_Prover
-
-val smt2_builtins = Attrib.setup_config_bool @{binding sledgehammer_smt2_builtins} (K true)
-val smt2_triggers = Attrib.setup_config_bool @{binding sledgehammer_smt2_triggers} (K true)
-
-val is_smt2_prover = member (op =) o SMT2_Config.available_solvers_of
-
-(* "SMT2_Failure.Abnormal_Termination" carries the solver's return code. Until these are sorted out
- properly in the SMT module, we must interpret these here. *)
-val z3_failures =
- [(101, OutOfResources),
- (103, MalformedInput),
- (110, MalformedInput),
- (112, TimedOut)]
-val unix_failures =
- [(138, Crashed),
- (139, Crashed)]
-val smt2_failures = z3_failures @ unix_failures
-
-fun failure_of_smt2_failure (SMT2_Failure.Counterexample genuine) =
- if genuine then Unprovable else GaveUp
- | failure_of_smt2_failure SMT2_Failure.Time_Out = TimedOut
- | failure_of_smt2_failure (SMT2_Failure.Abnormal_Termination code) =
- (case AList.lookup (op =) smt2_failures code of
- SOME failure => failure
- | NONE => UnknownError ("Abnormal termination with exit code " ^ string_of_int code ^ "."))
- | failure_of_smt2_failure SMT2_Failure.Out_Of_Memory = OutOfResources
- | failure_of_smt2_failure (SMT2_Failure.Other_Failure s) = UnknownError s
-
-(* FUDGE *)
-val smt2_max_slices = Attrib.setup_config_int @{binding sledgehammer_smt2_max_slices} (K 8)
-val smt2_slice_fact_frac =
- Attrib.setup_config_real @{binding sledgehammer_smt2_slice_fact_frac} (K 0.667)
-val smt2_slice_time_frac =
- Attrib.setup_config_real @{binding sledgehammer_smt2_slice_time_frac} (K 0.333)
-val smt2_slice_min_secs = Attrib.setup_config_int @{binding sledgehammer_smt2_slice_min_secs} (K 3)
-
-val is_boring_builtin_typ =
- not o exists_subtype (member (op =) [@{typ nat}, @{typ int}, HOLogic.realT])
-
-fun smt2_filter_loop name ({debug, overlord, max_mono_iters, max_new_mono_instances, timeout, slice,
- ...} : params) state goal i =
- let
- fun repair_context ctxt =
- ctxt |> Context.proof_map (SMT2_Config.select_solver name)
- |> Config.put SMT2_Config.verbose debug
- |> (if overlord then
- Config.put SMT2_Config.debug_files
- (overlord_file_location_of_prover name |> (fn (path, name) => path ^ "/" ^ name))
- else
- I)
- |> Config.put SMT2_Config.infer_triggers (Config.get ctxt smt2_triggers)
- |> not (Config.get ctxt smt2_builtins)
- ? (SMT2_Builtin.filter_builtins is_boring_builtin_typ
- #> Config.put SMT2_Systems.z3_extensions false)
- |> repair_monomorph_context max_mono_iters default_max_mono_iters max_new_mono_instances
- default_max_new_mono_instances
-
- val state = Proof.map_context (repair_context) state
- val ctxt = Proof.context_of state
- val max_slices = if slice then Config.get ctxt smt2_max_slices else 1
-
- fun do_slice timeout slice outcome0 time_so_far (factss as (fact_filter, facts) :: _) =
- let
- val timer = Timer.startRealTimer ()
- val slice_timeout =
- if slice < max_slices then
- let val ms = Time.toMilliseconds timeout in
- Int.min (ms, Int.max (1000 * Config.get ctxt smt2_slice_min_secs,
- Real.ceil (Config.get ctxt smt2_slice_time_frac * Real.fromInt ms)))
- |> Time.fromMilliseconds
- end
- else
- timeout
- val num_facts = length facts
- val _ =
- if debug then
- quote name ^ " slice " ^ string_of_int slice ^ " with " ^ string_of_int num_facts ^
- " fact" ^ plural_s num_facts ^ " for " ^ string_of_time slice_timeout
- |> Output.urgent_message
- else
- ()
- val birth = Timer.checkRealTimer timer
-
- val filter_result as {outcome, ...} =
- SMT2_Solver.smt2_filter ctxt goal facts i slice_timeout
- handle exn =>
- if Exn.is_interrupt exn orelse debug then
- reraise exn
- else
- {outcome = SOME (SMT2_Failure.Other_Failure (Runtime.exn_message exn)),
- fact_ids = [], atp_proof = K []}
-
- val death = Timer.checkRealTimer timer
- val outcome0 = if is_none outcome0 then SOME outcome else outcome0
- val time_so_far = Time.+ (time_so_far, Time.- (death, birth))
- val timeout = Time.- (timeout, Timer.checkRealTimer timer)
-
- val too_many_facts_perhaps =
- (case outcome of
- NONE => false
- | SOME (SMT2_Failure.Counterexample _) => false
- | SOME SMT2_Failure.Time_Out => slice_timeout <> timeout
- | SOME (SMT2_Failure.Abnormal_Termination _) => true (* kind of *)
- | SOME SMT2_Failure.Out_Of_Memory => true
- | SOME (SMT2_Failure.Other_Failure _) => true)
- in
- if too_many_facts_perhaps andalso slice < max_slices andalso num_facts > 0 andalso
- Time.> (timeout, Time.zeroTime) then
- let
- val new_num_facts =
- Real.ceil (Config.get ctxt smt2_slice_fact_frac * Real.fromInt num_facts)
- val factss as (new_fact_filter, _) :: _ =
- factss
- |> (fn (x :: xs) => xs @ [x])
- |> app_hd (apsnd (take new_num_facts))
- val show_filter = fact_filter <> new_fact_filter
-
- fun num_of_facts fact_filter num_facts =
- string_of_int num_facts ^ (if show_filter then " " ^ quote fact_filter else "") ^
- " fact" ^ plural_s num_facts
-
- val _ =
- if debug then
- quote name ^ " invoked with " ^
- num_of_facts fact_filter num_facts ^ ": " ^
- string_of_atp_failure (failure_of_smt2_failure (the outcome)) ^
- " Retrying with " ^ num_of_facts new_fact_filter new_num_facts ^
- "..."
- |> Output.urgent_message
- else
- ()
- in
- do_slice timeout (slice + 1) outcome0 time_so_far factss
- end
- else
- {outcome = if is_none outcome then NONE else the outcome0, filter_result = filter_result,
- used_from = facts, run_time = time_so_far}
- end
- in
- do_slice timeout 1 NONE Time.zeroTime
- end
-
-fun run_smt2_solver mode name (params as {debug, verbose, isar_proofs, compress, try0, smt_proofs,
- minimize, preplay_timeout, ...})
- ({state, goal, subgoal, subgoal_count, factss, ...} : prover_problem) =
- let
- val thy = Proof.theory_of state
- val ctxt = Proof.context_of state
-
- val factss = map (apsnd (map (apsnd (Thm.transfer thy)))) factss
-
- val {outcome, filter_result = {fact_ids, atp_proof, ...}, used_from, run_time} =
- smt2_filter_loop name params state goal subgoal factss
- val used_named_facts = map snd fact_ids
- val used_facts = sort_wrt fst (map fst used_named_facts)
- val outcome = Option.map failure_of_smt2_failure outcome
-
- val (preferred_methss, message) =
- (case outcome of
- NONE =>
- let
- val preferred_methss =
- (SMT2_Method, bunches_of_proof_methods try0 (smt_proofs <> SOME false) false liftingN)
- in
- (preferred_methss,
- fn preplay =>
- let
- val _ = if verbose then Output.urgent_message "Generating proof text..." else ()
-
- fun isar_params () =
- (verbose, (NONE, NONE), preplay_timeout, compress, try0, minimize, atp_proof (),
- goal)
-
- val one_line_params = (preplay (), proof_banner mode name, subgoal, subgoal_count)
- val num_chained = length (#facts (Proof.goal state))
- in
- proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
- one_line_params
- end)
- end
- | SOME failure => ((Auto_Method (* dummy *), []), fn _ => string_of_atp_failure failure))
- in
- {outcome = outcome, used_facts = used_facts, used_from = used_from,
- preferred_methss = preferred_methss, run_time = run_time, message = message}
- end
-
-end;
--- a/src/HOL/Word/Tools/smt2_word.ML Thu Aug 28 00:40:38 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,138 +0,0 @@
-(* Title: HOL/Word/Tools/smt2_word.ML
- Author: Sascha Boehme, TU Muenchen
-
-SMT setup for words.
-*)
-
-structure SMT2_Word: sig end =
-struct
-
-open Word_Lib
-
-
-(* SMT-LIB logic *)
-
-(* "QF_AUFBV" is too restrictive for Isabelle's problems, which contain aritmetic and quantifiers.
- Better set the logic to "" and make at least Z3 happy. *)
-fun smtlib_logic ts =
- if exists (Term.exists_type (Term.exists_subtype is_wordT)) ts then SOME "" else NONE
-
-
-(* SMT-LIB builtins *)
-
-local
- val smtlib2C = SMTLIB2_Interface.smtlib2C
-
- val wordT = @{typ "'a::len word"}
-
- fun index1 s i = "(_ " ^ s ^ " " ^ string_of_int i ^ ")"
- fun index2 s i j = "(_ " ^ s ^ " " ^ string_of_int i ^ " " ^ string_of_int j ^ ")"
-
- fun word_typ (Type (@{type_name word}, [T])) = Option.map (index1 "BitVec") (try dest_binT T)
- | word_typ _ = NONE
-
- fun word_num (Type (@{type_name word}, [T])) k =
- Option.map (index1 ("bv" ^ string_of_int k)) (try dest_binT T)
- | word_num _ _ = NONE
-
- fun if_fixed pred m n T ts =
- let val (Us, U) = Term.strip_type T
- in
- if pred (U, Us) then SOME (n, length Us, ts, Term.list_comb o pair (Const (m, T))) else NONE
- end
-
- fun if_fixed_all m = if_fixed (forall (can dest_wordT) o (op ::)) m
- fun if_fixed_args m = if_fixed (forall (can dest_wordT) o snd) m
-
- fun add_word_fun f (t, n) =
- let val (m, _) = Term.dest_Const t
- in SMT2_Builtin.add_builtin_fun smtlib2C (Term.dest_Const t, K (f m n)) end
-
- val mk_nat = HOLogic.mk_number @{typ nat}
-
- fun mk_shift c [t, u] = Const c $ t $ mk_nat (snd (HOLogic.dest_number u))
- | mk_shift c ts = raise TERM ("bad arguments", Const c :: ts)
-
- fun shift m n T ts =
- let val U = Term.domain_type T
- in
- (case (can dest_wordT U, try (snd o HOLogic.dest_number o hd o tl) ts) of
- (true, SOME i) =>
- SOME (n, 2, [hd ts, HOLogic.mk_number U i], mk_shift (m, T))
- | _ => NONE) (* FIXME: also support non-numerical shifts *)
- end
-
- fun mk_extract c i ts = Term.list_comb (Const c, mk_nat i :: ts)
-
- fun extract m n T ts =
- let val U = Term.range_type (Term.range_type T)
- in
- (case (try (snd o HOLogic.dest_number o hd) ts, try dest_wordT U) of
- (SOME lb, SOME i) =>
- SOME (index2 n (i + lb - 1) lb, 1, tl ts, mk_extract (m, T) lb)
- | _ => NONE)
- end
-
- fun mk_extend c ts = Term.list_comb (Const c, ts)
-
- fun extend m n T ts =
- let val (U1, U2) = Term.dest_funT T
- in
- (case (try dest_wordT U1, try dest_wordT U2) of
- (SOME i, SOME j) =>
- if j-i >= 0 then SOME (index1 n (j-i), 1, ts, mk_extend (m, T))
- else NONE
- | _ => NONE)
- end
-
- fun mk_rotate c i ts = Term.list_comb (Const c, mk_nat i :: ts)
-
- fun rotate m n T ts =
- let val U = Term.domain_type (Term.range_type T)
- in
- (case (can dest_wordT U, try (snd o HOLogic.dest_number o hd) ts) of
- (true, SOME i) => SOME (index1 n i, 1, tl ts, mk_rotate (m, T) i)
- | _ => NONE)
- end
-in
-
-val setup_builtins =
- SMT2_Builtin.add_builtin_typ smtlib2C (wordT, word_typ, word_num) #>
- fold (add_word_fun if_fixed_all) [
- (@{term "uminus :: 'a::len word => _"}, "bvneg"),
- (@{term "plus :: 'a::len word => _"}, "bvadd"),
- (@{term "minus :: 'a::len word => _"}, "bvsub"),
- (@{term "times :: 'a::len word => _"}, "bvmul"),
- (@{term "bitNOT :: 'a::len word => _"}, "bvnot"),
- (@{term "bitAND :: 'a::len word => _"}, "bvand"),
- (@{term "bitOR :: 'a::len word => _"}, "bvor"),
- (@{term "bitXOR :: 'a::len word => _"}, "bvxor"),
- (@{term "word_cat :: 'a::len word => _"}, "concat") ] #>
- fold (add_word_fun shift) [
- (@{term "shiftl :: 'a::len word => _ "}, "bvshl"),
- (@{term "shiftr :: 'a::len word => _"}, "bvlshr"),
- (@{term "sshiftr :: 'a::len word => _"}, "bvashr") ] #>
- add_word_fun extract
- (@{term "slice :: _ => 'a::len word => _"}, "extract") #>
- fold (add_word_fun extend) [
- (@{term "ucast :: 'a::len word => _"}, "zero_extend"),
- (@{term "scast :: 'a::len word => _"}, "sign_extend") ] #>
- fold (add_word_fun rotate) [
- (@{term word_rotl}, "rotate_left"),
- (@{term word_rotr}, "rotate_right") ] #>
- fold (add_word_fun if_fixed_args) [
- (@{term "less :: 'a::len word => _"}, "bvult"),
- (@{term "less_eq :: 'a::len word => _"}, "bvule"),
- (@{term word_sless}, "bvslt"),
- (@{term word_sle}, "bvsle") ]
-
-end
-
-
-(* setup *)
-
-val _ = Theory.setup (Context.theory_map (
- SMTLIB2_Interface.add_logic (20, smtlib_logic) #>
- setup_builtins))
-
-end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Word/Tools/smt_word.ML Thu Aug 28 00:40:38 2014 +0200
@@ -0,0 +1,138 @@
+(* Title: HOL/Word/Tools/smt_word.ML
+ Author: Sascha Boehme, TU Muenchen
+
+SMT setup for words.
+*)
+
+structure SMT_Word: sig end =
+struct
+
+open Word_Lib
+
+
+(* SMT-LIB logic *)
+
+(* "QF_AUFBV" is too restrictive for Isabelle's problems, which contain aritmetic and quantifiers.
+ Better set the logic to "" and make at least Z3 happy. *)
+fun smtlib_logic ts =
+ if exists (Term.exists_type (Term.exists_subtype is_wordT)) ts then SOME "" else NONE
+
+
+(* SMT-LIB builtins *)
+
+local
+ val smtlibC = SMTLIB_Interface.smtlibC
+
+ val wordT = @{typ "'a::len word"}
+
+ fun index1 s i = "(_ " ^ s ^ " " ^ string_of_int i ^ ")"
+ fun index2 s i j = "(_ " ^ s ^ " " ^ string_of_int i ^ " " ^ string_of_int j ^ ")"
+
+ fun word_typ (Type (@{type_name word}, [T])) = Option.map (index1 "BitVec") (try dest_binT T)
+ | word_typ _ = NONE
+
+ fun word_num (Type (@{type_name word}, [T])) k =
+ Option.map (index1 ("bv" ^ string_of_int k)) (try dest_binT T)
+ | word_num _ _ = NONE
+
+ fun if_fixed pred m n T ts =
+ let val (Us, U) = Term.strip_type T
+ in
+ if pred (U, Us) then SOME (n, length Us, ts, Term.list_comb o pair (Const (m, T))) else NONE
+ end
+
+ fun if_fixed_all m = if_fixed (forall (can dest_wordT) o (op ::)) m
+ fun if_fixed_args m = if_fixed (forall (can dest_wordT) o snd) m
+
+ fun add_word_fun f (t, n) =
+ let val (m, _) = Term.dest_Const t
+ in SMT_Builtin.add_builtin_fun smtlibC (Term.dest_Const t, K (f m n)) end
+
+ val mk_nat = HOLogic.mk_number @{typ nat}
+
+ fun mk_shift c [t, u] = Const c $ t $ mk_nat (snd (HOLogic.dest_number u))
+ | mk_shift c ts = raise TERM ("bad arguments", Const c :: ts)
+
+ fun shift m n T ts =
+ let val U = Term.domain_type T
+ in
+ (case (can dest_wordT U, try (snd o HOLogic.dest_number o hd o tl) ts) of
+ (true, SOME i) =>
+ SOME (n, 2, [hd ts, HOLogic.mk_number U i], mk_shift (m, T))
+ | _ => NONE) (* FIXME: also support non-numerical shifts *)
+ end
+
+ fun mk_extract c i ts = Term.list_comb (Const c, mk_nat i :: ts)
+
+ fun extract m n T ts =
+ let val U = Term.range_type (Term.range_type T)
+ in
+ (case (try (snd o HOLogic.dest_number o hd) ts, try dest_wordT U) of
+ (SOME lb, SOME i) =>
+ SOME (index2 n (i + lb - 1) lb, 1, tl ts, mk_extract (m, T) lb)
+ | _ => NONE)
+ end
+
+ fun mk_extend c ts = Term.list_comb (Const c, ts)
+
+ fun extend m n T ts =
+ let val (U1, U2) = Term.dest_funT T
+ in
+ (case (try dest_wordT U1, try dest_wordT U2) of
+ (SOME i, SOME j) =>
+ if j-i >= 0 then SOME (index1 n (j-i), 1, ts, mk_extend (m, T))
+ else NONE
+ | _ => NONE)
+ end
+
+ fun mk_rotate c i ts = Term.list_comb (Const c, mk_nat i :: ts)
+
+ fun rotate m n T ts =
+ let val U = Term.domain_type (Term.range_type T)
+ in
+ (case (can dest_wordT U, try (snd o HOLogic.dest_number o hd) ts) of
+ (true, SOME i) => SOME (index1 n i, 1, tl ts, mk_rotate (m, T) i)
+ | _ => NONE)
+ end
+in
+
+val setup_builtins =
+ SMT_Builtin.add_builtin_typ smtlibC (wordT, word_typ, word_num) #>
+ fold (add_word_fun if_fixed_all) [
+ (@{term "uminus :: 'a::len word => _"}, "bvneg"),
+ (@{term "plus :: 'a::len word => _"}, "bvadd"),
+ (@{term "minus :: 'a::len word => _"}, "bvsub"),
+ (@{term "times :: 'a::len word => _"}, "bvmul"),
+ (@{term "bitNOT :: 'a::len word => _"}, "bvnot"),
+ (@{term "bitAND :: 'a::len word => _"}, "bvand"),
+ (@{term "bitOR :: 'a::len word => _"}, "bvor"),
+ (@{term "bitXOR :: 'a::len word => _"}, "bvxor"),
+ (@{term "word_cat :: 'a::len word => _"}, "concat") ] #>
+ fold (add_word_fun shift) [
+ (@{term "shiftl :: 'a::len word => _ "}, "bvshl"),
+ (@{term "shiftr :: 'a::len word => _"}, "bvlshr"),
+ (@{term "sshiftr :: 'a::len word => _"}, "bvashr") ] #>
+ add_word_fun extract
+ (@{term "slice :: _ => 'a::len word => _"}, "extract") #>
+ fold (add_word_fun extend) [
+ (@{term "ucast :: 'a::len word => _"}, "zero_extend"),
+ (@{term "scast :: 'a::len word => _"}, "sign_extend") ] #>
+ fold (add_word_fun rotate) [
+ (@{term word_rotl}, "rotate_left"),
+ (@{term word_rotr}, "rotate_right") ] #>
+ fold (add_word_fun if_fixed_args) [
+ (@{term "less :: 'a::len word => _"}, "bvult"),
+ (@{term "less_eq :: 'a::len word => _"}, "bvule"),
+ (@{term word_sless}, "bvslt"),
+ (@{term word_sle}, "bvsle") ]
+
+end
+
+
+(* setup *)
+
+val _ = Theory.setup (Context.theory_map (
+ SMTLIB_Interface.add_logic (20, smtlib_logic) #>
+ setup_builtins))
+
+end;
--- a/src/HOL/Word/Word.thy Thu Aug 28 00:40:38 2014 +0200
+++ b/src/HOL/Word/Word.thy Thu Aug 28 00:40:38 2014 +0200
@@ -4753,7 +4753,7 @@
declare bin_to_bl_def [simp]
ML_file "Tools/word_lib.ML"
-ML_file "Tools/smt2_word.ML"
+ML_file "Tools/smt_word.ML"
hide_const (open) Word