--- a/Admin/E/eproof Thu Sep 24 17:25:42 2009 +0200
+++ b/Admin/E/eproof Thu Sep 24 17:26:05 2009 +0200
@@ -11,6 +11,7 @@
use File::Basename qw/ dirname /;
use File::Temp qw/ tempfile /;
+use English;
# E executables
@@ -44,7 +45,7 @@
# run E, redirecting output into a temporary file
my ($fh, $filename) = tempfile(UNLINK => 1);
-my $r = system "$eprover_cmd > $filename";
+my $r = system "$eprover_cmd > '$filename'";
exit ($r >> 8) if $r != 0;
@@ -55,7 +56,7 @@
# Note: Like the original eproof, we only look at the last 60 lines.
if ($content =~ m/Total time\s*:\s*([0-9]+\.[0-9]+)/) {
- $timelimit = $timelimit - $1 - 1;
+ $timelimit = int($timelimit - $1 - 1);
if ($content =~ m/No proof found!/) {
print "# Problem is satisfiable (or invalid), " .
@@ -85,7 +86,7 @@
print if (m/# SZS status/ or m/"# Failure"/);
}
$r = system ("exec bash -c \"ulimit -S -t $timelimit; " .
- "'$epclextract' $format -f --competition-framing $filename\"");
+ "'$epclextract' $format -f --competition-framing '$filename'\"");
# Note: Setting the user time is not supported on Cygwin, i.e., ulimit fails
# and prints and error message. How could we then limit the execution time?
exit ($r >> 8);
--- a/Admin/isatest/isatest-makedist Thu Sep 24 17:25:42 2009 +0200
+++ b/Admin/isatest/isatest-makedist Thu Sep 24 17:26:05 2009 +0200
@@ -102,9 +102,9 @@
#sleep 15
$SSH macbroy21 "$MAKEALL $HOME/settings/at64-poly-5.1-para"
sleep 15
-$SSH macbroy23 -l HOL images "$MAKEALL $HOME/settings/at-sml-dev-e"
-sleep 15
-$SSH atbroy101 "$MAKEALL $HOME/settings/at64-poly"
+#$SSH macbroy23 -l HOL images "$MAKEALL $HOME/settings/at-sml-dev-e"
+#sleep 15
+$SSH atbroy99 "$MAKEALL $HOME/settings/at64-poly"
sleep 15
$SSH macbroy2 "$MAKEALL $HOME/settings/mac-poly-M4; $MAKEALL $HOME/settings/mac-poly-M8; $MAKEALL $HOME/settings/mac-poly64-M4; $MAKEALL $HOME/settings/mac-poly64-M8"
sleep 15
--- a/NEWS Thu Sep 24 17:25:42 2009 +0200
+++ b/NEWS Thu Sep 24 17:26:05 2009 +0200
@@ -102,6 +102,10 @@
INCOMPATIBILITY.
+* Rules inf_absorb1, inf_absorb2, sup_absorb1, sup_absorb2 are no
+simp rules by default any longer. The same applies to
+min_max.inf_absorb1 etc.! INCOMPATIBILITY.
+
* Power operations on relations and functions are now one dedicate
constant "compow" with infix syntax "^^". Power operations on
multiplicative monoids retains syntax "^" and is now defined generic
--- a/lib/Tools/usedir Thu Sep 24 17:25:42 2009 +0200
+++ b/lib/Tools/usedir Thu Sep 24 17:26:05 2009 +0200
@@ -262,7 +262,7 @@
else
{ echo "$ITEM FAILED";
echo "(see also $LOG)";
- echo; tail "$LOG"; echo; } >&2
+ echo; tail -n 20 "$LOG"; echo; } >&2
fi
exit "$RC"
--- a/src/HOL/Code_Eval.thy Thu Sep 24 17:25:42 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,271 +0,0 @@
-(* Title: HOL/Code_Eval.thy
- Author: Florian Haftmann, TU Muenchen
-*)
-
-header {* Term evaluation using the generic code generator *}
-
-theory Code_Eval
-imports Plain Typerep Code_Numeral
-begin
-
-subsection {* Term representation *}
-
-subsubsection {* Terms and class @{text term_of} *}
-
-datatype "term" = dummy_term
-
-definition Const :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
- "Const _ _ = dummy_term"
-
-definition App :: "term \<Rightarrow> term \<Rightarrow> term" where
- "App _ _ = dummy_term"
-
-code_datatype Const App
-
-class term_of = typerep +
- fixes term_of :: "'a \<Rightarrow> term"
-
-lemma term_of_anything: "term_of x \<equiv> t"
- by (rule eq_reflection) (cases "term_of x", cases t, simp)
-
-definition valapp :: "('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)
- \<Rightarrow> 'a \<times> (unit \<Rightarrow> term) \<Rightarrow> 'b \<times> (unit \<Rightarrow> term)" where
- "valapp f x = (fst f (fst x), \<lambda>u. App (snd f ()) (snd x ()))"
-
-lemma valapp_code [code, code_unfold]:
- "valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"
- by (simp only: valapp_def fst_conv snd_conv)
-
-
-subsubsection {* @{text term_of} instances *}
-
-instantiation "fun" :: (typerep, typerep) term_of
-begin
-
-definition
- "term_of (f \<Colon> 'a \<Rightarrow> 'b) = Const (STR ''dummy_pattern'') (Typerep.Typerep (STR ''fun'')
- [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
-
-instance ..
-
-end
-
-setup {*
-let
- fun add_term_of tyco raw_vs thy =
- let
- val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;
- val ty = Type (tyco, map TFree vs);
- val lhs = Const (@{const_name term_of}, ty --> @{typ term})
- $ Free ("x", ty);
- val rhs = @{term "undefined \<Colon> term"};
- val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
- fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst
- o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv";
- in
- thy
- |> TheoryTarget.instantiation ([tyco], vs, @{sort term_of})
- |> `(fn lthy => Syntax.check_term lthy eq)
- |-> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq)))
- |> snd
- |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
- end;
- fun ensure_term_of (tyco, (raw_vs, _)) thy =
- let
- val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of})
- andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep};
- in if need_inst then add_term_of tyco raw_vs thy else thy end;
-in
- Code.type_interpretation ensure_term_of
-end
-*}
-
-setup {*
-let
- fun mk_term_of_eq thy ty vs tyco (c, tys) =
- let
- val t = list_comb (Const (c, tys ---> ty),
- map Free (Name.names Name.context "a" tys));
- val (arg, rhs) = pairself (Thm.cterm_of thy o map_types Logic.unvarifyT o Logic.varify)
- (t, (map_aterms (fn t as Free (v, ty) => HOLogic.mk_term_of ty t | t => t) o HOLogic.reflect_term) t)
- val cty = Thm.ctyp_of thy ty;
- in
- @{thm term_of_anything}
- |> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]
- |> Thm.varifyT
- end;
- fun add_term_of_code tyco raw_vs raw_cs thy =
- let
- val algebra = Sign.classes_of thy;
- val vs = map (fn (v, sort) =>
- (v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) raw_vs;
- val ty = Type (tyco, map TFree vs);
- val cs = (map o apsnd o map o map_atyps)
- (fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs;
- val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
- val eqs = map (mk_term_of_eq thy ty vs tyco) cs;
- in
- thy
- |> Code.del_eqns const
- |> fold Code.add_eqn eqs
- end;
- fun ensure_term_of_code (tyco, (raw_vs, cs)) thy =
- let
- val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};
- in if has_inst then add_term_of_code tyco raw_vs cs thy else thy end;
-in
- Code.type_interpretation ensure_term_of_code
-end
-*}
-
-
-subsubsection {* Code generator setup *}
-
-lemmas [code del] = term.recs term.cases term.size
-lemma [code, code del]: "eq_class.eq (t1\<Colon>term) t2 \<longleftrightarrow> eq_class.eq t1 t2" ..
-
-lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..
-lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
-lemma [code, code del]: "(term_of \<Colon> String.literal \<Rightarrow> term) = term_of" ..
-lemma [code, code del]:
- "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
-lemma [code, code del]:
- "(Code_Eval.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Eval.term) = Code_Eval.term_of" ..
-
-lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]: "Code_Eval.term_of c =
- (let (n, m) = nibble_pair_of_char c
- in Code_Eval.App (Code_Eval.App (Code_Eval.Const (STR ''String.char.Char'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))
- (Code_Eval.term_of n)) (Code_Eval.term_of m))"
- by (subst term_of_anything) rule
-
-code_type "term"
- (Eval "Term.term")
-
-code_const Const and App
- (Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))")
-
-code_const "term_of \<Colon> String.literal \<Rightarrow> term"
- (Eval "HOLogic.mk'_message'_string")
-
-code_reserved Eval HOLogic
-
-
-subsubsection {* Syntax *}
-
-definition termify :: "'a \<Rightarrow> term" where
- [code del]: "termify x = dummy_term"
-
-abbreviation valtermify :: "'a \<Rightarrow> 'a \<times> (unit \<Rightarrow> term)" where
- "valtermify x \<equiv> (x, \<lambda>u. termify x)"
-
-setup {*
-let
- fun map_default f xs =
- let val ys = map f xs
- in if exists is_some ys
- then SOME (map2 the_default xs ys)
- else NONE
- end;
- fun subst_termify_app (Const (@{const_name termify}, T), [t]) =
- if not (Term.has_abs t)
- then if fold_aterms (fn Const _ => I | _ => K false) t true
- then SOME (HOLogic.reflect_term t)
- else error "Cannot termify expression containing variables"
- else error "Cannot termify expression containing abstraction"
- | subst_termify_app (t, ts) = case map_default subst_termify ts
- of SOME ts' => SOME (list_comb (t, ts'))
- | NONE => NONE
- and subst_termify (Abs (v, T, t)) = (case subst_termify t
- of SOME t' => SOME (Abs (v, T, t'))
- | NONE => NONE)
- | subst_termify t = subst_termify_app (strip_comb t)
- fun check_termify ts ctxt = map_default subst_termify ts
- |> Option.map (rpair ctxt)
-in
- Context.theory_map (Syntax.add_term_check 0 "termify" check_termify)
-end;
-*}
-
-locale term_syntax
-begin
-
-notation App (infixl "<\<cdot>>" 70)
- and valapp (infixl "{\<cdot>}" 70)
-
-end
-
-interpretation term_syntax .
-
-no_notation App (infixl "<\<cdot>>" 70)
- and valapp (infixl "{\<cdot>}" 70)
-
-
-subsection {* Numeric types *}
-
-definition term_of_num :: "'a\<Colon>{semiring_div} \<Rightarrow> 'a\<Colon>{semiring_div} \<Rightarrow> term" where
- "term_of_num two = (\<lambda>_. dummy_term)"
-
-lemma (in term_syntax) term_of_num_code [code]:
- "term_of_num two k = (if k = 0 then termify Int.Pls
- else (if k mod two = 0
- then termify Int.Bit0 <\<cdot>> term_of_num two (k div two)
- else termify Int.Bit1 <\<cdot>> term_of_num two (k div two)))"
- by (auto simp add: term_of_anything Const_def App_def term_of_num_def Let_def)
-
-lemma (in term_syntax) term_of_nat_code [code]:
- "term_of (n::nat) = termify (number_of :: int \<Rightarrow> nat) <\<cdot>> term_of_num (2::nat) n"
- by (simp only: term_of_anything)
-
-lemma (in term_syntax) term_of_int_code [code]:
- "term_of (k::int) = (if k = 0 then termify (0 :: int)
- else if k > 0 then termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) k
- else termify (uminus :: int \<Rightarrow> int) <\<cdot>> (termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) (- k)))"
- by (simp only: term_of_anything)
-
-lemma (in term_syntax) term_of_code_numeral_code [code]:
- "term_of (k::code_numeral) = termify (number_of :: int \<Rightarrow> code_numeral) <\<cdot>> term_of_num (2::code_numeral) k"
- by (simp only: term_of_anything)
-
-subsection {* Obfuscate *}
-
-print_translation {*
-let
- val term = Const ("<TERM>", dummyT);
- fun tr1' [_, _] = term;
- fun tr2' [] = term;
-in
- [(@{const_syntax Const}, tr1'),
- (@{const_syntax App}, tr1'),
- (@{const_syntax dummy_term}, tr2')]
-end
-*}
-
-hide const dummy_term App valapp
-hide (open) const Const termify valtermify term_of term_of_num
-
-
-subsection {* Evaluation setup *}
-
-ML {*
-signature EVAL =
-sig
- val eval_ref: (unit -> term) option ref
- val eval_term: theory -> term -> term
-end;
-
-structure Eval : EVAL =
-struct
-
-val eval_ref = ref (NONE : (unit -> term) option);
-
-fun eval_term thy t =
- Code_ML.eval NONE ("Eval.eval_ref", eval_ref) I thy (HOLogic.mk_term_of (fastype_of t) t) [];
-
-end;
-*}
-
-setup {*
- Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)
-*}
-
-end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Code_Evaluation.thy Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,271 @@
+(* Title: HOL/Code_Evaluation.thy
+ Author: Florian Haftmann, TU Muenchen
+*)
+
+header {* Term evaluation using the generic code generator *}
+
+theory Code_Evaluation
+imports Plain Typerep Code_Numeral
+begin
+
+subsection {* Term representation *}
+
+subsubsection {* Terms and class @{text term_of} *}
+
+datatype "term" = dummy_term
+
+definition Const :: "String.literal \<Rightarrow> typerep \<Rightarrow> term" where
+ "Const _ _ = dummy_term"
+
+definition App :: "term \<Rightarrow> term \<Rightarrow> term" where
+ "App _ _ = dummy_term"
+
+code_datatype Const App
+
+class term_of = typerep +
+ fixes term_of :: "'a \<Rightarrow> term"
+
+lemma term_of_anything: "term_of x \<equiv> t"
+ by (rule eq_reflection) (cases "term_of x", cases t, simp)
+
+definition valapp :: "('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)
+ \<Rightarrow> 'a \<times> (unit \<Rightarrow> term) \<Rightarrow> 'b \<times> (unit \<Rightarrow> term)" where
+ "valapp f x = (fst f (fst x), \<lambda>u. App (snd f ()) (snd x ()))"
+
+lemma valapp_code [code, code_unfold]:
+ "valapp (f, tf) (x, tx) = (f x, \<lambda>u. App (tf ()) (tx ()))"
+ by (simp only: valapp_def fst_conv snd_conv)
+
+
+subsubsection {* @{text term_of} instances *}
+
+instantiation "fun" :: (typerep, typerep) term_of
+begin
+
+definition
+ "term_of (f \<Colon> 'a \<Rightarrow> 'b) = Const (STR ''dummy_pattern'') (Typerep.Typerep (STR ''fun'')
+ [Typerep.typerep TYPE('a), Typerep.typerep TYPE('b)])"
+
+instance ..
+
+end
+
+setup {*
+let
+ fun add_term_of tyco raw_vs thy =
+ let
+ val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs;
+ val ty = Type (tyco, map TFree vs);
+ val lhs = Const (@{const_name term_of}, ty --> @{typ term})
+ $ Free ("x", ty);
+ val rhs = @{term "undefined \<Colon> term"};
+ val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
+ fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst
+ o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv";
+ in
+ thy
+ |> TheoryTarget.instantiation ([tyco], vs, @{sort term_of})
+ |> `(fn lthy => Syntax.check_term lthy eq)
+ |-> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq)))
+ |> snd
+ |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
+ end;
+ fun ensure_term_of (tyco, (raw_vs, _)) thy =
+ let
+ val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of})
+ andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep};
+ in if need_inst then add_term_of tyco raw_vs thy else thy end;
+in
+ Code.type_interpretation ensure_term_of
+end
+*}
+
+setup {*
+let
+ fun mk_term_of_eq thy ty vs tyco (c, tys) =
+ let
+ val t = list_comb (Const (c, tys ---> ty),
+ map Free (Name.names Name.context "a" tys));
+ val (arg, rhs) = pairself (Thm.cterm_of thy o map_types Logic.unvarifyT o Logic.varify)
+ (t, (map_aterms (fn t as Free (v, ty) => HOLogic.mk_term_of ty t | t => t) o HOLogic.reflect_term) t)
+ val cty = Thm.ctyp_of thy ty;
+ in
+ @{thm term_of_anything}
+ |> Drule.instantiate' [SOME cty] [SOME arg, SOME rhs]
+ |> Thm.varifyT
+ end;
+ fun add_term_of_code tyco raw_vs raw_cs thy =
+ let
+ val algebra = Sign.classes_of thy;
+ val vs = map (fn (v, sort) =>
+ (v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) raw_vs;
+ val ty = Type (tyco, map TFree vs);
+ val cs = (map o apsnd o map o map_atyps)
+ (fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs;
+ val const = AxClass.param_of_inst thy (@{const_name term_of}, tyco);
+ val eqs = map (mk_term_of_eq thy ty vs tyco) cs;
+ in
+ thy
+ |> Code.del_eqns const
+ |> fold Code.add_eqn eqs
+ end;
+ fun ensure_term_of_code (tyco, (raw_vs, cs)) thy =
+ let
+ val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort term_of};
+ in if has_inst then add_term_of_code tyco raw_vs cs thy else thy end;
+in
+ Code.type_interpretation ensure_term_of_code
+end
+*}
+
+
+subsubsection {* Code generator setup *}
+
+lemmas [code del] = term.recs term.cases term.size
+lemma [code, code del]: "eq_class.eq (t1\<Colon>term) t2 \<longleftrightarrow> eq_class.eq t1 t2" ..
+
+lemma [code, code del]: "(term_of \<Colon> typerep \<Rightarrow> term) = term_of" ..
+lemma [code, code del]: "(term_of \<Colon> term \<Rightarrow> term) = term_of" ..
+lemma [code, code del]: "(term_of \<Colon> String.literal \<Rightarrow> term) = term_of" ..
+lemma [code, code del]:
+ "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.pred \<Rightarrow> Code_Evaluation.term) = Code_Evaluation.term_of" ..
+lemma [code, code del]:
+ "(Code_Evaluation.term_of \<Colon> 'a::{type, term_of} Predicate.seq \<Rightarrow> Code_Evaluation.term) = Code_Evaluation.term_of" ..
+
+lemma term_of_char [unfolded typerep_fun_def typerep_char_def typerep_nibble_def, code]: "Code_Evaluation.term_of c =
+ (let (n, m) = nibble_pair_of_char c
+ in Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.Const (STR ''String.char.Char'') (TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char)))
+ (Code_Evaluation.term_of n)) (Code_Evaluation.term_of m))"
+ by (subst term_of_anything) rule
+
+code_type "term"
+ (Eval "Term.term")
+
+code_const Const and App
+ (Eval "Term.Const/ ((_), (_))" and "Term.$/ ((_), (_))")
+
+code_const "term_of \<Colon> String.literal \<Rightarrow> term"
+ (Eval "HOLogic.mk'_message'_string")
+
+code_reserved Eval HOLogic
+
+
+subsubsection {* Syntax *}
+
+definition termify :: "'a \<Rightarrow> term" where
+ [code del]: "termify x = dummy_term"
+
+abbreviation valtermify :: "'a \<Rightarrow> 'a \<times> (unit \<Rightarrow> term)" where
+ "valtermify x \<equiv> (x, \<lambda>u. termify x)"
+
+setup {*
+let
+ fun map_default f xs =
+ let val ys = map f xs
+ in if exists is_some ys
+ then SOME (map2 the_default xs ys)
+ else NONE
+ end;
+ fun subst_termify_app (Const (@{const_name termify}, T), [t]) =
+ if not (Term.has_abs t)
+ then if fold_aterms (fn Const _ => I | _ => K false) t true
+ then SOME (HOLogic.reflect_term t)
+ else error "Cannot termify expression containing variables"
+ else error "Cannot termify expression containing abstraction"
+ | subst_termify_app (t, ts) = case map_default subst_termify ts
+ of SOME ts' => SOME (list_comb (t, ts'))
+ | NONE => NONE
+ and subst_termify (Abs (v, T, t)) = (case subst_termify t
+ of SOME t' => SOME (Abs (v, T, t'))
+ | NONE => NONE)
+ | subst_termify t = subst_termify_app (strip_comb t)
+ fun check_termify ts ctxt = map_default subst_termify ts
+ |> Option.map (rpair ctxt)
+in
+ Context.theory_map (Syntax.add_term_check 0 "termify" check_termify)
+end;
+*}
+
+locale term_syntax
+begin
+
+notation App (infixl "<\<cdot>>" 70)
+ and valapp (infixl "{\<cdot>}" 70)
+
+end
+
+interpretation term_syntax .
+
+no_notation App (infixl "<\<cdot>>" 70)
+ and valapp (infixl "{\<cdot>}" 70)
+
+
+subsection {* Numeric types *}
+
+definition term_of_num :: "'a\<Colon>{semiring_div} \<Rightarrow> 'a\<Colon>{semiring_div} \<Rightarrow> term" where
+ "term_of_num two = (\<lambda>_. dummy_term)"
+
+lemma (in term_syntax) term_of_num_code [code]:
+ "term_of_num two k = (if k = 0 then termify Int.Pls
+ else (if k mod two = 0
+ then termify Int.Bit0 <\<cdot>> term_of_num two (k div two)
+ else termify Int.Bit1 <\<cdot>> term_of_num two (k div two)))"
+ by (auto simp add: term_of_anything Const_def App_def term_of_num_def Let_def)
+
+lemma (in term_syntax) term_of_nat_code [code]:
+ "term_of (n::nat) = termify (number_of :: int \<Rightarrow> nat) <\<cdot>> term_of_num (2::nat) n"
+ by (simp only: term_of_anything)
+
+lemma (in term_syntax) term_of_int_code [code]:
+ "term_of (k::int) = (if k = 0 then termify (0 :: int)
+ else if k > 0 then termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) k
+ else termify (uminus :: int \<Rightarrow> int) <\<cdot>> (termify (number_of :: int \<Rightarrow> int) <\<cdot>> term_of_num (2::int) (- k)))"
+ by (simp only: term_of_anything)
+
+lemma (in term_syntax) term_of_code_numeral_code [code]:
+ "term_of (k::code_numeral) = termify (number_of :: int \<Rightarrow> code_numeral) <\<cdot>> term_of_num (2::code_numeral) k"
+ by (simp only: term_of_anything)
+
+subsection {* Obfuscate *}
+
+print_translation {*
+let
+ val term = Const ("<TERM>", dummyT);
+ fun tr1' [_, _] = term;
+ fun tr2' [] = term;
+in
+ [(@{const_syntax Const}, tr1'),
+ (@{const_syntax App}, tr1'),
+ (@{const_syntax dummy_term}, tr2')]
+end
+*}
+
+hide const dummy_term App valapp
+hide (open) const Const termify valtermify term_of term_of_num
+
+
+subsection {* Evaluation setup *}
+
+ML {*
+signature EVAL =
+sig
+ val eval_ref: (unit -> term) option ref
+ val eval_term: theory -> term -> term
+end;
+
+structure Eval : EVAL =
+struct
+
+val eval_ref = ref (NONE : (unit -> term) option);
+
+fun eval_term thy t =
+ Code_ML.eval NONE ("Eval.eval_ref", eval_ref) I thy (HOLogic.mk_term_of (fastype_of t) t) [];
+
+end;
+*}
+
+setup {*
+ Value.add_evaluator ("code", Eval.eval_term o ProofContext.theory_of)
+*}
+
+end
--- a/src/HOL/Complete_Lattice.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Complete_Lattice.thy Thu Sep 24 17:26:05 2009 +0200
@@ -76,11 +76,11 @@
lemma sup_bot [simp]:
"x \<squnion> bot = x"
- using bot_least [of x] by (simp add: sup_commute)
+ using bot_least [of x] by (simp add: sup_commute sup_absorb2)
lemma inf_top [simp]:
"x \<sqinter> top = x"
- using top_greatest [of x] by (simp add: inf_commute)
+ using top_greatest [of x] by (simp add: inf_commute inf_absorb2)
definition SUPR :: "'b set \<Rightarrow> ('b \<Rightarrow> 'a) \<Rightarrow> 'a" where
"SUPR A f = \<Squnion> (f ` A)"
--- a/src/HOL/Decision_Procs/Approximation.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Decision_Procs/Approximation.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1904,7 +1904,7 @@
show "0 < real x * 2/3" using * by auto
show "real ?max + 1 \<le> real x * 2/3" using * up
by (cases "0 < real x * real (lapprox_posrat prec 2 3) - 1",
- auto simp add: real_of_float_max)
+ auto simp add: real_of_float_max min_max.sup_absorb1)
qed
finally have "real (?lb_horner (Float 1 -1)) + real (?lb_horner ?max)
\<le> ln (real x)"
@@ -3246,12 +3246,13 @@
= map (` (variable_of_bound o prop_of)) prems
fun add_deps (name, bnds)
- = Graph.add_deps_acyclic
- (name, remove (op =) name (Term.add_free_names (prop_of bnds) []))
+ = Graph.add_deps_acyclic (name,
+ remove (op =) name (Term.add_free_names (prop_of bnds) []))
+
val order = Graph.empty
|> fold Graph.new_node variable_bounds
|> fold add_deps variable_bounds
- |> Graph.topological_order |> rev
+ |> Graph.strong_conn |> map the_single |> rev
|> map_filter (AList.lookup (op =) variable_bounds)
fun prepend_prem th tac
@@ -3338,7 +3339,7 @@
etac @{thm meta_eqE},
rtac @{thm impI}] i)
THEN Subgoal.FOCUS (fn {prems, ...} => reorder_bounds_tac prems i) @{context} i
- THEN TRY (filter_prems_tac (K false) i)
+ THEN DETERM (TRY (filter_prems_tac (K false) i))
THEN DETERM (Reflection.genreify_tac ctxt form_equations NONE i)
THEN rewrite_interpret_form_tac ctxt prec splitting taylor i
THEN gen_eval_tac eval_oracle ctxt i))
@@ -3350,7 +3351,7 @@
fun mk_approx' prec t = (@{const "approx'"}
$ HOLogic.mk_number @{typ nat} prec
- $ t $ @{term "[] :: (float * float) list"})
+ $ t $ @{term "[] :: (float * float) option list"})
fun dest_result (Const (@{const_name "Some"}, _) $
((Const (@{const_name "Pair"}, _)) $
--- a/src/HOL/Decision_Procs/Ferrack.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Decision_Procs/Ferrack.thy Thu Sep 24 17:26:05 2009 +0200
@@ -512,7 +512,7 @@
assumes g0: "numgcd t = 0"
shows "Inum bs t = 0"
using g0[simplified numgcd_def]
- by (induct t rule: numgcdh.induct, auto simp add: natabs0 maxcoeff_pos)
+ by (induct t rule: numgcdh.induct, auto simp add: natabs0 maxcoeff_pos min_max.sup_absorb2)
lemma numgcdh_pos: assumes gp: "g \<ge> 0" shows "numgcdh t g \<ge> 0"
using gp
--- a/src/HOL/Decision_Procs/ex/Approximation_Ex.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Decision_Procs/ex/Approximation_Ex.thy Thu Sep 24 17:26:05 2009 +0200
@@ -72,7 +72,9 @@
shows "g / v * tan (35 * d) \<in> { 3 * d .. 3.1 * d }"
using assms by (approximation 80)
-lemma "\<phi> \<in> { 0 .. 1 :: real } \<longrightarrow> \<phi> ^ 2 \<le> \<phi>"
- by (approximation 30 splitting: \<phi>=1 taylor: \<phi> = 3)
+lemma "x \<in> { 0 .. 1 :: real } \<longrightarrow> x ^ 2 \<le> x"
+ by (approximation 30 splitting: x=1 taylor: x = 3)
+
+value [approximate] "10"
end
--- a/src/HOL/Finite_Set.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Finite_Set.thy Thu Sep 24 17:26:05 2009 +0200
@@ -2966,11 +2966,11 @@
lemma dual_max:
"ord.max (op \<ge>) = min"
- by (auto simp add: ord.max_def_raw expand_fun_eq)
+ by (auto simp add: ord.max_def_raw min_def expand_fun_eq)
lemma dual_min:
"ord.min (op \<ge>) = max"
- by (auto simp add: ord.min_def_raw expand_fun_eq)
+ by (auto simp add: ord.min_def_raw max_def expand_fun_eq)
lemma strict_below_fold1_iff:
assumes "finite A" and "A \<noteq> {}"
--- a/src/HOL/HOL.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/HOL.thy Thu Sep 24 17:26:05 2009 +0200
@@ -2021,6 +2021,29 @@
quickcheck_params [size = 5, iterations = 50]
+subsection {* Preprocessing for the predicate compiler *}
+
+ML {*
+structure Predicate_Compile_Alternative_Defs = Named_Thms
+(
+ val name = "code_pred_def"
+ val description = "alternative definitions of constants for the Predicate Compiler"
+)
+*}
+
+ML {*
+structure Predicate_Compile_Inline_Defs = Named_Thms
+(
+ val name = "code_pred_inline"
+ val description = "inlining definitions for the Predicate Compiler"
+)
+*}
+
+setup {*
+ Predicate_Compile_Alternative_Defs.setup
+ #> Predicate_Compile_Inline_Defs.setup
+ #> Predicate_Compile_Preproc_Const_Defs.setup
+*}
subsection {* Nitpick setup *}
--- a/src/HOL/Hoare_Parallel/Graph.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Hoare_Parallel/Graph.thy Thu Sep 24 17:26:05 2009 +0200
@@ -187,6 +187,8 @@
subsubsection{* Graph 3 *}
+declare min_max.inf_absorb1 [simp] min_max.inf_absorb2 [simp]
+
lemma Graph3:
"\<lbrakk> T\<in>Reach E; R<length E \<rbrakk> \<Longrightarrow> Reach(E[R:=(fst(E!R),T)]) \<subseteq> Reach E"
apply (unfold Reach_def)
@@ -307,6 +309,8 @@
apply force
done
+declare min_max.inf_absorb1 [simp del] min_max.inf_absorb2 [simp del]
+
subsubsection {* Graph 5 *}
lemma Graph5:
--- a/src/HOL/Induct/LList.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Induct/LList.thy Thu Sep 24 17:26:05 2009 +0200
@@ -665,7 +665,7 @@
apply (subst LList_corec, force)
done
-lemma llist_corec:
+lemma llist_corec [nitpick_const_simp]:
"llist_corec a f =
(case f a of None => LNil | Some(z,w) => LCons z (llist_corec w f))"
apply (unfold llist_corec_def LNil_def LCons_def)
@@ -774,10 +774,11 @@
subsection{* The functional @{text lmap} *}
-lemma lmap_LNil [simp]: "lmap f LNil = LNil"
+lemma lmap_LNil [simp, nitpick_const_simp]: "lmap f LNil = LNil"
by (rule lmap_def [THEN def_llist_corec, THEN trans], simp)
-lemma lmap_LCons [simp]: "lmap f (LCons M N) = LCons (f M) (lmap f N)"
+lemma lmap_LCons [simp, nitpick_const_simp]:
+"lmap f (LCons M N) = LCons (f M) (lmap f N)"
by (rule lmap_def [THEN def_llist_corec, THEN trans], simp)
@@ -792,7 +793,7 @@
subsection{* iterates -- @{text llist_fun_equalityI} cannot be used! *}
-lemma iterates: "iterates f x = LCons x (iterates f (f x))"
+lemma iterates [nitpick_const_simp]: "iterates f x = LCons x (iterates f (f x))"
by (rule iterates_def [THEN def_llist_corec, THEN trans], simp)
lemma lmap_iterates [simp]: "lmap f (iterates f x) = iterates f (f x)"
@@ -847,18 +848,18 @@
subsection{* @{text lappend} -- its two arguments cause some complications! *}
-lemma lappend_LNil_LNil [simp]: "lappend LNil LNil = LNil"
+lemma lappend_LNil_LNil [simp, nitpick_const_simp]: "lappend LNil LNil = LNil"
apply (simp add: lappend_def)
apply (rule llist_corec [THEN trans], simp)
done
-lemma lappend_LNil_LCons [simp]:
+lemma lappend_LNil_LCons [simp, nitpick_const_simp]:
"lappend LNil (LCons l l') = LCons l (lappend LNil l')"
apply (simp add: lappend_def)
apply (rule llist_corec [THEN trans], simp)
done
-lemma lappend_LCons [simp]:
+lemma lappend_LCons [simp, nitpick_const_simp]:
"lappend (LCons l l') N = LCons l (lappend l' N)"
apply (simp add: lappend_def)
apply (rule llist_corec [THEN trans], simp)
--- a/src/HOL/Inductive.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Inductive.thy Thu Sep 24 17:26:05 2009 +0200
@@ -267,26 +267,6 @@
Ball_def Bex_def
induct_rulify_fallback
-ML {*
-val def_lfp_unfold = @{thm def_lfp_unfold}
-val def_gfp_unfold = @{thm def_gfp_unfold}
-val def_lfp_induct = @{thm def_lfp_induct}
-val def_coinduct = @{thm def_coinduct}
-val inf_bool_eq = @{thm inf_bool_eq} RS @{thm eq_reflection}
-val inf_fun_eq = @{thm inf_fun_eq} RS @{thm eq_reflection}
-val sup_bool_eq = @{thm sup_bool_eq} RS @{thm eq_reflection}
-val sup_fun_eq = @{thm sup_fun_eq} RS @{thm eq_reflection}
-val le_boolI = @{thm le_boolI}
-val le_boolI' = @{thm le_boolI'}
-val le_funI = @{thm le_funI}
-val le_boolE = @{thm le_boolE}
-val le_funE = @{thm le_funE}
-val le_boolD = @{thm le_boolD}
-val le_funD = @{thm le_funD}
-val le_bool_def = @{thm le_bool_def} RS @{thm eq_reflection}
-val le_fun_def = @{thm le_fun_def} RS @{thm eq_reflection}
-*}
-
use "Tools/inductive.ML"
setup Inductive.setup
--- a/src/HOL/IsaMakefile Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/IsaMakefile Thu Sep 24 17:26:05 2009 +0200
@@ -210,7 +210,7 @@
MAIN_DEPENDENCIES = $(PLAIN_DEPENDENCIES) \
ATP_Linkup.thy \
- Code_Eval.thy \
+ Code_Evaluation.thy \
Code_Numeral.thy \
Equiv_Relations.thy \
Groebner_Basis.thy \
@@ -909,7 +909,7 @@
ex/Sudoku.thy ex/Tarski.thy \
ex/Termination.thy ex/Transfer_Ex.thy ex/Unification.thy ex/document/root.bib \
ex/document/root.tex ex/set.thy ex/svc_funcs.ML ex/svc_test.thy \
- ex/Predicate_Compile.thy ex/predicate_compile.ML ex/Predicate_Compile_ex.thy
+ ex/Predicate_Compile.thy Tools/Predicate_Compile/predicate_compile_core.ML ex/Predicate_Compile_ex.thy
@$(ISABELLE_TOOL) usedir $(OUT)/HOL ex
--- a/src/HOL/Lattices.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Lattices.thy Thu Sep 24 17:26:05 2009 +0200
@@ -127,10 +127,10 @@
lemma inf_left_idem[simp]: "x \<sqinter> (x \<sqinter> y) = x \<sqinter> y"
by (rule antisym) (auto intro: le_infI2)
-lemma inf_absorb1[simp]: "x \<sqsubseteq> y \<Longrightarrow> x \<sqinter> y = x"
+lemma inf_absorb1: "x \<sqsubseteq> y \<Longrightarrow> x \<sqinter> y = x"
by (rule antisym) auto
-lemma inf_absorb2[simp]: "y \<sqsubseteq> x \<Longrightarrow> x \<sqinter> y = y"
+lemma inf_absorb2: "y \<sqsubseteq> x \<Longrightarrow> x \<sqinter> y = y"
by (rule antisym) auto
lemma inf_left_commute: "x \<sqinter> (y \<sqinter> z) = y \<sqinter> (x \<sqinter> z)"
@@ -155,10 +155,10 @@
lemma sup_left_idem[simp]: "x \<squnion> (x \<squnion> y) = x \<squnion> y"
by (rule antisym) (auto intro: le_supI2)
-lemma sup_absorb1[simp]: "y \<sqsubseteq> x \<Longrightarrow> x \<squnion> y = x"
+lemma sup_absorb1: "y \<sqsubseteq> x \<Longrightarrow> x \<squnion> y = x"
by (rule antisym) auto
-lemma sup_absorb2[simp]: "x \<sqsubseteq> y \<Longrightarrow> x \<squnion> y = y"
+lemma sup_absorb2: "x \<sqsubseteq> y \<Longrightarrow> x \<squnion> y = y"
by (rule antisym) auto
lemma sup_left_commute: "x \<squnion> (y \<squnion> z) = y \<squnion> (x \<squnion> z)"
@@ -229,11 +229,11 @@
lemma less_infI1:
"a \<sqsubset> x \<Longrightarrow> a \<sqinter> b \<sqsubset> x"
- by (auto simp add: less_le intro: le_infI1)
+ by (auto simp add: less_le inf_absorb1 intro: le_infI1)
lemma less_infI2:
"b \<sqsubset> x \<Longrightarrow> a \<sqinter> b \<sqsubset> x"
- by (auto simp add: less_le intro: le_infI2)
+ by (auto simp add: less_le inf_absorb2 intro: le_infI2)
end
--- a/src/HOL/Library/Code_Char.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Code_Char.thy Thu Sep 24 17:26:05 2009 +0200
@@ -5,7 +5,7 @@
header {* Code generation of pretty characters (and strings) *}
theory Code_Char
-imports List Code_Eval Main
+imports List Code_Evaluation Main
begin
code_type char
@@ -32,7 +32,7 @@
(OCaml "!((_ : char) = _)")
(Haskell infixl 4 "==")
-code_const "Code_Eval.term_of \<Colon> char \<Rightarrow> term"
+code_const "Code_Evaluation.term_of \<Colon> char \<Rightarrow> term"
(Eval "HOLogic.mk'_char/ (IntInf.fromInt/ (Char.ord/ _))")
end
--- a/src/HOL/Library/Code_Integer.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Code_Integer.thy Thu Sep 24 17:26:05 2009 +0200
@@ -100,7 +100,7 @@
text {* Evaluation *}
-code_const "Code_Eval.term_of \<Colon> int \<Rightarrow> term"
+code_const "Code_Evaluation.term_of \<Colon> int \<Rightarrow> term"
(Eval "HOLogic.mk'_number/ HOLogic.intT")
end
\ No newline at end of file
--- a/src/HOL/Library/Coinductive_List.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Coinductive_List.thy Thu Sep 24 17:26:05 2009 +0200
@@ -260,7 +260,7 @@
qed
qed
-lemma llist_corec [code]:
+lemma llist_corec [code, nitpick_const_simp]:
"llist_corec a f =
(case f a of None \<Rightarrow> LNil | Some (z, w) \<Rightarrow> LCons z (llist_corec w f))"
proof (cases "f a")
@@ -656,8 +656,9 @@
qed
qed
-lemma lmap_LNil [simp]: "lmap f LNil = LNil"
- and lmap_LCons [simp]: "lmap f (LCons M N) = LCons (f M) (lmap f N)"
+lemma lmap_LNil [simp, nitpick_const_simp]: "lmap f LNil = LNil"
+ and lmap_LCons [simp, nitpick_const_simp]:
+ "lmap f (LCons M N) = LCons (f M) (lmap f N)"
by (simp_all add: lmap_def llist_corec)
lemma lmap_compose [simp]: "lmap (f o g) l = lmap f (lmap g l)"
@@ -728,9 +729,9 @@
qed
qed
-lemma lappend_LNil_LNil [simp]: "lappend LNil LNil = LNil"
- and lappend_LNil_LCons [simp]: "lappend LNil (LCons l l') = LCons l (lappend LNil l')"
- and lappend_LCons [simp]: "lappend (LCons l l') m = LCons l (lappend l' m)"
+lemma lappend_LNil_LNil [simp, nitpick_const_simp]: "lappend LNil LNil = LNil"
+ and lappend_LNil_LCons [simp, nitpick_const_simp]: "lappend LNil (LCons l l') = LCons l (lappend LNil l')"
+ and lappend_LCons [simp, nitpick_const_simp]: "lappend (LCons l l') m = LCons l (lappend l' m)"
by (simp_all add: lappend_def llist_corec)
lemma lappend_LNil1 [simp]: "lappend LNil l = l"
@@ -754,7 +755,7 @@
iterates :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a llist" where
"iterates f a = llist_corec a (\<lambda>x. Some (x, f x))"
-lemma iterates: "iterates f x = LCons x (iterates f (f x))"
+lemma iterates [nitpick_const_simp]: "iterates f x = LCons x (iterates f (f x))"
apply (unfold iterates_def)
apply (subst llist_corec)
apply simp
--- a/src/HOL/Library/Efficient_Nat.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Efficient_Nat.thy Thu Sep 24 17:26:05 2009 +0200
@@ -415,9 +415,9 @@
text {* Evaluation *}
lemma [code, code del]:
- "(Code_Eval.term_of \<Colon> nat \<Rightarrow> term) = Code_Eval.term_of" ..
+ "(Code_Evaluation.term_of \<Colon> nat \<Rightarrow> term) = Code_Evaluation.term_of" ..
-code_const "Code_Eval.term_of \<Colon> nat \<Rightarrow> term"
+code_const "Code_Evaluation.term_of \<Colon> nat \<Rightarrow> term"
(SML "HOLogic.mk'_number/ HOLogic.natT")
--- a/src/HOL/Library/Executable_Set.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Executable_Set.thy Thu Sep 24 17:26:05 2009 +0200
@@ -85,4 +85,6 @@
card ("{*Fset.card*}")
fold ("{*foldl o flip*}")
+hide (open) const subset eq_set Inter Union flip
+
end
\ No newline at end of file
--- a/src/HOL/Library/Fin_Fun.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Fin_Fun.thy Thu Sep 24 17:26:05 2009 +0200
@@ -311,17 +311,17 @@
notation scomp (infixl "o\<rightarrow>" 60)
definition (in term_syntax) valtermify_finfun_const ::
- "'b\<Colon>typerep \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> ('a\<Colon>typerep \<Rightarrow>\<^isub>f 'b) \<times> (unit \<Rightarrow> Code_Eval.term)" where
- "valtermify_finfun_const y = Code_Eval.valtermify finfun_const {\<cdot>} y"
+ "'b\<Colon>typerep \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> ('a\<Colon>typerep \<Rightarrow>\<^isub>f 'b) \<times> (unit \<Rightarrow> Code_Evaluation.term)" where
+ "valtermify_finfun_const y = Code_Evaluation.valtermify finfun_const {\<cdot>} y"
definition (in term_syntax) valtermify_finfun_update_code ::
- "'a\<Colon>typerep \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> 'b\<Colon>typerep \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> ('a \<Rightarrow>\<^isub>f 'b) \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> ('a \<Rightarrow>\<^isub>f 'b) \<times> (unit \<Rightarrow> Code_Eval.term)" where
- "valtermify_finfun_update_code x y f = Code_Eval.valtermify finfun_update_code {\<cdot>} f {\<cdot>} x {\<cdot>} y"
+ "'a\<Colon>typerep \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> 'b\<Colon>typerep \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> ('a \<Rightarrow>\<^isub>f 'b) \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> ('a \<Rightarrow>\<^isub>f 'b) \<times> (unit \<Rightarrow> Code_Evaluation.term)" where
+ "valtermify_finfun_update_code x y f = Code_Evaluation.valtermify finfun_update_code {\<cdot>} f {\<cdot>} x {\<cdot>} y"
instantiation finfun :: (random, random) random
begin
-primrec random_finfun_aux :: "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a \<Rightarrow>\<^isub>f 'b \<times> (unit \<Rightarrow> Code_Eval.term)) \<times> Random.seed" where
+primrec random_finfun_aux :: "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a \<Rightarrow>\<^isub>f 'b \<times> (unit \<Rightarrow> Code_Evaluation.term)) \<times> Random.seed" where
"random_finfun_aux 0 j = Quickcheck.collapse (Random.select_weight
[(1, Quickcheck.random j o\<rightarrow> (\<lambda>y. Pair (valtermify_finfun_const y)))])"
| "random_finfun_aux (Suc_code_numeral i) j = Quickcheck.collapse (Random.select_weight
--- a/src/HOL/Library/Nested_Environment.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Nested_Environment.thy Thu Sep 24 17:26:05 2009 +0200
@@ -567,6 +567,6 @@
qed simp_all
lemma [code, code del]:
- "(Code_Eval.term_of :: ('a::{term_of, type}, 'b::{term_of, type}, 'c::{term_of, type}) env \<Rightarrow> term) = Code_Eval.term_of" ..
+ "(Code_Evaluation.term_of :: ('a::{term_of, type}, 'b::{term_of, type}, 'c::{term_of, type}) env \<Rightarrow> term) = Code_Evaluation.term_of" ..
end
--- a/src/HOL/Library/Sum_Of_Squares.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Sum_Of_Squares.thy Thu Sep 24 17:26:05 2009 +0200
@@ -10,6 +10,7 @@
uses
("positivstellensatz.ML") (* duplicate use!? -- cf. Euclidian_Space.thy *)
("Sum_Of_Squares/sum_of_squares.ML")
+ ("Sum_Of_Squares/positivstellensatz_tools.ML")
("Sum_Of_Squares/sos_wrapper.ML")
begin
@@ -22,112 +23,142 @@
of a minute for one sos call, because sos calls CSDP repeatedly. If
you install CSDP locally, sos calls typically takes only a few
seconds.
+ sos generates a certificate which can be used to repeat the proof
+ without calling an external prover.
*}
text {* setup sos tactic *}
use "positivstellensatz.ML"
+use "Sum_Of_Squares/positivstellensatz_tools.ML"
use "Sum_Of_Squares/sum_of_squares.ML"
use "Sum_Of_Squares/sos_wrapper.ML"
setup SosWrapper.setup
-text {* Tests -- commented since they work only when csdp is installed
- or take too long with remote csdps *}
+text {* Tests *}
+
+lemma "(3::real) * x + 7 * a < 4 & 3 < 2 * x \<Longrightarrow> a < 0"
+by (sos_cert "((R<1 + (((A<1 * R<1) * (R<2 * [1]^2)) + (((A<0 * R<1) * (R<3 * [1]^2)) + ((A<=0 * R<1) * (R<14 * [1]^2))))))")
+
+lemma "a1 >= 0 & a2 >= 0 \<and> (a1 * a1 + a2 * a2 = b1 * b1 + b2 * b2 + 2) \<and> (a1 * b1 + a2 * b2 = 0) --> a1 * a2 - b1 * b2 >= (0::real)"
+by (sos_cert "(((A<0 * R<1) + (([~1/2*a1*b2 + ~1/2*a2*b1] * A=0) + (([~1/2*a1*a2 + 1/2*b1*b2] * A=1) + (((A<0 * R<1) * ((R<1/2 * [b2]^2) + (R<1/2 * [b1]^2))) + ((A<=0 * (A<=1 * R<1)) * ((R<1/2 * [b2]^2) + ((R<1/2 * [b1]^2) + ((R<1/2 * [a2]^2) + (R<1/2 * [a1]^2))))))))))")
-(*
-lemma "(3::real) * x + 7 * a < 4 & 3 < 2 * x \<Longrightarrow> a < 0" by sos
+lemma "(3::real) * x + 7 * a < 4 & 3 < 2 * x --> a < 0"
+by (sos_cert "((R<1 + (((A<1 * R<1) * (R<2 * [1]^2)) + (((A<0 * R<1) * (R<3 * [1]^2)) + ((A<=0 * R<1) * (R<14 * [1]^2))))))")
+
+lemma "(0::real) <= x & x <= 1 & 0 <= y & y <= 1 --> x^2 + y^2 < 1 |(x - 1)^2 + y^2 < 1 | x^2 + (y - 1)^2 < 1 | (x - 1)^2 + (y - 1)^2 < 1"
+by (sos_cert "((R<1 + (((A<=3 * (A<=4 * R<1)) * (R<1 * [1]^2)) + (((A<=2 * (A<=7 * R<1)) * (R<1 * [1]^2)) + (((A<=1 * (A<=6 * R<1)) * (R<1 * [1]^2)) + ((A<=0 * (A<=5 * R<1)) * (R<1 * [1]^2)))))))")
-lemma "a1 >= 0 & a2 >= 0 \<and> (a1 * a1 + a2 * a2 = b1 * b1 + b2 * b2 + 2) \<and>
- (a1 * b1 + a2 * b2 = 0) --> a1 * a2 - b1 * b2 >= (0::real)" by sos
+lemma "(0::real) <= x & 0 <= y & 0 <= z & x + y + z <= 3 --> x * y + x * z + y * z >= 3 * x * y * z"
+by (sos_cert "(((A<0 * R<1) + (((A<0 * R<1) * (R<1/2 * [1]^2)) + (((A<=2 * R<1) * (R<1/2 * [~1*x + y]^2)) + (((A<=1 * R<1) * (R<1/2 * [~1*x + z]^2)) + (((A<=1 * (A<=2 * (A<=3 * R<1))) * (R<1/2 * [1]^2)) + (((A<=0 * R<1) * (R<1/2 * [~1*y + z]^2)) + (((A<=0 * (A<=2 * (A<=3 * R<1))) * (R<1/2 * [1]^2)) + ((A<=0 * (A<=1 * (A<=3 * R<1))) * (R<1/2 * [1]^2))))))))))")
+
+lemma "((x::real)^2 + y^2 + z^2 = 1) --> (x + y + z)^2 <= 3"
+by (sos_cert "(((A<0 * R<1) + (([~3] * A=0) + (R<1 * ((R<2 * [~1/2*x + ~1/2*y + z]^2) + (R<3/2 * [~1*x + y]^2))))))")
-lemma "(3::real) * x + 7 * a < 4 & 3 < 2 * x --> a < 0" by sos
+lemma "(w^2 + x^2 + y^2 + z^2 = 1) --> (w + x + y + z)^2 <= (4::real)"
+by (sos_cert "(((A<0 * R<1) + (([~4] * A=0) + (R<1 * ((R<3 * [~1/3*w + ~1/3*x + ~1/3*y + z]^2) + ((R<8/3 * [~1/2*w + ~1/2*x + y]^2) + (R<2 * [~1*w + x]^2)))))))")
-lemma "(0::real) <= x & x <= 1 & 0 <= y & y <= 1 -->
- x^2 + y^2 < 1 |(x - 1)^2 + y^2 < 1 | x^2 + (y - 1)^2 < 1 | (x - 1)^2 + (y - 1)^2 < 1" by sos
+lemma "(x::real) >= 1 & y >= 1 --> x * y >= x + y - 1"
+by (sos_cert "(((A<0 * R<1) + ((A<=0 * (A<=1 * R<1)) * (R<1 * [1]^2))))")
+
+lemma "(x::real) > 1 & y > 1 --> x * y > x + y - 1"
+by (sos_cert "((((A<0 * A<1) * R<1) + ((A<=0 * R<1) * (R<1 * [1]^2))))")
-lemma "(0::real) <= x & 0 <= y & 0 <= z & x + y + z <= 3 -->
- x * y + x * z + y * z >= 3 * x * y * z" by sos
+lemma "abs(x) <= 1 --> abs(64 * x^7 - 112 * x^5 + 56 * x^3 - 7 * x) <= (1::real)"
+by (sos_cert "((((A<0 * R<1) + ((A<=1 * R<1) * (R<1 * [~8*x^3 + ~4*x^2 + 4*x + 1]^2)))) & ((((A<0 * A<1) * R<1) + ((A<=1 * (A<0 * R<1)) * (R<1 * [8*x^3 + ~4*x^2 + ~4*x + 1]^2)))))")
+
+(* ------------------------------------------------------------------------- *)
+(* One component of denominator in dodecahedral example. *)
+(* ------------------------------------------------------------------------- *)
-lemma "((x::real)^2 + y^2 + z^2 = 1) --> (x + y + z)^2 <= 3" by sos
+lemma "2 <= x & x <= 125841 / 50000 & 2 <= y & y <= 125841 / 50000 & 2 <= z & z <= 125841 / 50000 --> 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z) >= (0::real)"
+by (sos_cert "(((A<0 * R<1) + ((R<1 * ((R<5749028157/5000000000 * [~25000/222477*x + ~25000/222477*y + ~25000/222477*z + 1]^2) + ((R<864067/1779816 * [419113/864067*x + 419113/864067*y + z]^2) + ((R<320795/864067 * [419113/1283180*x + y]^2) + (R<1702293/5132720 * [x]^2))))) + (((A<=4 * (A<=5 * R<1)) * (R<3/2 * [1]^2)) + (((A<=3 * (A<=5 * R<1)) * (R<1/2 * [1]^2)) + (((A<=2 * (A<=4 * R<1)) * (R<1 * [1]^2)) + (((A<=2 * (A<=3 * R<1)) * (R<3/2 * [1]^2)) + (((A<=1 * (A<=5 * R<1)) * (R<1/2 * [1]^2)) + (((A<=1 * (A<=3 * R<1)) * (R<1/2 * [1]^2)) + (((A<=0 * (A<=4 * R<1)) * (R<1 * [1]^2)) + (((A<=0 * (A<=2 * R<1)) * (R<1 * [1]^2)) + ((A<=0 * (A<=1 * R<1)) * (R<3/2 * [1]^2)))))))))))))")
-lemma "(w^2 + x^2 + y^2 + z^2 = 1) --> (w + x + y + z)^2 <= (4::real)" by sos
+(* ------------------------------------------------------------------------- *)
+(* Over a larger but simpler interval. *)
+(* ------------------------------------------------------------------------- *)
-lemma "(x::real) >= 1 & y >= 1 --> x * y >= x + y - 1" by sos
+lemma "(2::real) <= x & x <= 4 & 2 <= y & y <= 4 & 2 <= z & z <= 4 --> 0 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z)"
+by (sos_cert "((R<1 + ((R<1 * ((R<1 * [~1/6*x + ~1/6*y + ~1/6*z + 1]^2) + ((R<1/18 * [~1/2*x + ~1/2*y + z]^2) + (R<1/24 * [~1*x + y]^2)))) + (((A<0 * R<1) * (R<1/12 * [1]^2)) + (((A<=4 * (A<=5 * R<1)) * (R<1/6 * [1]^2)) + (((A<=2 * (A<=4 * R<1)) * (R<1/6 * [1]^2)) + (((A<=2 * (A<=3 * R<1)) * (R<1/6 * [1]^2)) + (((A<=0 * (A<=4 * R<1)) * (R<1/6 * [1]^2)) + (((A<=0 * (A<=2 * R<1)) * (R<1/6 * [1]^2)) + ((A<=0 * (A<=1 * R<1)) * (R<1/6 * [1]^2)))))))))))")
-lemma "(x::real) > 1 & y > 1 --> x * y > x + y - 1" by sos;
+(* ------------------------------------------------------------------------- *)
+(* We can do 12. I think 12 is a sharp bound; see PP's certificate. *)
+(* ------------------------------------------------------------------------- *)
+
+lemma "2 <= (x::real) & x <= 4 & 2 <= y & y <= 4 & 2 <= z & z <= 4 --> 12 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z)"
+by (sos_cert "(((A<0 * R<1) + (((A<=4 * R<1) * (R<2/3 * [1]^2)) + (((A<=4 * (A<=5 * R<1)) * (R<1 * [1]^2)) + (((A<=3 * (A<=4 * R<1)) * (R<1/3 * [1]^2)) + (((A<=2 * R<1) * (R<2/3 * [1]^2)) + (((A<=2 * (A<=5 * R<1)) * (R<1/3 * [1]^2)) + (((A<=2 * (A<=4 * R<1)) * (R<8/3 * [1]^2)) + (((A<=2 * (A<=3 * R<1)) * (R<1 * [1]^2)) + (((A<=1 * (A<=4 * R<1)) * (R<1/3 * [1]^2)) + (((A<=1 * (A<=2 * R<1)) * (R<1/3 * [1]^2)) + (((A<=0 * R<1) * (R<2/3 * [1]^2)) + (((A<=0 * (A<=5 * R<1)) * (R<1/3 * [1]^2)) + (((A<=0 * (A<=4 * R<1)) * (R<8/3 * [1]^2)) + (((A<=0 * (A<=3 * R<1)) * (R<1/3 * [1]^2)) + (((A<=0 * (A<=2 * R<1)) * (R<8/3 * [1]^2)) + ((A<=0 * (A<=1 * R<1)) * (R<1 * [1]^2))))))))))))))))))")
-lemma "abs(x) <= 1 --> abs(64 * x^7 - 112 * x^5 + 56 * x^3 - 7 * x) <= (1::real)" by sos
+(* ------------------------------------------------------------------------- *)
+(* Inequality from sci.math (see "Leon-Sotelo, por favor"). *)
+(* ------------------------------------------------------------------------- *)
+lemma "0 <= (x::real) & 0 <= y & (x * y = 1) --> x + y <= x^2 + y^2"
+by (sos_cert "(((A<0 * R<1) + (([1] * A=0) + (R<1 * ((R<1 * [~1/2*x + ~1/2*y + 1]^2) + (R<3/4 * [~1*x + y]^2))))))")
-text {* One component of denominator in dodecahedral example. *}
+lemma "0 <= (x::real) & 0 <= y & (x * y = 1) --> x * y * (x + y) <= x^2 + y^2"
+by (sos_cert "(((A<0 * R<1) + (([~1*x + ~1*y + 1] * A=0) + (R<1 * ((R<1 * [~1/2*x + ~1/2*y + 1]^2) + (R<3/4 * [~1*x + y]^2))))))")
-lemma "2 <= x & x <= 125841 / 50000 & 2 <= y & y <= 125841 / 50000 & 2 <= z &
- z <= 125841 / 50000 --> 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z) >= (0::real)" by sos
+lemma "0 <= (x::real) & 0 <= y --> x * y * (x + y)^2 <= (x^2 + y^2)^2"
+by (sos_cert "(((A<0 * R<1) + (R<1 * ((R<1 * [~1/2*x^2 + y^2 + ~1/2*x*y]^2) + (R<3/4 * [~1*x^2 + x*y]^2)))))")
+lemma "(0::real) <= a & 0 <= b & 0 <= c & c * (2 * a + b)^3/ 27 <= x \<longrightarrow> c * a^2 * b <= x"
+by (sos_cert "(((A<0 * R<1) + (((A<=3 * R<1) * (R<1 * [1]^2)) + (((A<=1 * (A<=2 * R<1)) * (R<1/27 * [~1*a + b]^2)) + ((A<=0 * (A<=2 * R<1)) * (R<8/27 * [~1*a + b]^2))))))")
+
+lemma "(0::real) < x --> 0 < 1 + x + x^2"
+by (sos_cert "((R<1 + ((R<1 * (R<1 * [x]^2)) + (((A<0 * R<1) * (R<1 * [1]^2)) + ((A<=0 * R<1) * (R<1 * [1]^2))))))")
-text {* Over a larger but simpler interval. *}
+lemma "(0::real) <= x --> 0 < 1 + x + x^2"
+by (sos_cert "((R<1 + ((R<1 * (R<1 * [x]^2)) + (((A<=1 * R<1) * (R<1 * [1]^2)) + ((A<=0 * R<1) * (R<1 * [1]^2))))))")
-lemma "(2::real) <= x & x <= 4 & 2 <= y & y <= 4 & 2 <= z &
- z <= 4 --> 0 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z)" by sos
+lemma "(0::real) < 1 + x^2"
+by (sos_cert "((R<1 + ((R<1 * (R<1 * [x]^2)) + ((A<=0 * R<1) * (R<1 * [1]^2)))))")
+
+lemma "(0::real) <= 1 + 2 * x + x^2"
+by (sos_cert "(((A<0 * R<1) + (R<1 * (R<1 * [x + 1]^2))))")
-text {* We can do 12. I think 12 is a sharp bound; see PP's certificate. *}
+lemma "(0::real) < 1 + abs x"
+by (sos_cert "((R<1 + (((A<=1 * R<1) * (R<1/2 * [1]^2)) + ((A<=0 * R<1) * (R<1/2 * [1]^2)))))")
-lemma "2 <= (x::real) & x <= 4 & 2 <= y & y <= 4 & 2 <= z & z <= 4 -->
- 12 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z)" by sos
+lemma "(0::real) < 1 + (1 + x)^2 * (abs x)"
+by (sos_cert "(((R<1 + (((A<=1 * R<1) * (R<1 * [1]^2)) + ((A<=0 * R<1) * (R<1 * [x + 1]^2))))) & ((R<1 + (((A<0 * R<1) * (R<1 * [x + 1]^2)) + ((A<=0 * R<1) * (R<1 * [1]^2))))))")
-text {* Inequality from sci.math (see "Leon-Sotelo, por favor"). *}
-lemma "0 <= (x::real) & 0 <= y & (x * y = 1) --> x + y <= x^2 + y^2" by sos
-
-lemma "0 <= (x::real) & 0 <= y & (x * y = 1) --> x * y * (x + y) <= x^2 + y^2" by sos
-
-lemma "0 <= (x::real) & 0 <= y --> x * y * (x + y)^2 <= (x^2 + y^2)^2" by sos
+lemma "abs ((1::real) + x^2) = (1::real) + x^2"
+by (sos_cert "(() & (((R<1 + ((R<1 * (R<1 * [x]^2)) + ((A<1 * R<1) * (R<1/2 * [1]^2))))) & ((R<1 + ((R<1 * (R<1 * [x]^2)) + ((A<0 * R<1) * (R<1 * [1]^2)))))))")
+lemma "(3::real) * x + 7 * a < 4 \<and> 3 < 2 * x \<longrightarrow> a < 0"
+by (sos_cert "((R<1 + (((A<1 * R<1) * (R<2 * [1]^2)) + (((A<0 * R<1) * (R<3 * [1]^2)) + ((A<=0 * R<1) * (R<14 * [1]^2))))))")
-lemma "(0::real) <= a & 0 <= b & 0 <= c & c * (2 * a + b)^3/ 27 <= x \<longrightarrow> c * a^2 * b <= x" by sos
-
-lemma "(0::real) < x --> 0 < 1 + x + x^2" by sos
-
-lemma "(0::real) <= x --> 0 < 1 + x + x^2" by sos
-
-lemma "(0::real) < 1 + x^2" by sos
-
-lemma "(0::real) <= 1 + 2 * x + x^2" by sos
-
-lemma "(0::real) < 1 + abs x" by sos
-
-lemma "(0::real) < 1 + (1 + x)^2 * (abs x)" by sos
+lemma "(0::real) < x --> 1 < y --> y * x <= z --> x < z"
+by (sos_cert "((((A<0 * A<1) * R<1) + (((A<=1 * R<1) * (R<1 * [1]^2)) + ((A<=0 * R<1) * (R<1 * [1]^2)))))")
+lemma "(1::real) < x --> x^2 < y --> 1 < y"
+by (sos_cert "((((A<0 * A<1) * R<1) + ((R<1 * ((R<1/10 * [~2*x + y + 1]^2) + (R<1/10 * [~1*x + y]^2))) + (((A<1 * R<1) * (R<1/2 * [1]^2)) + (((A<0 * R<1) * (R<1 * [x]^2)) + (((A<=0 * R<1) * ((R<1/10 * [x + 1]^2) + (R<1/10 * [x]^2))) + (((A<=0 * (A<1 * R<1)) * (R<1/5 * [1]^2)) + ((A<=0 * (A<0 * R<1)) * (R<1/5 * [1]^2)))))))))")
+lemma "(b::real)^2 < 4 * a * c --> ~(a * x^2 + b * x + c = 0)"
+by (sos_cert "(((A<0 * R<1) + (R<1 * (R<1 * [2*a*x + b]^2))))")
+lemma "(b::real)^2 < 4 * a * c --> ~(a * x^2 + b * x + c = 0)"
+by (sos_cert "(((A<0 * R<1) + (R<1 * (R<1 * [2*a*x + b]^2))))")
+lemma "((a::real) * x^2 + b * x + c = 0) --> b^2 >= 4 * a * c"
+by (sos_cert "(((A<0 * R<1) + (R<1 * (R<1 * [2*a*x + b]^2))))")
+lemma "(0::real) <= b & 0 <= c & 0 <= x & 0 <= y & (x^2 = c) & (y^2 = a^2 * c + b) --> a * c <= y * x"
+by (sos_cert "(((A<0 * (A<0 * R<1)) + (((A<=2 * (A<=3 * (A<0 * R<1))) * (R<2 * [1]^2)) + ((A<=0 * (A<=1 * R<1)) * (R<1 * [1]^2)))))")
+lemma "abs(x - z) <= e & abs(y - z) <= e & 0 <= u & 0 <= v & (u + v = 1) --> abs((u * x + v * y) - z) <= (e::real)"
+by (sos_cert "((((A<0 * R<1) + (((A<=3 * (A<=6 * R<1)) * (R<1 * [1]^2)) + ((A<=1 * (A<=5 * R<1)) * (R<1 * [1]^2))))) & ((((A<0 * A<1) * R<1) + (((A<=3 * (A<=5 * (A<0 * R<1))) * (R<1 * [1]^2)) + ((A<=1 * (A<=4 * (A<0 * R<1))) * (R<1 * [1]^2))))))")
-lemma "abs ((1::real) + x^2) = (1::real) + x^2" by sos
-lemma "(3::real) * x + 7 * a < 4 \<and> 3 < 2 * x \<longrightarrow> a < 0" by sos
-
-lemma "(0::real) < x --> 1 < y --> y * x <= z --> x < z" by sos
-lemma "(1::real) < x --> x^2 < y --> 1 < y" by sos
-lemma "(b::real)^2 < 4 * a * c --> ~(a * x^2 + b * x + c = 0)" by sos
-lemma "(b::real)^2 < 4 * a * c --> ~(a * x^2 + b * x + c = 0)" by sos
-lemma "((a::real) * x^2 + b * x + c = 0) --> b^2 >= 4 * a * c" by sos
-lemma "(0::real) <= b & 0 <= c & 0 <= x & 0 <= y & (x^2 = c) & (y^2 = a^2 * c + b) --> a * c <= y * x" by sos
-lemma "abs(x - z) <= e & abs(y - z) <= e & 0 <= u & 0 <= v & (u + v = 1) -->
- abs((u * x + v * y) - z) <= (e::real)" by sos
-
-(*
-lemma "((x::real) - y - 2 * x^4 = 0) & 0 <= x & x <= 2 & 0 <= y & y <= 3 -->
- y^2 - 7 * y - 12 * x + 17 >= 0" by sos -- {* Too hard?*}
-*)
+(* lemma "((x::real) - y - 2 * x^4 = 0) & 0 <= x & x <= 2 & 0 <= y & y <= 3 --> y^2 - 7 * y - 12 * x + 17 >= 0" by sos *) (* Too hard?*)
lemma "(0::real) <= x --> (1 + x + x^2)/(1 + x^2) <= 1 + x"
- by sos
+by (sos_cert "(((((A<0 * A<1) * R<1) + ((A<=0 * (A<0 * R<1)) * (R<1 * [x]^2)))) & ((R<1 + ((R<1 * (R<1 * [x]^2)) + ((A<0 * R<1) * (R<1 * [1]^2))))))")
lemma "(0::real) <= x --> 1 - x <= 1 / (1 + x + x^2)"
- by sos
+by (sos_cert "(((R<1 + (([~4/3] * A=0) + ((R<1 * ((R<1/3 * [3/2*x + 1]^2) + (R<7/12 * [x]^2))) + ((A<=0 * R<1) * (R<1/3 * [1]^2)))))) & (((((A<0 * A<1) * R<1) + ((A<=0 * (A<0 * R<1)) * (R<1 * [x]^2)))) & ((R<1 + ((R<1 * (R<1 * [x]^2)) + (((A<0 * R<1) * (R<1 * [1]^2)) + ((A<=0 * R<1) * (R<1 * [1]^2))))))))")
lemma "(x::real) <= 1 / 2 --> - x - 2 * x^2 <= - x / (1 - x)"
- by sos
+by (sos_cert "((((A<0 * A<1) * R<1) + ((A<=0 * (A<0 * R<1)) * (R<1 * [x]^2))))")
-lemma "4*r^2 = p^2 - 4*q & r >= (0::real) & x^2 + p*x + q = 0 -->
- 2*(x::real) = - p + 2*r | 2*x = -p - 2*r" by sos
-*)
+lemma "4*r^2 = p^2 - 4*q & r >= (0::real) & x^2 + p*x + q = 0 --> 2*(x::real) = - p + 2*r | 2*x = -p - 2*r"
+by (sos_cert "((((((A<0 * A<1) * R<1) + ([~4] * A=0))) & ((((A<0 * A<1) * R<1) + ([4] * A=0)))) & (((((A<0 * A<1) * R<1) + ([4] * A=0))) & ((((A<0 * A<1) * R<1) + ([~4] * A=0)))))")
end
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Sum_Of_Squares/positivstellensatz_tools.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,158 @@
+(* Title: positivstellensatz_tools.ML
+ Author: Philipp Meyer, TU Muenchen
+
+Functions for generating a certificate from a positivstellensatz and vice versa
+*)
+
+signature POSITIVSTELLENSATZ_TOOLS =
+sig
+ val pss_tree_to_cert : RealArith.pss_tree -> string
+
+ val cert_to_pss_tree : Proof.context -> string -> RealArith.pss_tree
+
+end
+
+
+structure PositivstellensatzTools : POSITIVSTELLENSATZ_TOOLS =
+struct
+
+open RealArith FuncUtil
+
+(*** certificate generation ***)
+
+fun string_of_rat r =
+ let
+ val (nom, den) = Rat.quotient_of_rat r
+ in
+ if den = 1 then string_of_int nom
+ else string_of_int nom ^ "/" ^ string_of_int den
+ end
+
+(* map polynomials to strings *)
+
+fun string_of_varpow x k =
+ let
+ val term = term_of x
+ val name = case term of
+ Free (n, _) => n
+ | _ => error "Term in monomial not free variable"
+ in
+ if k = 1 then name else name ^ "^" ^ string_of_int k
+ end
+
+fun string_of_monomial m =
+ if Ctermfunc.is_undefined m then "1"
+ else
+ let
+ val m' = dest_monomial m
+ val vps = fold_rev (fn (x,k) => cons (string_of_varpow x k)) m' []
+ in foldr1 (fn (s, t) => s ^ "*" ^ t) vps
+ end
+
+fun string_of_cmonomial (m,c) =
+ if Ctermfunc.is_undefined m then string_of_rat c
+ else if c = Rat.one then string_of_monomial m
+ else (string_of_rat c) ^ "*" ^ (string_of_monomial m);
+
+fun string_of_poly p =
+ if Monomialfunc.is_undefined p then "0"
+ else
+ let
+ val cms = map string_of_cmonomial
+ (sort (prod_ord monomial_order (K EQUAL)) (Monomialfunc.graph p))
+ in foldr1 (fn (t1, t2) => t1 ^ " + " ^ t2) cms
+ end;
+
+fun pss_to_cert (Axiom_eq i) = "A=" ^ string_of_int i
+ | pss_to_cert (Axiom_le i) = "A<=" ^ string_of_int i
+ | pss_to_cert (Axiom_lt i) = "A<" ^ string_of_int i
+ | pss_to_cert (Rational_eq r) = "R=" ^ string_of_rat r
+ | pss_to_cert (Rational_le r) = "R<=" ^ string_of_rat r
+ | pss_to_cert (Rational_lt r) = "R<" ^ string_of_rat r
+ | pss_to_cert (Square p) = "[" ^ string_of_poly p ^ "]^2"
+ | pss_to_cert (Eqmul (p, pss)) = "([" ^ string_of_poly p ^ "] * " ^ pss_to_cert pss ^ ")"
+ | pss_to_cert (Sum (pss1, pss2)) = "(" ^ pss_to_cert pss1 ^ " + " ^ pss_to_cert pss2 ^ ")"
+ | pss_to_cert (Product (pss1, pss2)) = "(" ^ pss_to_cert pss1 ^ " * " ^ pss_to_cert pss2 ^ ")"
+
+fun pss_tree_to_cert Trivial = "()"
+ | pss_tree_to_cert (Cert pss) = "(" ^ pss_to_cert pss ^ ")"
+ | pss_tree_to_cert (Branch (t1, t2)) = "(" ^ pss_tree_to_cert t1 ^ " & " ^ pss_tree_to_cert t2 ^ ")"
+
+(*** certificate parsing ***)
+
+(* basic parser *)
+
+val str = Scan.this_string
+
+val number = Scan.repeat1 (Scan.one Symbol.is_ascii_digit >>
+ (fn s => ord s - ord "0")) >>
+ foldl1 (fn (n, d) => n * 10 + d)
+
+val nat = number
+val int = Scan.optional (str "~" >> K ~1) 1 -- nat >> op *;
+val rat = int --| str "/" -- int >> Rat.rat_of_quotient
+val rat_int = rat || int >> Rat.rat_of_int
+
+(* polynomial parser *)
+
+fun repeat_sep s f = f ::: Scan.repeat (str s |-- f)
+
+val parse_id = Scan.one Symbol.is_letter ::: Scan.many Symbol.is_letdig >> implode
+
+fun parse_varpow ctxt = parse_id -- Scan.optional (str "^" |-- nat) 1 >>
+ (fn (x, k) => (cterm_of (Context.theory_of_proof ctxt) (Free (x, @{typ real})), k))
+
+fun parse_monomial ctxt = repeat_sep "*" (parse_varpow ctxt) >>
+ foldl (uncurry Ctermfunc.update) Ctermfunc.undefined
+
+fun parse_cmonomial ctxt =
+ rat_int --| str "*" -- (parse_monomial ctxt) >> swap ||
+ (parse_monomial ctxt) >> (fn m => (m, Rat.one)) ||
+ rat_int >> (fn r => (Ctermfunc.undefined, r))
+
+fun parse_poly ctxt = repeat_sep "+" (parse_cmonomial ctxt) >>
+ foldl (uncurry Monomialfunc.update) Monomialfunc.undefined
+
+(* positivstellensatz parser *)
+
+val parse_axiom =
+ (str "A=" |-- int >> Axiom_eq) ||
+ (str "A<=" |-- int >> Axiom_le) ||
+ (str "A<" |-- int >> Axiom_lt)
+
+val parse_rational =
+ (str "R=" |-- rat_int >> Rational_eq) ||
+ (str "R<=" |-- rat_int >> Rational_le) ||
+ (str "R<" |-- rat_int >> Rational_lt)
+
+fun parse_cert ctxt input =
+ let
+ val pc = parse_cert ctxt
+ val pp = parse_poly ctxt
+ in
+ (parse_axiom ||
+ parse_rational ||
+ str "[" |-- pp --| str "]^2" >> Square ||
+ str "([" |-- pp --| str "]*" -- pc --| str ")" >> Eqmul ||
+ str "(" |-- pc --| str "*" -- pc --| str ")" >> Product ||
+ str "(" |-- pc --| str "+" -- pc --| str ")" >> Sum) input
+ end
+
+fun parse_cert_tree ctxt input =
+ let
+ val pc = parse_cert ctxt
+ val pt = parse_cert_tree ctxt
+ in
+ (str "()" >> K Trivial ||
+ str "(" |-- pc --| str ")" >> Cert ||
+ str "(" |-- pt --| str "&" -- pt --| str ")" >> Branch) input
+ end
+
+(* scanner *)
+
+fun cert_to_pss_tree ctxt input_str = Symbol.scanner "bad certificate" (parse_cert_tree ctxt)
+ (filter_out Symbol.is_blank (Symbol.explode input_str))
+
+end
+
+
--- a/src/HOL/Library/Sum_Of_Squares/sos_wrapper.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Sum_Of_Squares/sos_wrapper.ML Thu Sep 24 17:26:05 2009 +0200
@@ -136,13 +136,32 @@
run_solver name (Path.explode cmd) find_failure
end
+(* certificate output *)
+
+fun output_line cert = "To repeat this proof with a certifiate use this command:\n" ^
+ (Markup.markup Markup.sendback) ("by (sos_cert \"" ^ cert ^ "\")")
+
+val print_cert = Output.writeln o output_line o PositivstellensatzTools.pss_tree_to_cert
+
(* setup tactic *)
-fun sos_solver name = (SIMPLE_METHOD' o (Sos.sos_tac (call_solver name)))
+fun parse_cert (input as (ctxt, _)) =
+ (Scan.lift OuterParse.string >>
+ PositivstellensatzTools.cert_to_pss_tree (Context.proof_of ctxt)) input
+
+fun sos_solver print method = (SIMPLE_METHOD' o (Sos.sos_tac print method))
-val sos_method = Scan.option (Scan.lift OuterParse.xname) >> sos_solver
+val sos_method =
+ Scan.lift (Scan.option OuterParse.xname) >> (fn n => Sos.Prover (call_solver n)) >>
+ sos_solver print_cert
-val setup = Method.setup @{binding sos} sos_method
- "Prove universal problems over the reals using sums of squares"
+val sos_cert_method =
+ parse_cert >> Sos.Certificate >> sos_solver ignore
+
+val setup =
+ Method.setup @{binding sos} sos_method
+ "Prove universal problems over the reals using sums of squares"
+ #> Method.setup @{binding sos_cert} sos_cert_method
+ "Prove universal problems over the reals using sums of squares with certificates"
end
--- a/src/HOL/Library/Sum_Of_Squares/sum_of_squares.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/Sum_Of_Squares/sum_of_squares.ML Thu Sep 24 17:26:05 2009 +0200
@@ -8,7 +8,12 @@
signature SOS =
sig
- val sos_tac : (string -> string) -> Proof.context -> int -> Tactical.tactic
+ datatype proof_method =
+ Certificate of RealArith.pss_tree
+ | Prover of (string -> string)
+
+ val sos_tac : (RealArith.pss_tree -> unit) ->
+ proof_method -> Proof.context -> int -> tactic
val debugging : bool ref;
@@ -18,6 +23,8 @@
structure Sos : SOS =
struct
+open FuncUtil;
+
val rat_0 = Rat.zero;
val rat_1 = Rat.one;
val rat_2 = Rat.two;
@@ -59,6 +66,10 @@
exception Failure of string;
+datatype proof_method =
+ Certificate of RealArith.pss_tree
+ | Prover of (string -> string)
+
(* Turn a rational into a decimal string with d sig digits. *)
local
@@ -93,23 +104,11 @@
(* The main types. *)
-fun strict_ord ord (x,y) = case ord (x,y) of LESS => LESS | _ => GREATER
-
-structure Intpairfunc = FuncFun(type key = int*int val ord = prod_ord int_ord int_ord);
-
type vector = int* Rat.rat Intfunc.T;
type matrix = (int*int)*(Rat.rat Intpairfunc.T);
-type monomial = int Ctermfunc.T;
-
-val cterm_ord = (fn (s,t) => TermOrd.fast_term_ord(term_of s, term_of t))
- fun monomial_ord (m1,m2) = list_ord (prod_ord cterm_ord int_ord) (Ctermfunc.graph m1, Ctermfunc.graph m2)
-structure Monomialfunc = FuncFun(type key = monomial val ord = monomial_ord)
-
-type poly = Rat.rat Monomialfunc.T;
-
- fun iszero (k,r) = r =/ rat_0;
+fun iszero (k,r) = r =/ rat_0;
fun fold_rev2 f l1 l2 b =
case (l1,l2) of
@@ -346,11 +345,6 @@
sort humanorder_varpow (Ctermfunc.graph m2))
end;
-fun fold1 f l = case l of
- [] => error "fold1"
- | [x] => x
- | (h::t) => f h (fold1 f t);
-
(* Conversions to strings. *)
fun string_of_vector min_size max_size (v:vector) =
@@ -359,7 +353,7 @@
let
val n = max min_size (min n_raw max_size)
val xs = map (Rat.string_of_rat o (fn i => Intfunc.tryapplyd (snd v) i rat_0)) (1 upto n)
- in "[" ^ fold1 (fn s => fn t => s ^ ", " ^ t) xs ^
+ in "[" ^ foldr1 (fn (s, t) => s ^ ", " ^ t) xs ^
(if n_raw > max_size then ", ...]" else "]")
end
end;
@@ -370,7 +364,7 @@
val i = min max_size i_raw
val j = min max_size j_raw
val rstr = map (fn k => string_of_vector j j (row k m)) (1 upto i)
- in "["^ fold1 (fn s => fn t => s^";\n "^t) rstr ^
+ in "["^ foldr1 (fn (s, t) => s^";\n "^t) rstr ^
(if j > max_size then "\n ...]" else "]")
end;
@@ -396,7 +390,7 @@
if Ctermfunc.is_undefined m then "1" else
let val vps = fold_rev (fn (x,k) => fn a => string_of_varpow x k :: a)
(sort humanorder_varpow (Ctermfunc.graph m)) []
- in fold1 (fn s => fn t => s^"*"^t) vps
+ in foldr1 (fn (s, t) => s^"*"^t) vps
end;
fun string_of_cmonomial (c,m) =
@@ -404,7 +398,7 @@
else if c =/ rat_1 then string_of_monomial m
else Rat.string_of_rat c ^ "*" ^ string_of_monomial m;;
-fun string_of_poly (p:poly) =
+fun string_of_poly p =
if Monomialfunc.is_undefined p then "<<0>>" else
let
val cms = sort (fn ((m1,_),(m2,_)) => humanorder_monomial m1 m2) (Monomialfunc.graph p)
@@ -478,10 +472,9 @@
let
val n = dim v
val strs = map (decimalize 20 o (fn i => Intfunc.tryapplyd (snd v) i rat_0)) (1 upto n)
- in fold1 (fn x => fn y => x ^ " " ^ y) strs ^ "\n"
+ in foldr1 (fn (x, y) => x ^ " " ^ y) strs ^ "\n"
end;
-fun increasing f ord (x,y) = ord (f x, f y);
fun triple_int_ord ((a,b,c),(a',b',c')) =
prod_ord int_ord (prod_ord int_ord int_ord)
((a,(b,c)),(a',(b',c')));
@@ -989,7 +982,7 @@
let val alts =
map (fn k => let val oths = enumerate_monomials (d - k) (tl vars)
in map (fn ks => if k = 0 then ks else Ctermfunc.update (hd vars, k) ks) oths end) (0 upto d)
- in fold1 (curry op @) alts
+ in foldr1 op @ alts
end;
(* Enumerate products of distinct input polys with degree <= d. *)
@@ -1040,7 +1033,7 @@
in
string_of_int m ^ "\n" ^
string_of_int nblocks ^ "\n" ^
- (fold1 (fn s => fn t => s^" "^t) (map string_of_int blocksizes)) ^
+ (foldr1 (fn (s, t) => s^" "^t) (map string_of_int blocksizes)) ^
"\n" ^
sdpa_of_vector obj ^
fold_rev2 (fn k => fn m => fn a => sdpa_of_blockdiagonal (k - 1) m ^ a)
@@ -1080,11 +1073,6 @@
fun tryfind f = tryfind_with "tryfind" f
end
-(*
-fun tryfind f [] = error "tryfind"
- | tryfind f (x::xs) = (f x handle ERROR _ => tryfind f xs);
-*)
-
(* Positiv- and Nullstellensatz. Flag "linf" forces a linear representation. *)
@@ -1210,61 +1198,17 @@
fun deepen f n =
(writeln ("Searching with depth limit " ^ string_of_int n) ; (f n handle Failure s => (writeln ("failed with message: " ^ s) ; deepen f (n+1))))
-(* The ordering so we can create canonical HOL polynomials. *)
-fun dest_monomial mon = sort (increasing fst cterm_ord) (Ctermfunc.graph mon);
-
-fun monomial_order (m1,m2) =
- if Ctermfunc.is_undefined m2 then LESS
- else if Ctermfunc.is_undefined m1 then GREATER
- else
- let val mon1 = dest_monomial m1
- val mon2 = dest_monomial m2
- val deg1 = fold (curry op + o snd) mon1 0
- val deg2 = fold (curry op + o snd) mon2 0
- in if deg1 < deg2 then GREATER else if deg1 > deg2 then LESS
- else list_ord (prod_ord cterm_ord int_ord) (mon1,mon2)
- end;
-
-fun dest_poly p =
- map (fn (m,c) => (c,dest_monomial m))
- (sort (prod_ord monomial_order (K EQUAL)) (Monomialfunc.graph p));
-
-(* Map back polynomials and their composites to HOL. *)
+(* Map back polynomials and their composites to a positivstellensatz. *)
local
open Thm Numeral RealArith
in
-fun cterm_of_varpow x k = if k = 1 then x else capply (capply @{cterm "op ^ :: real => _"} x)
- (mk_cnumber @{ctyp nat} k)
-
-fun cterm_of_monomial m =
- if Ctermfunc.is_undefined m then @{cterm "1::real"}
- else
- let
- val m' = dest_monomial m
- val vps = fold_rev (fn (x,k) => cons (cterm_of_varpow x k)) m' []
- in fold1 (fn s => fn t => capply (capply @{cterm "op * :: real => _"} s) t) vps
- end
-
-fun cterm_of_cmonomial (m,c) = if Ctermfunc.is_undefined m then cterm_of_rat c
- else if c = Rat.one then cterm_of_monomial m
- else capply (capply @{cterm "op *::real => _"} (cterm_of_rat c)) (cterm_of_monomial m);
-
-fun cterm_of_poly p =
- if Monomialfunc.is_undefined p then @{cterm "0::real"}
- else
- let
- val cms = map cterm_of_cmonomial
- (sort (prod_ord monomial_order (K EQUAL)) (Monomialfunc.graph p))
- in fold1 (fn t1 => fn t2 => capply(capply @{cterm "op + :: real => _"} t1) t2) cms
- end;
-
-fun cterm_of_sqterm (c,p) = Product(Rational_lt c,Square(cterm_of_poly p));
+fun cterm_of_sqterm (c,p) = Product(Rational_lt c,Square p);
fun cterm_of_sos (pr,sqs) = if null sqs then pr
- else Product(pr,fold1 (fn a => fn b => Sum(a,b)) (map cterm_of_sqterm sqs));
+ else Product(pr,foldr1 (fn (a, b) => Sum(a,b)) (map cterm_of_sqterm sqs));
end
@@ -1275,14 +1219,14 @@
fun simple_cterm_ord t u = TermOrd.fast_term_ord (term_of t, term_of u) = LESS
in
(* FIXME: Replace tryfind by get_first !! *)
-fun real_nonlinear_prover prover ctxt =
+fun real_nonlinear_prover proof_method ctxt =
let
val {add,mul,neg,pow,sub,main} = Normalizer.semiring_normalizers_ord_wrapper ctxt
(valOf (NormalizerData.match ctxt @{cterm "(0::real) + 1"}))
simple_cterm_ord
val (real_poly_add_conv,real_poly_mul_conv,real_poly_neg_conv,
real_poly_pow_conv,real_poly_sub_conv,real_poly_conv) = (add,mul,neg,pow,sub,main)
- fun mainf translator (eqs,les,lts) =
+ fun mainf cert_choice translator (eqs,les,lts) =
let
val eq0 = map (poly_of_term o dest_arg1 o concl) eqs
val le0 = map (poly_of_term o dest_arg o concl) les
@@ -1303,33 +1247,49 @@
else raise Failure "trivial_axiom: Not a trivial axiom"
| _ => error "trivial_axiom: Not a trivial axiom"
in
- ((let val th = tryfind trivial_axiom (keq @ klep @ kltp)
- in fconv_rule (arg_conv (arg1_conv real_poly_conv) then_conv field_comp_conv) th end)
- handle Failure _ => (
- let
- val pol = fold_rev poly_mul (map fst ltp) (poly_const Rat.one)
- val leq = lep @ ltp
- fun tryall d =
- let val e = multidegree pol
- val k = if e = 0 then 0 else d div e
- val eq' = map fst eq
- in tryfind (fn i => (d,i,real_positivnullstellensatz_general prover false d eq' leq
- (poly_neg(poly_pow pol i))))
- (0 upto k)
- end
- val (d,i,(cert_ideal,cert_cone)) = deepen tryall 0
- val proofs_ideal =
- map2 (fn q => fn (p,ax) => Eqmul(cterm_of_poly q,ax)) cert_ideal eq
- val proofs_cone = map cterm_of_sos cert_cone
- val proof_ne = if null ltp then Rational_lt Rat.one else
- let val p = fold1 (fn s => fn t => Product(s,t)) (map snd ltp)
- in funpow i (fn q => Product(p,q)) (Rational_lt Rat.one)
- end
- val proof = fold1 (fn s => fn t => Sum(s,t))
- (proof_ne :: proofs_ideal @ proofs_cone)
- in writeln "Translating proof certificate to HOL";
- translator (eqs,les,lts) proof
- end))
+ (let val th = tryfind trivial_axiom (keq @ klep @ kltp)
+ in
+ (fconv_rule (arg_conv (arg1_conv real_poly_conv) then_conv field_comp_conv) th, Trivial)
+ end)
+ handle Failure _ =>
+ (let val proof =
+ (case proof_method of Certificate certs =>
+ (* choose certificate *)
+ let
+ fun chose_cert [] (Cert c) = c
+ | chose_cert (Left::s) (Branch (l, _)) = chose_cert s l
+ | chose_cert (Right::s) (Branch (_, r)) = chose_cert s r
+ | chose_cert _ _ = error "certificate tree in invalid form"
+ in
+ chose_cert cert_choice certs
+ end
+ | Prover prover =>
+ (* call prover *)
+ let
+ val pol = fold_rev poly_mul (map fst ltp) (poly_const Rat.one)
+ val leq = lep @ ltp
+ fun tryall d =
+ let val e = multidegree pol
+ val k = if e = 0 then 0 else d div e
+ val eq' = map fst eq
+ in tryfind (fn i => (d,i,real_positivnullstellensatz_general prover false d eq' leq
+ (poly_neg(poly_pow pol i))))
+ (0 upto k)
+ end
+ val (d,i,(cert_ideal,cert_cone)) = deepen tryall 0
+ val proofs_ideal =
+ map2 (fn q => fn (p,ax) => Eqmul(q,ax)) cert_ideal eq
+ val proofs_cone = map cterm_of_sos cert_cone
+ val proof_ne = if null ltp then Rational_lt Rat.one else
+ let val p = foldr1 (fn (s, t) => Product(s,t)) (map snd ltp)
+ in funpow i (fn q => Product(p,q)) (Rational_lt Rat.one)
+ end
+ in
+ foldr1 (fn (s, t) => Sum(s,t)) (proof_ne :: proofs_ideal @ proofs_cone)
+ end)
+ in
+ (translator (eqs,les,lts) proof, Cert proof)
+ end)
end
in mainf end
end
@@ -1396,7 +1356,7 @@
orelse g aconvc @{cterm "op < :: real => _"}
then arg_conv cv ct else arg1_conv cv ct
end
- fun mainf translator =
+ fun mainf cert_choice translator =
let
fun substfirst(eqs,les,lts) =
((let
@@ -1407,7 +1367,7 @@
aconvc @{cterm "0::real"}) (map modify eqs),
map modify les,map modify lts)
end)
- handle Failure _ => real_nonlinear_prover prover ctxt translator (rev eqs, rev les, rev lts))
+ handle Failure _ => real_nonlinear_prover prover ctxt cert_choice translator (rev eqs, rev les, rev lts))
in substfirst
end
@@ -1417,7 +1377,8 @@
(* Overall function. *)
-fun real_sos prover ctxt t = gen_prover_real_arith ctxt (real_nonlinear_subst_prover prover ctxt) t;
+fun real_sos prover ctxt =
+ gen_prover_real_arith ctxt (real_nonlinear_subst_prover prover ctxt)
end;
(* A tactic *)
@@ -1429,8 +1390,6 @@
end
| _ => ([],ct)
-fun core_sos_conv prover ctxt t = Drule.arg_cong_rule @{cterm Trueprop} (real_sos prover ctxt (Thm.dest_arg t) RS @{thm Eq_TrueI})
-
val known_sos_constants =
[@{term "op ==>"}, @{term "Trueprop"},
@{term "op -->"}, @{term "op &"}, @{term "op |"},
@@ -1458,17 +1417,19 @@
val _ = if exists (fn ((_,T)) => not (T = @{typ "real"})) fs
then error "SOS: not sos. Variables with type not real" else ()
val vs = Term.add_vars t []
- val _ = if exists (fn ((_,T)) => not (T = @{typ "real"})) fs
+ val _ = if exists (fn ((_,T)) => not (T = @{typ "real"})) vs
then error "SOS: not sos. Variables with type not real" else ()
val ukcs = subtract (fn (t,p) => Const p aconv t) kcts (Term.add_consts t [])
val _ = if null ukcs then ()
else error ("SOSO: Unknown constants in Subgoal:" ^ commas (map fst ukcs))
in () end
-fun core_sos_tac prover ctxt = CSUBGOAL (fn (ct, i) =>
+fun core_sos_tac print_cert prover ctxt = CSUBGOAL (fn (ct, i) =>
let val _ = check_sos known_sos_constants ct
val (avs, p) = strip_all ct
- val th = standard (fold_rev forall_intr avs (real_sos prover ctxt (Thm.dest_arg p)))
+ val (ths, certificates) = real_sos prover ctxt (Thm.dest_arg p)
+ val th = standard (fold_rev forall_intr avs ths)
+ val _ = print_cert certificates
in rtac th i end);
fun default_SOME f NONE v = SOME v
@@ -1506,7 +1467,7 @@
fun elim_denom_tac ctxt i = REPEAT (elim_one_denom_tac ctxt i);
-fun sos_tac prover ctxt = ObjectLogic.full_atomize_tac THEN' elim_denom_tac ctxt THEN' core_sos_tac prover ctxt
+fun sos_tac print_cert prover ctxt = ObjectLogic.full_atomize_tac THEN' elim_denom_tac ctxt THEN' core_sos_tac print_cert prover ctxt
end;
--- a/src/HOL/Library/normarith.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/normarith.ML Thu Sep 24 17:26:05 2009 +0200
@@ -15,7 +15,7 @@
structure NormArith : NORM_ARITH =
struct
- open Conv Thm;
+ open Conv Thm FuncUtil;
val bool_eq = op = : bool *bool -> bool
fun dest_ratconst t = case term_of t of
Const(@{const_name divide}, _)$a$b => Rat.rat_of_quotient(HOLogic.dest_number a |> snd, HOLogic.dest_number b |> snd)
@@ -330,13 +330,13 @@
val zerodests = filter
(fn t => null (Ctermfunc.dom (vector_lincomb t))) (map snd rawdests)
- in RealArith.real_linear_prover translator
+ in fst (RealArith.real_linear_prover translator
(map (fn t => instantiate ([(tv_n, ctyp_of_term t)],[]) pth_zero)
zerodests,
map (fconv_rule (try_conv (More_Conv.top_sweep_conv (K norm_canon_conv) ctxt) then_conv
arg_conv (arg_conv real_poly_conv))) ges',
map (fconv_rule (try_conv (More_Conv.top_sweep_conv (K norm_canon_conv) ctxt) then_conv
- arg_conv (arg_conv real_poly_conv))) gts)
+ arg_conv (arg_conv real_poly_conv))) gts))
end
in val real_vector_combo_prover = real_vector_combo_prover
end;
@@ -389,9 +389,9 @@
val (th1,th2) = conj_pair(rawrule th)
in th1::fconv_rule (arg_conv (arg_conv real_poly_neg_conv)) th2::acc
end
-in fun real_vector_prover ctxt translator (eqs,ges,gts) =
- real_vector_ineq_prover ctxt translator
- (fold_rev (splitequation ctxt) eqs ges,gts)
+in fun real_vector_prover ctxt _ translator (eqs,ges,gts) =
+ (real_vector_ineq_prover ctxt translator
+ (fold_rev (splitequation ctxt) eqs ges,gts), RealArith.Trivial)
end;
fun init_conv ctxt =
@@ -400,7 +400,7 @@
then_conv field_comp_conv
then_conv nnf_conv
- fun pure ctxt = RealArith.gen_prover_real_arith ctxt (real_vector_prover ctxt);
+ fun pure ctxt = fst o RealArith.gen_prover_real_arith ctxt (real_vector_prover ctxt);
fun norm_arith ctxt ct =
let
val ctxt' = Variable.declare_term (term_of ct) ctxt
--- a/src/HOL/Library/positivstellensatz.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Library/positivstellensatz.ML Thu Sep 24 17:26:05 2009 +0200
@@ -1,10 +1,11 @@
-(* Title: Library/positivstellensatz
+(* Title: Library/Sum_Of_Squares/positivstellensatz
Author: Amine Chaieb, University of Cambridge
Description: A generic arithmetic prover based on Positivstellensatz certificates ---
also implements Fourrier-Motzkin elimination as a special case Fourrier-Motzkin elimination.
*)
(* A functor for finite mappings based on Tables *)
+
signature FUNC =
sig
type 'a T
@@ -75,27 +76,54 @@
end
end;
+(* Some standard functors and utility functions for them *)
+
+structure FuncUtil =
+struct
+
+fun increasing f ord (x,y) = ord (f x, f y);
+
structure Intfunc = FuncFun(type key = int val ord = int_ord);
+structure Ratfunc = FuncFun(type key = Rat.rat val ord = Rat.ord);
+structure Intpairfunc = FuncFun(type key = int*int val ord = prod_ord int_ord int_ord);
structure Symfunc = FuncFun(type key = string val ord = fast_string_ord);
structure Termfunc = FuncFun(type key = term val ord = TermOrd.fast_term_ord);
-structure Ctermfunc = FuncFun(type key = cterm val ord = (fn (s,t) => TermOrd.fast_term_ord(term_of s, term_of t)));
+
+val cterm_ord = (fn (s,t) => TermOrd.fast_term_ord(term_of s, term_of t))
+
+structure Ctermfunc = FuncFun(type key = cterm val ord = cterm_ord);
+
+type monomial = int Ctermfunc.T;
-structure Ratfunc = FuncFun(type key = Rat.rat val ord = Rat.ord);
+fun monomial_ord (m1,m2) = list_ord (prod_ord cterm_ord int_ord) (Ctermfunc.graph m1, Ctermfunc.graph m2)
+
+structure Monomialfunc = FuncFun(type key = monomial val ord = monomial_ord)
+type poly = Rat.rat Monomialfunc.T;
+
+(* The ordering so we can create canonical HOL polynomials. *)
- (* Some useful derived rules *)
-fun deduct_antisym_rule tha thb =
- equal_intr (implies_intr (cprop_of thb) tha)
- (implies_intr (cprop_of tha) thb);
+fun dest_monomial mon = sort (increasing fst cterm_ord) (Ctermfunc.graph mon);
-fun prove_hyp tha thb =
- if exists (curry op aconv (concl_of tha)) (#hyps (rep_thm thb))
- then equal_elim (symmetric (deduct_antisym_rule tha thb)) tha else thb;
+fun monomial_order (m1,m2) =
+ if Ctermfunc.is_undefined m2 then LESS
+ else if Ctermfunc.is_undefined m1 then GREATER
+ else
+ let val mon1 = dest_monomial m1
+ val mon2 = dest_monomial m2
+ val deg1 = fold (curry op + o snd) mon1 0
+ val deg2 = fold (curry op + o snd) mon2 0
+ in if deg1 < deg2 then GREATER else if deg1 > deg2 then LESS
+ else list_ord (prod_ord cterm_ord int_ord) (mon1,mon2)
+ end;
+end
+(* positivstellensatz datatype and prover generation *)
signature REAL_ARITH =
sig
+
datatype positivstellensatz =
Axiom_eq of int
| Axiom_le of int
@@ -103,34 +131,41 @@
| Rational_eq of Rat.rat
| Rational_le of Rat.rat
| Rational_lt of Rat.rat
- | Square of cterm
- | Eqmul of cterm * positivstellensatz
+ | Square of FuncUtil.poly
+ | Eqmul of FuncUtil.poly * positivstellensatz
| Sum of positivstellensatz * positivstellensatz
| Product of positivstellensatz * positivstellensatz;
+datatype pss_tree = Trivial | Cert of positivstellensatz | Branch of pss_tree * pss_tree
+
+datatype tree_choice = Left | Right
+
+type prover = tree_choice list ->
+ (thm list * thm list * thm list -> positivstellensatz -> thm) ->
+ thm list * thm list * thm list -> thm * pss_tree
+type cert_conv = cterm -> thm * pss_tree
+
val gen_gen_real_arith :
- Proof.context -> (Rat.rat -> Thm.cterm) * conv * conv * conv *
- conv * conv * conv * conv * conv * conv *
- ( (thm list * thm list * thm list -> positivstellensatz -> thm) ->
- thm list * thm list * thm list -> thm) -> conv
-val real_linear_prover :
- (thm list * thm list * thm list -> positivstellensatz -> thm) ->
- thm list * thm list * thm list -> thm
+ Proof.context -> (Rat.rat -> cterm) * conv * conv * conv *
+ conv * conv * conv * conv * conv * conv * prover -> cert_conv
+val real_linear_prover : (thm list * thm list * thm list -> positivstellensatz -> thm) ->
+ thm list * thm list * thm list -> thm * pss_tree
val gen_real_arith : Proof.context ->
- (Rat.rat -> cterm) * conv * conv * conv * conv * conv * conv * conv *
- ( (thm list * thm list * thm list -> positivstellensatz -> thm) ->
- thm list * thm list * thm list -> thm) -> conv
-val gen_prover_real_arith : Proof.context ->
- ((thm list * thm list * thm list -> positivstellensatz -> thm) ->
- thm list * thm list * thm list -> thm) -> conv
-val real_arith : Proof.context -> conv
+ (Rat.rat -> cterm) * conv * conv * conv * conv * conv * conv * conv * prover -> cert_conv
+
+val gen_prover_real_arith : Proof.context -> prover -> cert_conv
+
+val is_ratconst : cterm -> bool
+val dest_ratconst : cterm -> Rat.rat
+val cterm_of_rat : Rat.rat -> cterm
+
end
-structure RealArith (* : REAL_ARITH *)=
+structure RealArith : REAL_ARITH =
struct
- open Conv Thm;;
+ open Conv Thm FuncUtil;;
(* ------------------------------------------------------------------------- *)
(* Data structure for Positivstellensatz refutations. *)
(* ------------------------------------------------------------------------- *)
@@ -142,12 +177,18 @@
| Rational_eq of Rat.rat
| Rational_le of Rat.rat
| Rational_lt of Rat.rat
- | Square of cterm
- | Eqmul of cterm * positivstellensatz
+ | Square of FuncUtil.poly
+ | Eqmul of FuncUtil.poly * positivstellensatz
| Sum of positivstellensatz * positivstellensatz
| Product of positivstellensatz * positivstellensatz;
(* Theorems used in the procedure *)
+datatype pss_tree = Trivial | Cert of positivstellensatz | Branch of pss_tree * pss_tree
+datatype tree_choice = Left | Right
+type prover = tree_choice list ->
+ (thm list * thm list * thm list -> positivstellensatz -> thm) ->
+ thm list * thm list * thm list -> thm * pss_tree
+type cert_conv = cterm -> thm * pss_tree
val my_eqs = ref ([] : thm list);
val my_les = ref ([] : thm list);
@@ -164,6 +205,16 @@
val my_poly_add_conv = ref no_conv;
val my_poly_mul_conv = ref no_conv;
+
+ (* Some useful derived rules *)
+fun deduct_antisym_rule tha thb =
+ equal_intr (implies_intr (cprop_of thb) tha)
+ (implies_intr (cprop_of tha) thb);
+
+fun prove_hyp tha thb =
+ if exists (curry op aconv (concl_of tha)) (#hyps (rep_thm thb))
+ then equal_elim (symmetric (deduct_antisym_rule tha thb)) tha else thb;
+
fun conjunctions th = case try Conjunction.elim th of
SOME (th1,th2) => (conjunctions th1) @ conjunctions th2
| NONE => [th];
@@ -292,7 +343,6 @@
| Abs (_,_,t') => find_cterm p (Thm.dest_abs NONE t |> snd)
| _ => raise CTERM ("find_cterm",[t]);
-
(* Some conversions-related stuff which has been forbidden entrance into Pure/conv.ML*)
fun instantiate_cterm' ty tms = Drule.cterm_rule (Drule.instantiate' ty tms)
fun is_comb t = case (term_of t) of _$_ => true | _ => false;
@@ -300,6 +350,39 @@
fun is_binop ct ct' = ct aconvc (Thm.dest_fun (Thm.dest_fun ct'))
handle CTERM _ => false;
+
+(* Map back polynomials to HOL. *)
+
+local
+ open Thm Numeral
+in
+
+fun cterm_of_varpow x k = if k = 1 then x else capply (capply @{cterm "op ^ :: real => _"} x)
+ (mk_cnumber @{ctyp nat} k)
+
+fun cterm_of_monomial m =
+ if Ctermfunc.is_undefined m then @{cterm "1::real"}
+ else
+ let
+ val m' = dest_monomial m
+ val vps = fold_rev (fn (x,k) => cons (cterm_of_varpow x k)) m' []
+ in foldr1 (fn (s, t) => capply (capply @{cterm "op * :: real => _"} s) t) vps
+ end
+
+fun cterm_of_cmonomial (m,c) = if Ctermfunc.is_undefined m then cterm_of_rat c
+ else if c = Rat.one then cterm_of_monomial m
+ else capply (capply @{cterm "op *::real => _"} (cterm_of_rat c)) (cterm_of_monomial m);
+
+fun cterm_of_poly p =
+ if Monomialfunc.is_undefined p then @{cterm "0::real"}
+ else
+ let
+ val cms = map cterm_of_cmonomial
+ (sort (prod_ord monomial_order (K EQUAL)) (Monomialfunc.graph p))
+ in foldr1 (fn (t1, t2) => capply(capply @{cterm "op + :: real => _"} t1) t2) cms
+ end;
+
+end;
(* A general real arithmetic prover *)
fun gen_gen_real_arith ctxt (mk_numeric,
@@ -368,8 +451,8 @@
| Rational_lt x => eqT_elim(numeric_gt_conv(capply @{cterm Trueprop}
(capply (capply @{cterm "op <::real => _"} @{cterm "0::real"})
(mk_numeric x))))
- | Square t => square_rule t
- | Eqmul(t,p) => emul_rule t (translate p)
+ | Square pt => square_rule (cterm_of_poly pt)
+ | Eqmul(pt,p) => emul_rule (cterm_of_poly pt) (translate p)
| Sum(p1,p2) => add_rule (translate p1) (translate p2)
| Product(p1,p2) => mul_rule (translate p1) (translate p2)
in fconv_rule (first_conv [numeric_ge_conv, numeric_gt_conv, numeric_eq_conv, all_conv])
@@ -394,13 +477,13 @@
val _ = if c aconvc (concl th2) then () else error "disj_cases : conclusions not alpha convertible"
in implies_elim (implies_elim (implies_elim (instantiate' [] (map SOME [p,q,c]) @{thm disjE}) th) (implies_intr (capply @{cterm Trueprop} p) th1)) (implies_intr (capply @{cterm Trueprop} q) th2)
end
- fun overall dun ths = case ths of
+ fun overall cert_choice dun ths = case ths of
[] =>
let
val (eq,ne) = List.partition (is_req o concl) dun
val (le,nl) = List.partition (is_ge o concl) ne
val lt = filter (is_gt o concl) nl
- in prover hol_of_positivstellensatz (eq,le,lt) end
+ in prover (rev cert_choice) hol_of_positivstellensatz (eq,le,lt) end
| th::oths =>
let
val ct = concl th
@@ -408,13 +491,13 @@
if is_conj ct then
let
val (th1,th2) = conj_pair th in
- overall dun (th1::th2::oths) end
+ overall cert_choice dun (th1::th2::oths) end
else if is_disj ct then
let
- val th1 = overall dun (assume (capply @{cterm Trueprop} (dest_arg1 ct))::oths)
- val th2 = overall dun (assume (capply @{cterm Trueprop} (dest_arg ct))::oths)
- in disj_cases th th1 th2 end
- else overall (th::dun) oths
+ val (th1, cert1) = overall (Left::cert_choice) dun (assume (capply @{cterm Trueprop} (dest_arg1 ct))::oths)
+ val (th2, cert2) = overall (Right::cert_choice) dun (assume (capply @{cterm Trueprop} (dest_arg ct))::oths)
+ in (disj_cases th th1 th2, Branch (cert1, cert2)) end
+ else overall cert_choice (th::dun) oths
end
fun dest_binary b ct = if is_binop b ct then dest_binop ct
else raise CTERM ("dest_binary",[b,ct])
@@ -496,16 +579,16 @@
val nct = capply @{cterm Trueprop} (capply @{cterm "Not"} ct)
val th0 = (init_conv then_conv arg_conv nnf_norm_conv') nct
val tm0 = dest_arg (rhs_of th0)
- val th = if tm0 aconvc @{cterm False} then equal_implies_1_rule th0 else
+ val (th, certificates) = if tm0 aconvc @{cterm False} then (equal_implies_1_rule th0, Trivial) else
let
val (evs,bod) = strip_exists tm0
val (avs,ibod) = strip_forall bod
val th1 = Drule.arg_cong_rule @{cterm Trueprop} (fold mk_forall avs (absremover ibod))
- val th2 = overall [] [specl avs (assume (rhs_of th1))]
+ val (th2, certs) = overall [] [] [specl avs (assume (rhs_of th1))]
val th3 = fold simple_choose evs (prove_hyp (equal_elim th1 (assume (capply @{cterm Trueprop} bod))) th2)
- in Drule.implies_intr_hyps (prove_hyp (equal_elim th0 (assume nct)) th3)
+ in (Drule.implies_intr_hyps (prove_hyp (equal_elim th0 (assume nct)) th3), certs)
end
- in implies_elim (instantiate' [] [SOME ct] pth_final) th
+ in (implies_elim (instantiate' [] [SOME ct] pth_final) th, certificates)
end
in f
end;
@@ -580,7 +663,7 @@
val k = (Rat.neg d) */ Rat.abs c // c
val e' = linear_cmul k e
val t' = linear_cmul (Rat.abs c) t
- val p' = Eqmul(cterm_of_rat k,p)
+ val p' = Eqmul(Monomialfunc.onefunc (Ctermfunc.undefined, k),p)
val q' = Product(Rational_lt(Rat.abs c),q)
in (linear_add e' t',Sum(p',q'))
end
@@ -632,7 +715,7 @@
val le_pols' = le_pols @ map (fn v => Ctermfunc.onefunc (v,Rat.one)) aliens
val (_,proof) = linear_prover (eq_pols,le_pols',lt_pols)
val le' = le @ map (fn a => instantiate' [] [SOME (dest_arg a)] @{thm real_of_nat_ge_zero}) aliens
- in (translator (eq,le',lt) proof) : thm
+ in ((translator (eq,le',lt) proof), Trivial)
end
end;
@@ -698,5 +781,4 @@
main,neg,add,mul, prover)
end;
-fun real_arith ctxt = gen_prover_real_arith ctxt real_linear_prover;
end
--- a/src/HOL/Lim.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Lim.thy Thu Sep 24 17:26:05 2009 +0200
@@ -84,6 +84,8 @@
lemma LIM_const [simp]: "(%x. k) -- x --> k"
by (simp add: LIM_def)
+lemma LIM_cong_limit: "\<lbrakk> f -- x --> L ; K = L \<rbrakk> \<Longrightarrow> f -- x --> K" by simp
+
lemma LIM_add:
fixes f g :: "'a::metric_space \<Rightarrow> 'b::real_normed_vector"
assumes f: "f -- a --> L" and g: "g -- a --> M"
@@ -544,7 +546,7 @@
case True thus ?thesis using `0 < s` by auto
next
case False hence "s / 2 \<ge> (x - b) / 2" by auto
- hence "?x = (x + b) / 2" by(simp add:field_simps)
+ hence "?x = (x + b) / 2" by (simp add: field_simps min_max.inf_absorb2)
thus ?thesis using `b < x` by auto
qed
hence "0 \<le> f ?x" using all_le `?x < x` by auto
--- a/src/HOL/MicroJava/BV/Effect.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/MicroJava/BV/Effect.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1,5 +1,4 @@
(* Title: HOL/MicroJava/BV/Effect.thy
- ID: $Id$
Author: Gerwin Klein
Copyright 2000 Technische Universitaet Muenchen
*)
@@ -391,7 +390,7 @@
with Pair
have "?app s \<Longrightarrow> ?P s" by (simp only:)
moreover
- have "?P s \<Longrightarrow> ?app s" by (unfold app_def) (clarsimp)
+ have "?P s \<Longrightarrow> ?app s" by (clarsimp simp add: min_max.inf_absorb2)
ultimately
show ?thesis by (rule iffI)
qed
--- a/src/HOL/MicroJava/BV/LBVSpec.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/MicroJava/BV/LBVSpec.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1,5 +1,4 @@
(* Title: HOL/MicroJava/BV/LBVSpec.thy
- ID: $Id$
Author: Gerwin Klein
Copyright 1999 Technische Universitaet Muenchen
*)
@@ -293,7 +292,7 @@
shows "wtl (take (pc+1) is) c 0 s = wtc c pc (wtl (take pc is) c 0 s)"
proof -
from suc have "take (pc+1) is=(take pc is)@[is!pc]" by (simp add: take_Suc)
- with suc wtl show ?thesis by (simp)
+ with suc wtl show ?thesis by (simp add: min_max.inf_absorb2)
qed
lemma (in lbv) wtl_all:
@@ -308,7 +307,7 @@
with all have take: "?wtl (take pc is@i#r) \<noteq> \<top>" by simp
from pc have "is!pc = drop pc is ! 0" by simp
with Cons have "is!pc = i" by simp
- with take pc show ?thesis by (auto)
+ with take pc show ?thesis by (auto simp add: min_max.inf_absorb2)
qed
section "preserves-type"
--- a/src/HOL/MicroJava/Comp/CorrCompTp.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/MicroJava/Comp/CorrCompTp.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1,5 +1,4 @@
(* Title: HOL/MicroJava/Comp/CorrCompTp.thy
- ID: $Id$
Author: Martin Strecker
*)
@@ -1058,7 +1057,7 @@
lemma bc_mt_corresp_New: "\<lbrakk>is_class cG cname \<rbrakk>
\<Longrightarrow> bc_mt_corresp [New cname] (pushST [Class cname]) (ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def pushST_def wt_instr_altern_def
- max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def)
+ max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def min_max.sup_absorb2)
apply (intro strip)
apply (rule conjI)
apply (rule check_type_mono, assumption, simp)
@@ -1069,7 +1068,7 @@
bc_mt_corresp [Pop] (popST (Suc 0)) (T # ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def popST_def wt_instr_altern_def eff_def norm_eff_def)
apply (simp add: max_ssize_def ssize_sto_def max_of_list_def)
- apply (simp add: check_type_simps)
+ apply (simp add: check_type_simps min_max.sup_absorb1)
apply clarify
apply (rule_tac x="(length ST)" in exI)
apply simp+
@@ -1092,7 +1091,7 @@
\<Longrightarrow> bc_mt_corresp [LitPush val] (pushST [T]) sttp cG rT mxr (Suc 0)"
apply (subgoal_tac "\<exists> ST LT. sttp= (ST, LT)", (erule exE)+)
apply (simp add: bc_mt_corresp_def pushST_def wt_instr_altern_def
- max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def)
+ max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def min_max.sup_absorb2)
apply (intro strip)
apply (rule conjI)
apply (rule check_type_mono, assumption, simp)
@@ -1111,7 +1110,7 @@
\<Longrightarrow> bc_mt_corresp [LitPush val] (pushST [T']) sttp cG rT mxr (Suc 0)"
apply (subgoal_tac "\<exists> ST LT. sttp= (ST, LT)", (erule exE)+)
apply (simp add: bc_mt_corresp_def pushST_def wt_instr_altern_def
- max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def)
+ max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def min_max.sup_absorb2)
apply (intro strip)
apply (rule conjI)
apply (rule check_type_mono, assumption, simp)
@@ -1127,7 +1126,7 @@
\<Longrightarrow> bc_mt_corresp [Load i]
(\<lambda>(ST, LT). pushST [ok_val (LT ! i)] (ST, LT)) (ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def pushST_def wt_instr_altern_def
- max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def)
+ max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def min_max.sup_absorb2)
apply (intro strip)
apply (rule conjI)
apply (rule check_type_mono, assumption, simp)
@@ -1148,10 +1147,10 @@
lemma bc_mt_corresp_Store_init: "\<lbrakk> i < length LT \<rbrakk>
\<Longrightarrow> bc_mt_corresp [Store i] (storeST i T) (T # ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def storeST_def wt_instr_altern_def eff_def norm_eff_def)
- apply (simp add: max_ssize_def max_of_list_def )
+ apply (simp add: max_ssize_def max_of_list_def)
apply (simp add: ssize_sto_def)
apply (intro strip)
-apply (simp add: check_type_simps)
+apply (simp add: check_type_simps min_max.sup_absorb1)
apply clarify
apply (rule conjI)
apply (rule_tac x="(length ST)" in exI)
@@ -1159,14 +1158,13 @@
done
-
lemma bc_mt_corresp_Store: "\<lbrakk> i < length LT; cG \<turnstile> LT[i := OK T] <=l LT \<rbrakk>
\<Longrightarrow> bc_mt_corresp [Store i] (popST (Suc 0)) (T # ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def popST_def wt_instr_altern_def eff_def norm_eff_def)
apply (simp add: sup_state_conv)
apply (simp add: max_ssize_def max_of_list_def ssize_sto_def)
apply (intro strip)
-apply (simp add: check_type_simps)
+apply (simp add: check_type_simps min_max.sup_absorb1)
apply clarify
apply (rule_tac x="(length ST)" in exI)
apply simp+
@@ -1176,7 +1174,7 @@
lemma bc_mt_corresp_Dup: "
bc_mt_corresp [Dup] dupST (T # ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def dupST_def wt_instr_altern_def
- max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def)
+ max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def min_max.sup_absorb2)
apply (intro strip)
apply (rule conjI)
apply (rule check_type_mono, assumption, simp)
@@ -1189,7 +1187,7 @@
lemma bc_mt_corresp_Dup_x1: "
bc_mt_corresp [Dup_x1] dup_x1ST (T1 # T2 # ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def dup_x1ST_def wt_instr_altern_def
- max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def)
+ max_ssize_def max_of_list_def ssize_sto_def eff_def norm_eff_def min_max.sup_absorb2)
apply (intro strip)
apply (rule conjI)
apply (rule check_type_mono, assumption, simp)
@@ -1206,7 +1204,7 @@
(PrimT Integer # PrimT Integer # ST, LT) cG rT mxr (Suc 0)"
apply (simp add: bc_mt_corresp_def replST_def wt_instr_altern_def eff_def norm_eff_def)
apply (simp add: max_ssize_def max_of_list_def ssize_sto_def)
- apply (simp add: check_type_simps)
+ apply (simp add: check_type_simps min_max.sup_absorb1)
apply clarify
apply (rule_tac x="Suc (length ST)" in exI)
apply simp+
@@ -1249,7 +1247,7 @@
apply (simp add: max_ssize_def max_of_list_def ssize_sto_def)
apply (intro strip)
-apply (simp add: check_type_simps)
+apply (simp add: check_type_simps min_max.sup_absorb1)
apply clarify
apply (rule_tac x="Suc (length ST)" in exI)
apply simp+
--- a/src/HOL/OrderedGroup.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/OrderedGroup.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1075,17 +1075,16 @@
lemma nprt_0[simp]: "nprt 0 = 0" by (simp add: nprt_def)
lemma pprt_eq_id [simp, noatp]: "0 \<le> x \<Longrightarrow> pprt x = x"
-by (simp add: pprt_def sup_aci)
-
+ by (simp add: pprt_def sup_aci sup_absorb1)
lemma nprt_eq_id [simp, noatp]: "x \<le> 0 \<Longrightarrow> nprt x = x"
-by (simp add: nprt_def inf_aci)
+ by (simp add: nprt_def inf_aci inf_absorb1)
lemma pprt_eq_0 [simp, noatp]: "x \<le> 0 \<Longrightarrow> pprt x = 0"
-by (simp add: pprt_def sup_aci)
+ by (simp add: pprt_def sup_aci sup_absorb2)
lemma nprt_eq_0 [simp, noatp]: "0 \<le> x \<Longrightarrow> nprt x = 0"
-by (simp add: nprt_def inf_aci)
+ by (simp add: nprt_def inf_aci inf_absorb2)
lemma sup_0_imp_0: "sup a (- a) = 0 \<Longrightarrow> a = 0"
proof -
@@ -1119,7 +1118,7 @@
"0 \<le> a + a \<longleftrightarrow> 0 \<le> a"
proof
assume "0 <= a + a"
- hence a:"inf (a+a) 0 = 0" by (simp add: inf_commute)
+ hence a:"inf (a+a) 0 = 0" by (simp add: inf_commute inf_absorb1)
have "(inf a 0)+(inf a 0) = inf (inf (a+a) 0) a" (is "?l=_")
by (simp add: add_sup_inf_distribs inf_aci)
hence "?l = 0 + inf a 0" by (simp add: a, simp add: inf_commute)
@@ -1135,7 +1134,7 @@
assume assm: "a + a = 0"
then have "a + a + - a = - a" by simp
then have "a + (a + - a) = - a" by (simp only: add_assoc)
- then have a: "- a = a" by simp (*FIXME tune proof*)
+ then have a: "- a = a" by simp
show "a = 0" apply (rule antisym)
apply (unfold neg_le_iff_le [symmetric, of a])
unfolding a apply simp
@@ -1275,7 +1274,7 @@
proof -
note add_le_cancel_right [of a a "- a", symmetric, simplified]
moreover note add_le_cancel_right [of "-a" a a, symmetric, simplified]
- then show ?thesis by (auto simp: sup_max)
+ then show ?thesis by (auto simp: sup_max min_max.sup_absorb1 min_max.sup_absorb2)
qed
lemma abs_if_lattice:
--- a/src/HOL/Predicate.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Predicate.thy Thu Sep 24 17:26:05 2009 +0200
@@ -797,6 +797,10 @@
(auto simp add: Seq_def the_only_singleton is_empty_def
null_is_empty singleton_bot singleton_single singleton_sup Let_def)
+lemma meta_fun_cong:
+"f == g ==> f x == g x"
+by simp
+
ML {*
signature PREDICATE =
sig
--- a/src/HOL/Quickcheck.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Quickcheck.thy Thu Sep 24 17:26:05 2009 +0200
@@ -3,7 +3,7 @@
header {* A simple counterexample generator *}
theory Quickcheck
-imports Random Code_Eval
+imports Random Code_Evaluation
uses ("Tools/quickcheck_generators.ML")
begin
@@ -24,7 +24,7 @@
definition
"random i = Random.range 2 o\<rightarrow>
- (\<lambda>k. Pair (if k = 0 then Code_Eval.valtermify False else Code_Eval.valtermify True))"
+ (\<lambda>k. Pair (if k = 0 then Code_Evaluation.valtermify False else Code_Evaluation.valtermify True))"
instance ..
@@ -34,7 +34,7 @@
begin
definition random_itself :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
- "random_itself _ = Pair (Code_Eval.valtermify TYPE('a))"
+ "random_itself _ = Pair (Code_Evaluation.valtermify TYPE('a))"
instance ..
@@ -44,7 +44,7 @@
begin
definition
- "random _ = Random.select chars o\<rightarrow> (\<lambda>c. Pair (c, \<lambda>u. Code_Eval.term_of c))"
+ "random _ = Random.select chars o\<rightarrow> (\<lambda>c. Pair (c, \<lambda>u. Code_Evaluation.term_of c))"
instance ..
@@ -54,7 +54,7 @@
begin
definition
- "random _ = Pair (STR '''', \<lambda>u. Code_Eval.term_of (STR ''''))"
+ "random _ = Pair (STR '''', \<lambda>u. Code_Evaluation.term_of (STR ''''))"
instance ..
@@ -63,10 +63,10 @@
instantiation nat :: random
begin
-definition random_nat :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Eval.term)) \<times> Random.seed" where
+definition random_nat :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Evaluation.term)) \<times> Random.seed" where
"random_nat i = Random.range (i + 1) o\<rightarrow> (\<lambda>k. Pair (
let n = Code_Numeral.nat_of k
- in (n, \<lambda>_. Code_Eval.term_of n)))"
+ in (n, \<lambda>_. Code_Evaluation.term_of n)))"
instance ..
@@ -78,7 +78,7 @@
definition
"random i = Random.range (2 * i + 1) o\<rightarrow> (\<lambda>k. Pair (
let j = (if k \<ge> i then Code_Numeral.int_of (k - i) else - Code_Numeral.int_of (i - k))
- in (j, \<lambda>_. Code_Eval.term_of j)))"
+ in (j, \<lambda>_. Code_Evaluation.term_of j)))"
instance ..
@@ -95,7 +95,7 @@
definition random_fun_lift :: "(Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed)
\<Rightarrow> Random.seed \<Rightarrow> (('a\<Colon>term_of \<Rightarrow> 'b\<Colon>typerep) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
- "random_fun_lift f = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of f Random.split_seed"
+ "random_fun_lift f = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Evaluation.term_of f Random.split_seed"
instantiation "fun" :: ("{eq, term_of}", random) random
begin
--- a/src/HOL/Rational.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Rational.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1002,8 +1002,8 @@
by simp
definition (in term_syntax)
- valterm_fract :: "int \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> int \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> rat \<times> (unit \<Rightarrow> Code_Eval.term)" where
- [code_unfold]: "valterm_fract k l = Code_Eval.valtermify Fract {\<cdot>} k {\<cdot>} l"
+ valterm_fract :: "int \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> int \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> rat \<times> (unit \<Rightarrow> Code_Evaluation.term)" where
+ [code_unfold]: "valterm_fract k l = Code_Evaluation.valtermify Fract {\<cdot>} k {\<cdot>} l"
notation fcomp (infixl "o>" 60)
notation scomp (infixl "o\<rightarrow>" 60)
@@ -1014,7 +1014,7 @@
definition
"Quickcheck.random i = Quickcheck.random i o\<rightarrow> (\<lambda>num. Random.range i o\<rightarrow> (\<lambda>denom. Pair (
let j = Code_Numeral.int_of (denom + 1)
- in valterm_fract num (j, \<lambda>u. Code_Eval.term_of j))))"
+ in valterm_fract num (j, \<lambda>u. Code_Evaluation.term_of j))))"
instance ..
--- a/src/HOL/RealDef.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/RealDef.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1128,8 +1128,8 @@
by (simp add: of_rat_divide)
definition (in term_syntax)
- valterm_ratreal :: "rat \<times> (unit \<Rightarrow> Code_Eval.term) \<Rightarrow> real \<times> (unit \<Rightarrow> Code_Eval.term)" where
- [code_unfold]: "valterm_ratreal k = Code_Eval.valtermify Ratreal {\<cdot>} k"
+ valterm_ratreal :: "rat \<times> (unit \<Rightarrow> Code_Evaluation.term) \<Rightarrow> real \<times> (unit \<Rightarrow> Code_Evaluation.term)" where
+ [code_unfold]: "valterm_ratreal k = Code_Evaluation.valtermify Ratreal {\<cdot>} k"
notation fcomp (infixl "o>" 60)
notation scomp (infixl "o\<rightarrow>" 60)
--- a/src/HOL/Tools/Datatype/datatype.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Tools/Datatype/datatype.ML Thu Sep 24 17:26:05 2009 +0200
@@ -26,7 +26,7 @@
val info_of_case : theory -> string -> info option
val interpretation : (config -> string list -> theory -> theory) -> theory -> theory
val distinct_simproc : simproc
- val make_case : Proof.context -> bool -> string list -> term ->
+ val make_case : Proof.context -> DatatypeCase.config -> string list -> term ->
(term * term) list -> term * (term * (int * bool)) list
val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option
val read_typ: theory ->
--- a/src/HOL/Tools/Datatype/datatype_case.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Tools/Datatype/datatype_case.ML Thu Sep 24 17:26:05 2009 +0200
@@ -7,8 +7,9 @@
signature DATATYPE_CASE =
sig
+ datatype config = Error | Warning | Quiet;
val make_case: (string -> DatatypeAux.info option) ->
- Proof.context -> bool -> string list -> term -> (term * term) list ->
+ Proof.context -> config -> string list -> term -> (term * term) list ->
term * (term * (int * bool)) list
val dest_case: (string -> DatatypeAux.info option) -> bool ->
string list -> term -> (term * (term * term) list) option
@@ -23,6 +24,8 @@
structure DatatypeCase : DATATYPE_CASE =
struct
+datatype config = Error | Warning | Quiet;
+
exception CASE_ERROR of string * int;
fun match_type thy pat ob = Sign.typ_match thy (pat, ob) Vartab.empty;
@@ -260,7 +263,7 @@
else x :: xs)
| _ => I) pat [];
-fun gen_make_case ty_match ty_inst type_of tab ctxt err used x clauses =
+fun gen_make_case ty_match ty_inst type_of tab ctxt config used x clauses =
let
fun string_of_clause (pat, rhs) = Syntax.string_of_term ctxt
(Syntax.const "_case1" $ pat $ rhs);
@@ -285,7 +288,7 @@
val originals = map (row_of_pat o #2) rows
val _ = case originals \\ finals of
[] => ()
- | is => (if err then case_error else warning)
+ | is => (case config of Error => case_error | Warning => warning | Quiet => fn _ => {})
("The following clauses are redundant (covered by preceding clauses):\n" ^
cat_lines (map (string_of_clause o nth clauses) is));
in
@@ -338,7 +341,8 @@
fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
| dest_case2 t = [t];
val (cases, cnstrts) = split_list (map dest_case1 (dest_case2 u));
- val (case_tm, _) = make_case_untyped (tab_of thy) ctxt err []
+ val (case_tm, _) = make_case_untyped (tab_of thy) ctxt
+ (if err then Error else Warning) []
(fold (fn tT => fn t => Syntax.const "_constrain" $ t $ tT)
(flat cnstrts) t) cases;
in case_tm end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/pred_compile_aux.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,100 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+Auxilary functions for predicate compiler
+*)
+
+structure Predicate_Compile_Aux =
+struct
+
+(* syntactic functions *)
+
+fun is_equationlike_term (Const ("==", _) $ _ $ _) = true
+ | is_equationlike_term (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ _)) = true
+ | is_equationlike_term _ = false
+
+val is_equationlike = is_equationlike_term o prop_of
+
+fun is_pred_equation_term (Const ("==", _) $ u $ v) =
+ (fastype_of u = @{typ bool}) andalso (fastype_of v = @{typ bool})
+ | is_pred_equation_term _ = false
+
+val is_pred_equation = is_pred_equation_term o prop_of
+
+fun is_intro_term constname t =
+ case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
+ Const (c, _) => c = constname
+ | _ => false
+
+fun is_intro constname t = is_intro_term constname (prop_of t)
+
+fun is_pred thy constname =
+ let
+ val T = (Sign.the_const_type thy constname)
+ in body_type T = @{typ "bool"} end;
+
+
+fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
+ | is_predT _ = false
+
+
+(*** check if a term contains only constructor functions ***)
+fun is_constrt thy =
+ let
+ val cnstrs = flat (maps
+ (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
+ (Symtab.dest (Datatype.get_all thy)));
+ fun check t = (case strip_comb t of
+ (Free _, []) => true
+ | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
+ (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
+ | _ => false)
+ | _ => false)
+ in check end;
+
+fun strip_ex (Const ("Ex", _) $ Abs (x, T, t)) =
+ let
+ val (xTs, t') = strip_ex t
+ in
+ ((x, T) :: xTs, t')
+ end
+ | strip_ex t = ([], t)
+
+fun focus_ex t nctxt =
+ let
+ val ((xs, Ts), t') = apfst split_list (strip_ex t)
+ val (xs', nctxt') = Name.variants xs nctxt;
+ val ps' = xs' ~~ Ts;
+ val vs = map Free ps';
+ val t'' = Term.subst_bounds (rev vs, t');
+ in ((ps', t''), nctxt') end;
+
+
+
+
+(*
+fun map_atoms f intro =
+fun fold_atoms f intro =
+*)
+fun fold_map_atoms f intro s =
+ let
+ val (literals, head) = Logic.strip_horn intro
+ fun appl t s = (case t of
+ (@{term "Not"} $ t') =>
+ let
+ val (t'', s') = f t' s
+ in (@{term "Not"} $ t'', s') end
+ | _ => f t s)
+ val (literals', s') = fold_map appl (map HOLogic.dest_Trueprop literals) s
+ in
+ (Logic.list_implies (map HOLogic.mk_Trueprop literals', head), s')
+ end;
+
+(*
+fun equals_conv lhs_cv rhs_cv ct =
+ case Thm.term_of ct of
+ Const ("==", _) $ _ $ _ => Conv.arg_conv cv ct
+ | _ => error "equals_conv"
+*)
+
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/pred_compile_data.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,223 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+Book-keeping datastructure for the predicate compiler
+
+*)
+signature PRED_COMPILE_DATA =
+sig
+ type specification_table;
+ val make_const_spec_table : theory -> specification_table
+ val get_specification : specification_table -> string -> thm list
+ val obtain_specification_graph : specification_table -> string -> thm list Graph.T
+ val normalize_equation : theory -> thm -> thm
+end;
+
+structure Pred_Compile_Data : PRED_COMPILE_DATA =
+struct
+
+open Predicate_Compile_Aux;
+
+structure Data = TheoryDataFun
+(
+ type T =
+ {const_spec_table : thm list Symtab.table};
+ val empty =
+ {const_spec_table = Symtab.empty};
+ val copy = I;
+ val extend = I;
+ fun merge _
+ ({const_spec_table = const_spec_table1},
+ {const_spec_table = const_spec_table2}) =
+ {const_spec_table = Symtab.merge (K true) (const_spec_table1, const_spec_table2)}
+);
+
+fun mk_data c = {const_spec_table = c}
+fun map_data f {const_spec_table = c} = mk_data (f c)
+
+type specification_table = thm list Symtab.table
+
+fun defining_const_of_introrule_term t =
+ let
+ val _ $ u = Logic.strip_imp_concl t
+ val (pred, all_args) = strip_comb u
+ in case pred of
+ Const (c, T) => c
+ | _ => raise TERM ("defining_const_of_introrule_term failed: Not a constant", [t])
+ end
+
+val defining_const_of_introrule = defining_const_of_introrule_term o prop_of
+
+(*TODO*)
+fun is_introlike_term t = true
+
+val is_introlike = is_introlike_term o prop_of
+
+fun check_equation_format_term (t as (Const ("==", _) $ u $ v)) =
+ (case strip_comb u of
+ (Const (c, T), args) =>
+ if (length (binder_types T) = length args) then
+ true
+ else
+ raise TERM ("check_equation_format_term failed: Number of arguments mismatch", [t])
+ | _ => raise TERM ("check_equation_format_term failed: Not a constant", [t]))
+ | check_equation_format_term t =
+ raise TERM ("check_equation_format_term failed: Not an equation", [t])
+
+val check_equation_format = check_equation_format_term o prop_of
+
+fun defining_const_of_equation_term (t as (Const ("==", _) $ u $ v)) =
+ (case fst (strip_comb u) of
+ Const (c, _) => c
+ | _ => raise TERM ("defining_const_of_equation_term failed: Not a constant", [t]))
+ | defining_const_of_equation_term t =
+ raise TERM ("defining_const_of_equation_term failed: Not an equation", [t])
+
+val defining_const_of_equation = defining_const_of_equation_term o prop_of
+
+(* Normalizing equations *)
+
+fun mk_meta_equation th =
+ case prop_of th of
+ Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ _) => th RS @{thm eq_reflection}
+ | _ => th
+
+fun full_fun_cong_expand th =
+ let
+ val (f, args) = strip_comb (fst (Logic.dest_equals (prop_of th)))
+ val i = length (binder_types (fastype_of f)) - length args
+ in funpow i (fn th => th RS @{thm meta_fun_cong}) th end;
+
+fun declare_names s xs ctxt =
+ let
+ val res = Name.names ctxt s xs
+ in (res, fold Name.declare (map fst res) ctxt) end
+
+fun split_all_pairs thy th =
+ let
+ val ctxt = ProofContext.init thy
+ val ((_, [th']), ctxt') = Variable.import true [th] ctxt
+ val t = prop_of th'
+ val frees = Term.add_frees t []
+ val freenames = Term.add_free_names t []
+ val nctxt = Name.make_context freenames
+ fun mk_tuple_rewrites (x, T) nctxt =
+ let
+ val Ts = HOLogic.flatten_tupleT T
+ val (xTs, nctxt') = declare_names x Ts nctxt
+ val paths = HOLogic.flat_tupleT_paths T
+ in ((Free (x, T), HOLogic.mk_ptuple paths T (map Free xTs)), nctxt') end
+ val (rewr, _) = fold_map mk_tuple_rewrites frees nctxt
+ val t' = Pattern.rewrite_term thy rewr [] t
+ val tac = setmp quick_and_dirty true (SkipProof.cheat_tac thy)
+ val th'' = Goal.prove ctxt (Term.add_free_names t' []) [] t' (fn {...} => tac)
+ val th''' = LocalDefs.unfold ctxt [@{thm split_conv}] th''
+ in
+ th'''
+ end;
+
+fun normalize_equation thy th =
+ mk_meta_equation th
+ |> Pred_Compile_Set.unfold_set_notation
+ |> full_fun_cong_expand
+ |> split_all_pairs thy
+ |> tap check_equation_format
+
+fun inline_equations thy th = Conv.fconv_rule (Simplifier.rewrite
+((Simplifier.theory_context thy Simplifier.empty_ss) addsimps (Predicate_Compile_Inline_Defs.get (ProofContext.init thy)))) th
+
+fun store_thm_in_table ignore_consts thy th=
+ let
+ val th = AxClass.unoverload thy th
+ |> inline_equations thy
+ val (const, th) =
+ if is_equationlike th then
+ let
+ val _ = priority "Normalizing definition..."
+ val eq = normalize_equation thy th
+ in
+ (defining_const_of_equation eq, eq)
+ end
+ else if (is_introlike th) then
+ let val th = Pred_Compile_Set.unfold_set_notation th
+ in (defining_const_of_introrule th, th) end
+ else error "store_thm: unexpected definition format"
+ in
+ if not (member (op =) ignore_consts const) then
+ Symtab.cons_list (const, th)
+ else I
+ end
+
+(*
+fun make_const_spec_table_warning thy =
+ fold
+ (fn th => fn thy => case try (store_thm th) thy of
+ SOME thy => thy
+ | NONE => (warning ("store_thm fails for " ^ Display.string_of_thm_global thy th) ; thy))
+ (Predicate_Compile_Preproc_Const_Defs.get (ProofContext.init thy)) thy
+
+fun make_const_spec_table thy =
+ fold store_thm (Predicate_Compile_Preproc_Const_Defs.get (ProofContext.init thy)) thy
+ |> (fn thy => fold store_thm (Nitpick_Const_Simps.get (ProofContext.init thy)) thy)
+*)
+fun make_const_spec_table thy =
+ let
+ fun store ignore_const f = fold (store_thm_in_table ignore_const thy) (map (Thm.transfer thy) (f (ProofContext.init thy)))
+ val table = Symtab.empty
+ |> store [] Predicate_Compile_Alternative_Defs.get
+ val ignore_consts = Symtab.keys table
+ in
+ table
+ |> store ignore_consts Predicate_Compile_Preproc_Const_Defs.get
+ |> store ignore_consts Nitpick_Const_Simps.get
+ |> store ignore_consts Nitpick_Ind_Intros.get
+ end
+ (*
+fun get_specification thy constname =
+ case Symtab.lookup (#const_spec_table (Data.get thy)) constname of
+ SOME thms => thms
+ | NONE => error ("get_specification: lookup of constant " ^ quote constname ^ " failed")
+ *)
+fun get_specification table constname =
+ case Symtab.lookup table constname of
+ SOME thms =>
+ let
+ val _ = tracing ("Looking up specification of " ^ constname ^ ": "
+ ^ (commas (map Display.string_of_thm_without_context thms)))
+ in thms end
+ | NONE => error ("get_specification: lookup of constant " ^ quote constname ^ " failed")
+
+val logic_operator_names =
+ [@{const_name "=="}, @{const_name "op ="}, @{const_name "op -->"}, @{const_name "All"}, @{const_name "op &"}]
+
+val special_cases = member (op =) [@{const_name "Suc"}, @{const_name Nat.zero_nat_inst.zero_nat},
+ @{const_name Nat.one_nat_inst.one_nat},
+@{const_name "HOL.ord_class.less"}, @{const_name "HOL.ord_class.less_eq"}, @{const_name "HOL.zero_class.zero"},
+@{const_name "HOL.one_class.one"}, @{const_name HOL.plus_class.plus},
+@{const_name "Nat.nat.nat_case"}, @{const_name "List.list.list_case"},
+@{const_name "Option.option.option_case"},
+@{const_name Nat.ord_nat_inst.less_eq_nat},
+@{const_name number_nat_inst.number_of_nat},
+ @{const_name Int.Bit0},
+ @{const_name Int.Bit1},
+ @{const_name Int.Pls},
+@{const_name "Int.zero_int_inst.zero_int"},
+@{const_name "List.filter"}]
+
+fun obtain_specification_graph table constname =
+ let
+ fun is_nondefining_constname c = member (op =) logic_operator_names c
+ val is_defining_constname = member (op =) (Symtab.keys table)
+ fun defiants_of specs =
+ fold (Term.add_const_names o prop_of) specs []
+ |> filter is_defining_constname
+ |> filter_out special_cases
+ fun extend constname =
+ let
+ val specs = get_specification table constname
+ in (specs, defiants_of specs) end;
+ in
+ Graph.extend extend constname Graph.empty
+ end;
+
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/pred_compile_fun.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,424 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+Preprocessing functions to predicates
+*)
+
+signature PREDICATE_COMPILE_FUN =
+sig
+ val define_predicates : (string * thm list) list -> theory -> theory
+ val rewrite_intro : theory -> thm -> thm list
+ val setup_oracle : theory -> theory
+end;
+
+structure Predicate_Compile_Fun : PREDICATE_COMPILE_FUN =
+struct
+
+
+(* Oracle for preprocessing *)
+
+val (oracle : (string * (cterm -> thm)) option ref) = ref NONE;
+
+fun the_oracle () =
+ case !oracle of
+ NONE => error "Oracle is not setup"
+ | SOME (_, oracle) => oracle
+
+val setup_oracle = Thm.add_oracle (Binding.name "pred_compile_preprocessing", I) #->
+ (fn ora => fn thy => let val _ = (oracle := SOME ora) in thy end)
+
+
+fun is_funtype (Type ("fun", [_, _])) = true
+ | is_funtype _ = false;
+
+fun is_Type (Type _) = true
+ | is_Type _ = false
+
+(* returns true if t is an application of an datatype constructor *)
+(* which then consequently would be splitted *)
+(* else false *)
+(*
+fun is_constructor thy t =
+ if (is_Type (fastype_of t)) then
+ (case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
+ NONE => false
+ | SOME info => (let
+ val constr_consts = flat (map (fn (_, (_, _, constrs)) => map fst constrs) (#descr info))
+ val (c, _) = strip_comb t
+ in (case c of
+ Const (name, _) => name mem_string constr_consts
+ | _ => false) end))
+ else false
+*)
+
+(* must be exported in code.ML *)
+fun is_constr thy = is_some o Code.get_datatype_of_constr thy;
+
+(* Table from constant name (string) to term of inductive predicate *)
+structure Pred_Compile_Preproc = TheoryDataFun
+(
+ type T = string Symtab.table;
+ val empty = Symtab.empty;
+ val copy = I;
+ val extend = I;
+ fun merge _ = Symtab.merge (op =);
+)
+
+fun defined thy = Symtab.defined (Pred_Compile_Preproc.get thy)
+
+
+fun transform_ho_typ (T as Type ("fun", _)) =
+ let
+ val (Ts, T') = strip_type T
+ in if T' = @{typ "bool"} then T else (Ts @ [T']) ---> HOLogic.boolT end
+| transform_ho_typ t = t
+
+fun transform_ho_arg arg =
+ case (fastype_of arg) of
+ (T as Type ("fun", _)) =>
+ (case arg of
+ Free (name, _) => Free (name, transform_ho_typ T)
+ | _ => error "I am surprised")
+| _ => arg
+
+fun pred_type T =
+ let
+ val (Ts, T') = strip_type T
+ val Ts' = map transform_ho_typ Ts
+ in
+ (Ts' @ [T']) ---> HOLogic.boolT
+ end;
+
+(* FIXME: create new predicate name -- does not avoid nameclashing *)
+fun pred_of f =
+ let
+ val (name, T) = dest_Const f
+ in
+ if (body_type T = @{typ bool}) then
+ (Free (Long_Name.base_name name ^ "P", T))
+ else
+ (Free (Long_Name.base_name name ^ "P", pred_type T))
+ end
+
+fun mk_param lookup_pred (t as Free (v, _)) = lookup_pred t
+ | mk_param lookup_pred t =
+ let
+ val (vs, body) = strip_abs t
+ val names = Term.add_free_names body []
+ val vs_names = Name.variant_list names (map fst vs)
+ val vs' = map2 (curry Free) vs_names (map snd vs)
+ val body' = subst_bounds (rev vs', body)
+ val (f, args) = strip_comb body'
+ val resname = Name.variant (vs_names @ names) "res"
+ val resvar = Free (resname, body_type (fastype_of body'))
+ val P = lookup_pred f
+ val pred_body = list_comb (P, args @ [resvar])
+ val param = fold_rev lambda (vs' @ [resvar]) pred_body
+ in param end;
+
+
+(* creates the list of premises for every intro rule *)
+(* theory -> term -> (string list, term list list) *)
+
+fun dest_code_eqn eqn = let
+ val (lhs, rhs) = Logic.dest_equals (Logic.unvarify (Thm.prop_of eqn))
+ val (func, args) = strip_comb lhs
+in ((func, args), rhs) end;
+
+fun string_of_typ T = Syntax.string_of_typ_global @{theory} T
+
+fun string_of_term t =
+ case t of
+ Const (c, T) => "Const (" ^ c ^ ", " ^ string_of_typ T ^ ")"
+ | Free (c, T) => "Free (" ^ c ^ ", " ^ string_of_typ T ^ ")"
+ | Var ((c, i), T) => "Var ((" ^ c ^ ", " ^ string_of_int i ^ "), " ^ string_of_typ T ^ ")"
+ | Bound i => "Bound " ^ string_of_int i
+ | Abs (x, T, t) => "Abs (" ^ x ^ ", " ^ string_of_typ T ^ ", " ^ string_of_term t ^ ")"
+ | t1 $ t2 => "(" ^ string_of_term t1 ^ ") $ (" ^ string_of_term t2 ^ ")"
+
+fun ind_package_get_nparams thy name =
+ case try (Inductive.the_inductive (ProofContext.init thy)) name of
+ SOME (_, result) => length (Inductive.params_of (#raw_induct result))
+ | NONE => error ("No such predicate: " ^ quote name)
+
+(* TODO: does not work with higher order functions yet *)
+fun mk_rewr_eq (func, pred) =
+ let
+ val (argTs, resT) = (strip_type (fastype_of func))
+ val nctxt =
+ Name.make_context (Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) (func $ pred) [])
+ val (argnames, nctxt') = Name.variants (replicate (length argTs) "a") nctxt
+ val ([resname], nctxt'') = Name.variants ["r"] nctxt'
+ val args = map Free (argnames ~~ argTs)
+ val res = Free (resname, resT)
+ in Logic.mk_equals
+ (HOLogic.mk_eq (res, list_comb (func, args)), list_comb (pred, args @ [res]))
+ end;
+
+fun has_split_rule_cname @{const_name "nat_case"} = true
+ | has_split_rule_cname @{const_name "list_case"} = true
+ | has_split_rule_cname _ = false
+
+fun has_split_rule_term thy (Const (@{const_name "nat_case"}, _)) = true
+ | has_split_rule_term thy (Const (@{const_name "list_case"}, _)) = true
+ | has_split_rule_term thy _ = false
+
+fun has_split_rule_term' thy (Const (@{const_name "If"}, _)) = true
+ | has_split_rule_term' thy (Const (@{const_name "Let"}, _)) = true
+ | has_split_rule_term' thy c = has_split_rule_term thy c
+
+fun prepare_split_thm ctxt split_thm =
+ (split_thm RS @{thm iffD2})
+ |> LocalDefs.unfold ctxt [@{thm atomize_conjL[symmetric]},
+ @{thm atomize_all[symmetric]}, @{thm atomize_imp[symmetric]}]
+
+fun find_split_thm thy (Const (name, typ)) =
+ let
+ fun split_name str =
+ case first_field "." str
+ of (SOME (field, rest)) => field :: split_name rest
+ | NONE => [str]
+ val splitted_name = split_name name
+ in
+ if length splitted_name > 0 andalso
+ String.isSuffix "_case" (List.last splitted_name)
+ then
+ (List.take (splitted_name, length splitted_name - 1)) @ ["split"]
+ |> String.concatWith "."
+ |> PureThy.get_thm thy
+ |> SOME
+ handle ERROR msg => NONE
+ else NONE
+ end
+ | find_split_thm _ _ = NONE
+
+fun find_split_thm' thy (Const (@{const_name "If"}, _)) = SOME @{thm split_if}
+ | find_split_thm' thy (Const (@{const_name "Let"}, _)) = SOME @{thm refl} (* TODO *)
+ | find_split_thm' thy c = find_split_thm thy c
+
+fun strip_all t = (Term.strip_all_vars t, Term.strip_all_body t)
+
+fun folds_map f xs y =
+ let
+ fun folds_map' acc [] y = [(rev acc, y)]
+ | folds_map' acc (x :: xs) y =
+ maps (fn (x, y) => folds_map' (x :: acc) xs y) (f x y)
+ in
+ folds_map' [] xs y
+ end;
+
+fun mk_prems thy (lookup_pred, get_nparams) t (names, prems) =
+ let
+ fun mk_prems' (t as Const (name, T)) (names, prems) =
+ if is_constr thy name orelse (is_none (try lookup_pred t)) then
+ [(t ,(names, prems))]
+ else [(lookup_pred t, (names, prems))]
+ | mk_prems' (t as Free (f, T)) (names, prems) =
+ [(lookup_pred t, (names, prems))]
+ | mk_prems' t (names, prems) =
+ if Predicate_Compile_Aux.is_constrt thy t then
+ [(t, (names, prems))]
+ else
+ if has_split_rule_term' thy (fst (strip_comb t)) then
+ let
+ val (f, args) = strip_comb t
+ val split_thm = prepare_split_thm (ProofContext.init thy) (the (find_split_thm' thy f))
+ (* TODO: contextify things - this line is to unvarify the split_thm *)
+ (*val ((_, [isplit_thm]), _) = Variable.import true [split_thm] (ProofContext.init thy)*)
+ val (assms, concl) = Logic.strip_horn (Thm.prop_of split_thm)
+ val (P, [split_t]) = strip_comb (HOLogic.dest_Trueprop concl)
+ val subst = Pattern.match thy (split_t, t) (Vartab.empty, Vartab.empty)
+ val (_, split_args) = strip_comb split_t
+ val match = split_args ~~ args
+ fun mk_prems_of_assm assm =
+ let
+ val (vTs, assm') = strip_all (Envir.beta_norm (Envir.subst_term subst assm))
+ val var_names = Name.variant_list names (map fst vTs)
+ val vars = map Free (var_names ~~ (map snd vTs))
+ val (prems', pre_res) = Logic.strip_horn (subst_bounds (rev vars, assm'))
+ val (_, [inner_t]) = strip_comb (HOLogic.dest_Trueprop pre_res)
+ in
+ mk_prems' inner_t (var_names @ names, prems' @ prems)
+ end
+ in
+ maps mk_prems_of_assm assms
+ end
+ else
+ let
+ val (f, args) = strip_comb t
+ val resname = Name.variant names "res"
+ val resvar = Free (resname, body_type (fastype_of t))
+ val names' = resname :: names
+ fun mk_prems'' (t as Const (c, _)) =
+ if is_constr thy c orelse (is_none (try lookup_pred t)) then
+ folds_map mk_prems' args (names', prems) |>
+ map
+ (fn (argvs, (names'', prems')) =>
+ let
+ val prem = HOLogic.mk_Trueprop (HOLogic.mk_eq (resvar, list_comb (f, argvs)))
+ in (names'', prem :: prems') end)
+ else
+ let
+ val pred = lookup_pred t
+ val nparams = get_nparams pred
+ val (params, args) = chop nparams args
+ val _ = tracing ("mk_prems'': " ^ (Syntax.string_of_term_global thy t) ^ " has " ^ string_of_int nparams ^ " parameters.")
+ val params' = map (mk_param lookup_pred) params
+ in
+ folds_map mk_prems' args (names', prems)
+ |> map (fn (argvs, (names'', prems')) =>
+ let
+ val prem = HOLogic.mk_Trueprop (list_comb (pred, params' @ argvs @ [resvar]))
+ in (names'', prem :: prems') end)
+ end
+ | mk_prems'' (t as Free (_, _)) =
+ let
+ (* higher order argument call *)
+ val pred = lookup_pred t
+ in
+ folds_map mk_prems' args (resname :: names, prems)
+ |> map (fn (argvs, (names', prems')) =>
+ let
+ val prem = HOLogic.mk_Trueprop (list_comb (pred, argvs @ [resvar]))
+ in (names', prem :: prems') end)
+ end
+ | mk_prems'' t = error ("Invalid term: " ^ Syntax.string_of_term_global thy t)
+ in
+ map (pair resvar) (mk_prems'' f)
+ end
+ in
+ mk_prems' t (names, prems)
+ end;
+
+(* assumption: mutual recursive predicates all have the same parameters. *)
+fun define_predicates specs thy =
+ if forall (fn (const, _) => member (op =) (Symtab.keys (Pred_Compile_Preproc.get thy)) const) specs then
+ thy
+ else
+ let
+ val consts = map fst specs
+ val eqns = maps snd specs
+ (*val eqns = maps (Predicate_Compile_Preproc_Data.get_specification thy) consts*)
+ (* create prednames *)
+ val ((funs, argss), rhss) = map_split dest_code_eqn eqns |>> split_list
+ val argss' = map (map transform_ho_arg) argss
+ val pnames = map dest_Free (distinct (op =) (maps (filter (is_funtype o fastype_of)) argss'))
+ val preds = map pred_of funs
+ val prednames = map (fst o dest_Free) preds
+ val funnames = map (fst o dest_Const) funs
+ val fun_pred_names = (funnames ~~ prednames)
+ (* mapping from term (Free or Const) to term *)
+ fun lookup_pred (Const (@{const_name Cons}, T)) =
+ Const ("Preprocessing.ConsP", pred_type T) (* FIXME: temporary - Cons lookup *)
+ | lookup_pred (Const (name, T)) =
+ (case (Symtab.lookup (Pred_Compile_Preproc.get thy) name) of
+ SOME c => Const (c, pred_type T)
+ | NONE =>
+ (case AList.lookup op = fun_pred_names name of
+ SOME f => Free (f, pred_type T)
+ | NONE => Const (name, T)))
+ | lookup_pred (Free (name, T)) =
+ if member op = (map fst pnames) name then
+ Free (name, transform_ho_typ T)
+ else
+ Free (name, T)
+ | lookup_pred t =
+ error ("lookup function is not defined for " ^ Syntax.string_of_term_global thy t)
+
+ (* mapping from term (predicate term, not function term!) to int *)
+ fun get_nparams (Const (name, _)) =
+ the_default 0 (try (ind_package_get_nparams thy) name)
+ | get_nparams (Free (name, _)) =
+ (if member op = prednames name then
+ length pnames
+ else 0)
+ | get_nparams t = error ("No parameters for " ^ (Syntax.string_of_term_global thy t))
+
+ (* create intro rules *)
+
+ fun mk_intros ((func, pred), (args, rhs)) =
+ if (body_type (fastype_of func) = @{typ bool}) then
+ (*TODO: preprocess predicate definition of rhs *)
+ [Logic.list_implies ([HOLogic.mk_Trueprop rhs], HOLogic.mk_Trueprop (list_comb (pred, args)))]
+ else
+ let
+ val names = Term.add_free_names rhs []
+ in mk_prems thy (lookup_pred, get_nparams) rhs (names, [])
+ |> map (fn (resultt, (names', prems)) =>
+ Logic.list_implies (prems, HOLogic.mk_Trueprop (list_comb (pred, args @ [resultt]))))
+ end
+ fun mk_rewr_thm (func, pred) = @{thm refl}
+ in
+ case try (maps mk_intros) ((funs ~~ preds) ~~ (argss' ~~ rhss)) of
+ NONE => thy
+ | SOME intr_ts => let
+ val _ = map (tracing o (Syntax.string_of_term_global thy)) intr_ts
+ in
+ if is_some (try (map (cterm_of thy)) intr_ts) then
+ let
+ val (ind_result, thy') =
+ Inductive.add_inductive_global (serial_string ())
+ {quiet_mode = false, verbose = false, kind = Thm.internalK,
+ alt_name = Binding.empty, coind = false, no_elim = false,
+ no_ind = false, skip_mono = false, fork_mono = false}
+ (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (distinct (op =) (map dest_Free preds)))
+ pnames
+ (map (fn x => (Attrib.empty_binding, x)) intr_ts)
+ [] thy
+ val prednames = map (fst o dest_Const) (#preds ind_result)
+ (* val rewr_thms = map mk_rewr_eq ((distinct (op =) funs) ~~ (#preds ind_result)) *)
+ (* add constants to my table *)
+ in Pred_Compile_Preproc.map (fold Symtab.update_new (consts ~~ prednames)) thy' end
+ else
+ thy
+ end
+ end
+
+(* preprocessing intro rules - uses oracle *)
+
+(* theory -> thm -> thm *)
+fun rewrite_intro thy intro =
+ let
+ fun lookup_pred (Const (name, T)) =
+ (case (Symtab.lookup (Pred_Compile_Preproc.get thy) name) of
+ SOME c => Const (c, pred_type T)
+ | NONE => error ("Function " ^ name ^ " is not inductified"))
+ | lookup_pred (Free (name, T)) = Free (name, T)
+ | lookup_pred _ = error "lookup function is not defined!"
+
+ fun get_nparams (Const (name, _)) =
+ the_default 0 (try (ind_package_get_nparams thy) name)
+ | get_nparams (Free _) = 0
+ | get_nparams t = error ("No parameters for " ^ (Syntax.string_of_term_global thy t))
+
+ val intro_t = (Logic.unvarify o prop_of) intro
+ val _ = tracing (Syntax.string_of_term_global thy intro_t)
+ val (prems, concl) = Logic.strip_horn intro_t
+ val frees = map fst (Term.add_frees intro_t [])
+ fun rewrite prem names =
+ let
+ val t = (HOLogic.dest_Trueprop prem)
+ val (lit, mk_lit) = case try HOLogic.dest_not t of
+ SOME t => (t, HOLogic.mk_not)
+ | NONE => (t, I)
+ val (P, args) = (strip_comb lit)
+ in
+ folds_map (
+ fn t => if (is_funtype (fastype_of t)) then (fn x => [(t, x)])
+ else mk_prems thy (lookup_pred, get_nparams) t) args (names, [])
+ |> map (fn (resargs, (names', prems')) =>
+ let
+ val prem' = HOLogic.mk_Trueprop (mk_lit (list_comb (P, resargs)))
+ in (prem'::prems', names') end)
+ end
+ val intro_ts' = folds_map rewrite prems frees
+ |> maps (fn (prems', frees') =>
+ rewrite concl frees'
+ |> map (fn (concl'::conclprems, _) =>
+ Logic.list_implies ((flat prems') @ conclprems, concl')))
+ val _ = Output.tracing ("intro_ts': " ^
+ commas (map (Syntax.string_of_term_global thy) intro_ts'))
+ in
+ map (Drule.standard o the_oracle () o cterm_of thy) intro_ts'
+ end;
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/pred_compile_pred.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,138 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+Preprocessing definitions of predicates to introduction rules
+*)
+
+signature PREDICATE_COMPILE_PRED =
+sig
+ (* preprocesses an equation to a set of intro rules; defines new constants *)
+ (*
+ val preprocess_pred_equation : thm -> theory -> thm list * theory
+ *)
+ val preprocess : string -> theory -> (thm list list * theory)
+ (* output is the term list of clauses of an unknown predicate *)
+ val preprocess_term : term -> theory -> (term list * theory)
+
+ (*val rewrite : thm -> thm*)
+
+end;
+(* : PREDICATE_COMPILE_PREPROC_PRED *)
+structure Predicate_Compile_Pred =
+struct
+
+open Predicate_Compile_Aux
+
+fun is_compound ((Const ("Not", _)) $ t) =
+ error "is_compound: Negation should not occur; preprocessing is defect"
+ | is_compound ((Const ("Ex", _)) $ _) = true
+ | is_compound ((Const (@{const_name "op |"}, _)) $ _ $ _) = true
+ | is_compound ((Const ("op &", _)) $ _ $ _) =
+ error "is_compound: Conjunction should not occur; preprocessing is defect"
+ | is_compound _ = false
+
+fun flatten constname atom (defs, thy) =
+ if is_compound atom then
+ let
+ val constname = Name.variant (map (Long_Name.base_name o fst) defs)
+ ((Long_Name.base_name constname) ^ "_aux")
+ val full_constname = Sign.full_bname thy constname
+ val (params, args) = List.partition (is_predT o fastype_of)
+ (map Free (Term.add_frees atom []))
+ val constT = map fastype_of (params @ args) ---> HOLogic.boolT
+ val lhs = list_comb (Const (full_constname, constT), params @ args)
+ val def = Logic.mk_equals (lhs, atom)
+ val ([definition], thy') = thy
+ |> Sign.add_consts_i [(Binding.name constname, constT, NoSyn)]
+ |> PureThy.add_defs false [((Binding.name (constname ^ "_def"), def), [])]
+ in
+ (lhs, ((full_constname, [definition]) :: defs, thy'))
+ end
+ else
+ (atom, (defs, thy))
+
+fun flatten_intros constname intros thy =
+ let
+ val ctxt = ProofContext.init thy
+ val ((_, intros), ctxt') = Variable.import true intros ctxt
+ val (intros', (local_defs, thy')) = (fold_map o fold_map_atoms)
+ (flatten constname) (map prop_of intros) ([], thy)
+ val tac = fn {...} => setmp quick_and_dirty true (SkipProof.cheat_tac thy')
+ val intros'' = map (fn t => Goal.prove ctxt' [] [] t tac) intros'
+ |> Variable.export ctxt' ctxt
+ in
+ (intros'', (local_defs, thy'))
+ end
+
+(* TODO: same function occurs in inductive package *)
+fun select_disj 1 1 = []
+ | select_disj _ 1 = [rtac @{thm disjI1}]
+ | select_disj n i = (rtac @{thm disjI2})::(select_disj (n - 1) (i - 1));
+
+fun introrulify thy ths =
+ let
+ val ctxt = ProofContext.init thy
+ val ((_, ths'), ctxt') = Variable.import true ths ctxt
+ fun introrulify' th =
+ let
+ val (lhs, rhs) = Logic.dest_equals (prop_of th)
+ val frees = Term.add_free_names rhs []
+ val disjuncts = HOLogic.dest_disj rhs
+ val nctxt = Name.make_context frees
+ fun mk_introrule t =
+ let
+ val ((ps, t'), nctxt') = focus_ex t nctxt
+ val prems = map HOLogic.mk_Trueprop (HOLogic.dest_conj t')
+ in
+ (ps, Logic.list_implies (prems, HOLogic.mk_Trueprop lhs))
+ end
+ val x = ((cterm_of thy) o the_single o snd o strip_comb o HOLogic.dest_Trueprop o fst o
+ Logic.dest_implies o prop_of) @{thm exI}
+ fun prove_introrule (index, (ps, introrule)) =
+ let
+ val tac = Simplifier.simp_tac (HOL_basic_ss addsimps [th]) 1
+ THEN EVERY1 (select_disj (length disjuncts) (index + 1))
+ THEN (EVERY (map (fn y =>
+ rtac (Drule.cterm_instantiate [(x, cterm_of thy (Free y))] @{thm exI}) 1) ps))
+ THEN REPEAT_DETERM (rtac @{thm conjI} 1 THEN atac 1)
+ THEN TRY (atac 1)
+ in
+ Goal.prove ctxt' (map fst ps) [] introrule (fn {...} => tac)
+ end
+ in
+ map_index prove_introrule (map mk_introrule disjuncts)
+ end
+ in maps introrulify' ths' |> Variable.export ctxt' ctxt end
+
+val rewrite =
+ Simplifier.simplify (HOL_basic_ss addsimps [@{thm Ball_def}, @{thm Bex_def}])
+ #> Simplifier.simplify (HOL_basic_ss addsimps [@{thm all_not_ex}])
+ #> Conv.fconv_rule nnf_conv
+ #> Simplifier.simplify (HOL_basic_ss addsimps [@{thm ex_disj_distrib}])
+
+val rewrite_intros =
+ Simplifier.simplify (HOL_basic_ss addsimps @{thms HOL.simp_thms(9)})
+
+fun preprocess (constname, specs) thy =
+ let
+ val ctxt = ProofContext.init thy
+ val intros =
+ if forall is_pred_equation specs then
+ introrulify thy (map rewrite specs)
+ else if forall (is_intro constname) specs then
+ map rewrite_intros specs
+ else
+ error ("unexpected specification for constant " ^ quote constname ^ ":\n"
+ ^ commas (map (quote o Display.string_of_thm_global thy) specs))
+ val _ = tracing ("Introduction rules of definitions before flattening: "
+ ^ commas (map (Display.string_of_thm ctxt) intros))
+ val _ = tracing "Defining local predicates and their intro rules..."
+ val (intros', (local_defs, thy')) = flatten_intros constname intros thy
+ val (intross, thy'') = fold_map preprocess local_defs thy'
+ in
+ (intros' :: flat intross,thy'')
+ end;
+
+fun preprocess_term t thy = error "preprocess_pred_term: to implement"
+
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/pred_compile_quickcheck.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,93 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+A quickcheck generator based on the predicate compiler
+*)
+
+signature PRED_COMPILE_QUICKCHECK =
+sig
+ val quickcheck : Proof.context -> term -> int -> term list option
+ val test_ref : ((unit -> int -> int * int -> term list Predicate.pred * (int * int)) option) ref
+end;
+
+structure Pred_Compile_Quickcheck : PRED_COMPILE_QUICKCHECK =
+struct
+
+val test_ref = ref (NONE : (unit -> int -> int * int -> term list Predicate.pred * (int * int)) option)
+val target = "Quickcheck"
+
+fun dest_compfuns (Predicate_Compile_Core.CompilationFuns funs) = funs
+val mk_predT = #mk_predT (dest_compfuns Predicate_Compile_Core.pred_compfuns)
+val mk_rpredT = #mk_predT (dest_compfuns Predicate_Compile_Core.rpred_compfuns)
+val mk_return = #mk_single (dest_compfuns Predicate_Compile_Core.rpred_compfuns)
+val mk_bind = #mk_bind (dest_compfuns Predicate_Compile_Core.rpred_compfuns)
+val lift_pred = #lift_pred (dest_compfuns Predicate_Compile_Core.rpred_compfuns)
+
+fun mk_split_lambda [] t = Abs ("u", HOLogic.unitT, t)
+ | mk_split_lambda [x] t = lambda x t
+ | mk_split_lambda xs t =
+ let
+ fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
+ | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
+ in
+ mk_split_lambda' xs t
+ end;
+
+fun strip_imp_prems (Const("op -->", _) $ A $ B) = A :: strip_imp_prems B
+ | strip_imp_prems _ = [];
+
+fun strip_imp_concl (Const("op -->", _) $ A $ B) = strip_imp_concl B
+ | strip_imp_concl A = A : term;
+
+fun strip_horn A = (strip_imp_prems A, strip_imp_concl A);
+
+fun quickcheck ctxt t =
+ let
+ val _ = tracing ("Starting quickcheck with " ^ (Syntax.string_of_term ctxt t))
+ val ctxt' = ProofContext.theory (Context.copy_thy) ctxt
+ val thy = (ProofContext.theory_of ctxt')
+ val (vs, t') = strip_abs t
+ val vs' = Variable.variant_frees ctxt' [] vs
+ val t'' = subst_bounds (map Free (rev vs'), t')
+ val (prems, concl) = strip_horn t''
+ val constname = "pred_compile_quickcheck"
+ val full_constname = Sign.full_bname thy constname
+ val constT = map snd vs' ---> @{typ bool}
+ val thy' = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
+ val t = Logic.list_implies
+ (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
+ HOLogic.mk_Trueprop (list_comb (Const (full_constname, constT), map Free vs')))
+ val tac = fn {...} => setmp quick_and_dirty true (SkipProof.cheat_tac thy')
+ val intro = Goal.prove (ProofContext.init thy') (map fst vs') [] t tac
+ val _ = tracing (Display.string_of_thm ctxt' intro)
+ val thy'' = thy'
+ |> Context.theory_map (Predicate_Compile_Preproc_Const_Defs.add_thm intro)
+ |> Predicate_Compile.preprocess full_constname
+ |> Predicate_Compile_Core.add_equations [full_constname]
+ |> Predicate_Compile_Core.add_sizelim_equations [full_constname]
+ |> Predicate_Compile_Core.add_quickcheck_equations [full_constname]
+ val sizelim_modes = Predicate_Compile_Core.sizelim_modes_of thy'' full_constname
+ val modes = Predicate_Compile_Core.generator_modes_of thy'' full_constname
+ val prog =
+ if member (op =) modes ([], []) then
+ let
+ val name = Predicate_Compile_Core.generator_name_of thy'' full_constname ([], [])
+ val T = @{typ code_numeral} --> (mk_rpredT (HOLogic.mk_tupleT (map snd vs')))
+ in Const (name, T) $ Bound 0 end
+ else if member (op =) sizelim_modes ([], []) then
+ let
+ val name = Predicate_Compile_Core.sizelim_function_name_of thy'' full_constname ([], [])
+ val T = @{typ code_numeral} --> (mk_predT (HOLogic.mk_tupleT (map snd vs')))
+ in lift_pred (Const (name, T) $ Bound 0) end
+ else error "Predicate Compile Quickcheck failed"
+ val qc_term = Abs ("size", @{typ code_numeral}, mk_bind (prog,
+ mk_split_lambda (map Free vs') (mk_return (HOLogic.mk_list @{typ term}
+ (map2 HOLogic.mk_term_of (map snd vs') (map Free vs'))))))
+ val _ = tracing (Syntax.string_of_term ctxt' qc_term)
+ val compile = Code_ML.eval (SOME target) ("Pred_Compile_Quickcheck.test_ref", test_ref)
+ (fn proc => fn g => fn s => g s #>> (Predicate.map o map) proc)
+ thy'' qc_term []
+ in
+ ((compile #> Random_Engine.run) #> (Option.map fst o Predicate.yield))
+ end
+
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/pred_compile_set.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,51 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+Preprocessing sets to predicates
+*)
+
+signature PRED_COMPILE_SET =
+sig
+(*
+ val preprocess_intro : thm -> theory -> thm * theory
+ val preprocess_clause : term -> theory -> term * theory
+*)
+ val unfold_set_notation : thm -> thm;
+end;
+
+structure Pred_Compile_Set : PRED_COMPILE_SET =
+struct
+(*FIXME: unfolding Ball in pretty adhoc here *)
+val unfold_set_lemmas = [@{thm Collect_def}, @{thm mem_def}, @{thm Ball_def}]
+
+val unfold_set_notation = Simplifier.rewrite_rule unfold_set_lemmas
+
+(*
+fun find_set_theorems ctxt cname =
+ let
+ val _ = cname
+*)
+
+(*
+fun preprocess_term t ctxt =
+ case t of
+ Const ("op :", _) $ x $ A =>
+ case strip_comb A of
+ (Const (cname, T), params) =>
+ let
+ val _ = find_set_theorems
+ in
+ (t, ctxt)
+ end
+ | _ => (t, ctxt)
+ | _ => (t, ctxt)
+*)
+(*
+fun preprocess_intro th thy =
+ let
+ val cnames = find_heads_of_prems
+ val set_cname = filter (has_set_definition
+ val _ = define_preds
+ val _ = prep_pred_def
+ in
+*)
+end;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,91 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+*)
+signature PREDICATE_COMPILE =
+sig
+ val setup : theory -> theory
+ val preprocess : string -> theory -> theory
+end;
+
+structure Predicate_Compile : PREDICATE_COMPILE =
+struct
+
+open Predicate_Compile_Aux;
+
+val priority = tracing;
+
+(* Some last processing *)
+fun remove_pointless_clauses intro =
+ if Logic.strip_imp_prems (prop_of intro) = [@{prop "False"}] then
+ []
+ else [intro]
+
+fun preprocess_strong_conn_constnames gr constnames thy =
+ let
+ val get_specs = map (fn k => (k, Graph.get_node gr k))
+ val _ = priority ("Preprocessing scc of " ^ commas constnames)
+ val (prednames, funnames) = List.partition (is_pred thy) constnames
+ (* untangle recursion by defining predicates for all functions *)
+ val _ = priority "Compiling functions to predicates..."
+ val _ = Output.tracing ("funnames: " ^ commas funnames)
+ val thy' =
+ thy |> not (null funnames) ? Predicate_Compile_Fun.define_predicates
+ (get_specs funnames)
+ val _ = priority "Compiling predicates to flat introrules..."
+ val (intross, thy'') = apfst flat (fold_map Predicate_Compile_Pred.preprocess
+ (get_specs prednames) thy')
+ val _ = tracing ("Flattened introduction rules: " ^
+ commas (map (Display.string_of_thm_global thy'') (flat intross)))
+ val _ = priority "Replacing functions in introrules..."
+ (* val _ = burrow (maps (Predicate_Compile_Fun.rewrite_intro thy'')) intross *)
+ val intross' =
+ case try (burrow (maps (Predicate_Compile_Fun.rewrite_intro thy''))) intross of
+ SOME intross' => intross'
+ | NONE => let val _ = warning "Function replacement failed!" in intross end
+ val _ = tracing ("Introduction rules with replaced functions: " ^
+ commas (map (Display.string_of_thm_global thy'') (flat intross')))
+ val intross'' = burrow (maps remove_pointless_clauses) intross'
+ val intross'' = burrow (map (AxClass.overload thy'')) intross''
+ val _ = priority "Registering intro rules..."
+ val thy''' = fold Predicate_Compile_Core.register_intros intross'' thy''
+ in
+ thy'''
+ end;
+
+fun preprocess const thy =
+ let
+ val _ = Output.tracing ("Fetching definitions from theory...")
+ val table = Pred_Compile_Data.make_const_spec_table thy
+ val gr = Pred_Compile_Data.obtain_specification_graph table const
+ val _ = Output.tracing (commas (Graph.all_succs gr [const]))
+ val gr = Graph.subgraph (member (op =) (Graph.all_succs gr [const])) gr
+ in fold_rev (preprocess_strong_conn_constnames gr)
+ (Graph.strong_conn gr) thy
+ end
+
+fun code_pred_cmd ((inductify_all, rpred), raw_const) lthy =
+ if inductify_all then
+ let
+ val thy = ProofContext.theory_of lthy
+ val const = Code.read_const thy raw_const
+ val lthy' = LocalTheory.theory (preprocess const) lthy
+ |> LocalTheory.checkpoint
+ val _ = tracing "Starting Predicate Compile Core..."
+ in Predicate_Compile_Core.code_pred_cmd rpred raw_const lthy' end
+ else
+ Predicate_Compile_Core.code_pred_cmd rpred raw_const lthy
+
+val setup = Predicate_Compile_Fun.setup_oracle #> Predicate_Compile_Core.setup
+
+val _ = List.app OuterKeyword.keyword ["inductify_all", "rpred"]
+
+local structure P = OuterParse
+in
+
+val _ = OuterSyntax.local_theory_to_proof "code_pred"
+ "prove equations for predicate specified by intro/elim rules"
+ OuterKeyword.thy_goal (P.opt_keyword "inductify_all" -- P.opt_keyword "rpred" -- P.term_group >> code_pred_cmd)
+
+end
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML Thu Sep 24 17:26:05 2009 +0200
@@ -0,0 +1,2425 @@
+(* Author: Lukas Bulwahn, TU Muenchen
+
+(Prototype of) A compiler from predicates specified by intro/elim rules
+to equations.
+*)
+
+signature PREDICATE_COMPILE_CORE =
+sig
+ val setup: theory -> theory
+ val code_pred: bool -> string -> Proof.context -> Proof.state
+ val code_pred_cmd: bool -> string -> Proof.context -> Proof.state
+ type smode = (int * int list option) list
+ type mode = smode option list * smode
+ datatype tmode = Mode of mode * smode * tmode option list;
+ (*val add_equations_of: bool -> string list -> theory -> theory *)
+ val register_predicate : (thm list * thm * int) -> theory -> theory
+ val register_intros : thm list -> theory -> theory
+ val is_registered : theory -> string -> bool
+ (* val fetch_pred_data : theory -> string -> (thm list * thm * int) *)
+ val predfun_intro_of: theory -> string -> mode -> thm
+ val predfun_elim_of: theory -> string -> mode -> thm
+ val strip_intro_concl: int -> term -> term * (term list * term list)
+ val predfun_name_of: theory -> string -> mode -> string
+ val all_preds_of : theory -> string list
+ val modes_of: theory -> string -> mode list
+ val sizelim_modes_of: theory -> string -> mode list
+ val sizelim_function_name_of : theory -> string -> mode -> string
+ val generator_modes_of: theory -> string -> mode list
+ val generator_name_of : theory -> string -> mode -> string
+ val string_of_mode : mode -> string
+ val intros_of: theory -> string -> thm list
+ val nparams_of: theory -> string -> int
+ val add_intro: thm -> theory -> theory
+ val set_elim: thm -> theory -> theory
+ val set_nparams : string -> int -> theory -> theory
+ val print_stored_rules: theory -> unit
+ val print_all_modes: theory -> unit
+ val do_proofs: bool ref
+ val mk_casesrule : Proof.context -> int -> thm list -> term
+ val analyze_compr: theory -> term -> term
+ val eval_ref: (unit -> term Predicate.pred) option ref
+ val add_equations : string list -> theory -> theory
+ val code_pred_intros_attrib : attribute
+ (* used by Quickcheck_Generator *)
+ (*val funT_of : mode -> typ -> typ
+ val mk_if_pred : term -> term
+ val mk_Eval : term * term -> term*)
+ val mk_tupleT : typ list -> typ
+(* val mk_predT : typ -> typ *)
+ (* temporary for testing of the compilation *)
+ datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
+ GeneratorPrem of term list * term | Generator of (string * typ);
+ (* val prepare_intrs: theory -> string list ->
+ (string * typ) list * int * string list * string list * (string * mode list) list *
+ (string * (term list * indprem list) list) list * (string * (int option list * int)) list*)
+ datatype compilation_funs = CompilationFuns of {
+ mk_predT : typ -> typ,
+ dest_predT : typ -> typ,
+ mk_bot : typ -> term,
+ mk_single : term -> term,
+ mk_bind : term * term -> term,
+ mk_sup : term * term -> term,
+ mk_if : term -> term,
+ mk_not : term -> term,
+ mk_map : typ -> typ -> term -> term -> term,
+ lift_pred : term -> term
+ };
+ type moded_clause = term list * (indprem * tmode) list
+ type 'a pred_mode_table = (string * (mode * 'a) list) list
+ val infer_modes : theory -> (string * mode list) list
+ -> (string * mode list) list
+ -> string list
+ -> (string * (term list * indprem list) list) list
+ -> (moded_clause list) pred_mode_table
+ val infer_modes_with_generator : theory -> (string * mode list) list
+ -> (string * mode list) list
+ -> string list
+ -> (string * (term list * indprem list) list) list
+ -> (moded_clause list) pred_mode_table
+ (*val compile_preds : theory -> compilation_funs -> string list -> string list
+ -> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table
+ val rpred_create_definitions :(string * typ) list -> string * mode list
+ -> theory -> theory
+ val split_smode : int list -> term list -> (term list * term list) *)
+ val print_moded_clauses :
+ theory -> (moded_clause list) pred_mode_table -> unit
+ val print_compiled_terms : theory -> term pred_mode_table -> unit
+ (*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*)
+ val pred_compfuns : compilation_funs
+ val rpred_compfuns : compilation_funs
+ val dest_funT : typ -> typ * typ
+ (* val depending_preds_of : theory -> thm list -> string list *)
+ val add_quickcheck_equations : string list -> theory -> theory
+ val add_sizelim_equations : string list -> theory -> theory
+ val is_inductive_predicate : theory -> string -> bool
+ val terms_vs : term list -> string list
+ val subsets : int -> int -> int list list
+ val check_mode_clause : bool -> theory -> string list ->
+ (string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list)
+ -> (term list * (indprem * tmode) list) option
+ val string_of_moded_prem : theory -> (indprem * tmode) -> string
+ val all_modes_of : theory -> (string * mode list) list
+ val all_generator_modes_of : theory -> (string * mode list) list
+ val compile_clause : compilation_funs -> term option -> (term list -> term) ->
+ theory -> string list -> string list -> mode -> term -> moded_clause -> term
+ val preprocess_intro : theory -> thm -> thm
+ val is_constrt : theory -> term -> bool
+ val is_predT : typ -> bool
+ val guess_nparams : typ -> int
+ val cprods_subset : 'a list list -> 'a list list
+end;
+
+structure Predicate_Compile_Core : PREDICATE_COMPILE_CORE =
+struct
+
+open Predicate_Compile_Aux;
+(** auxiliary **)
+
+(* debug stuff *)
+
+fun tracing s = (if ! Toplevel.debug then Output.tracing s else ());
+
+fun print_tac s = Seq.single; (*Tactical.print_tac s;*) (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *)
+fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *)
+
+val do_proofs = ref true;
+
+(* reference to preprocessing of InductiveSet package *)
+
+val ind_set_codegen_preproc = (fn thy => I) (*Inductive_Set.codegen_preproc;*)
+
+(** fundamentals **)
+
+(* syntactic operations *)
+
+fun mk_eq (x, xs) =
+ let fun mk_eqs _ [] = []
+ | mk_eqs a (b::cs) =
+ HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs
+ in mk_eqs x xs end;
+
+fun mk_tupleT [] = HOLogic.unitT
+ | mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts;
+
+fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = []
+ | dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2)
+ | dest_tupleT t = [t]
+
+fun mk_tuple [] = HOLogic.unit
+ | mk_tuple ts = foldr1 HOLogic.mk_prod ts;
+
+fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = []
+ | dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2)
+ | dest_tuple t = [t]
+
+fun mk_scomp (t, u) =
+ let
+ val T = fastype_of t
+ val U = fastype_of u
+ val [A] = binder_types T
+ val D = body_type U
+ in
+ Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u
+ end;
+
+fun dest_funT (Type ("fun",[S, T])) = (S, T)
+ | dest_funT T = raise TYPE ("dest_funT", [T], [])
+
+fun mk_fun_comp (t, u) =
+ let
+ val (_, B) = dest_funT (fastype_of t)
+ val (C, A) = dest_funT (fastype_of u)
+ in
+ Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u
+ end;
+
+fun dest_randomT (Type ("fun", [@{typ Random.seed},
+ Type ("*", [Type ("*", [T, @{typ "unit => Code_Evaluation.term"}]) ,@{typ Random.seed}])])) = T
+ | dest_randomT T = raise TYPE ("dest_randomT", [T], [])
+
+(* destruction of intro rules *)
+
+(* FIXME: look for other place where this functionality was used before *)
+fun strip_intro_concl nparams intro = let
+ val _ $ u = Logic.strip_imp_concl intro
+ val (pred, all_args) = strip_comb u
+ val (params, args) = chop nparams all_args
+in (pred, (params, args)) end
+
+(** data structures **)
+
+type smode = (int * int list option) list
+type mode = smode option list * smode;
+datatype tmode = Mode of mode * smode * tmode option list;
+
+fun gen_split_smode (mk_tuple, strip_tuple) smode ts =
+ let
+ fun split_tuple' _ _ [] = ([], [])
+ | split_tuple' is i (t::ts) =
+ (if i mem is then apfst else apsnd) (cons t)
+ (split_tuple' is (i+1) ts)
+ fun split_tuple is t = split_tuple' is 1 (strip_tuple t)
+ fun split_smode' _ _ [] = ([], [])
+ | split_smode' smode i (t::ts) =
+ (if i mem (map fst smode) then
+ case (the (AList.lookup (op =) smode i)) of
+ NONE => apfst (cons t)
+ | SOME is =>
+ let
+ val (ts1, ts2) = split_tuple is t
+ fun cons_tuple ts = if null ts then I else cons (mk_tuple ts)
+ in (apfst (cons_tuple ts1)) o (apsnd (cons_tuple ts2)) end
+ else apsnd (cons t))
+ (split_smode' smode (i+1) ts)
+ in split_smode' smode 1 ts end
+
+val split_smode = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple)
+val split_smodeT = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT)
+
+fun gen_split_mode split_smode (iss, is) ts =
+ let
+ val (t1, t2) = chop (length iss) ts
+ in (t1, split_smode is t2) end
+
+val split_mode = gen_split_mode split_smode
+val split_modeT = gen_split_mode split_smodeT
+
+fun string_of_smode js =
+ commas (map
+ (fn (i, is) =>
+ string_of_int i ^ (case is of NONE => ""
+ | SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js)
+
+fun string_of_mode (iss, is) = space_implode " -> " (map
+ (fn NONE => "X"
+ | SOME js => enclose "[" "]" (string_of_smode js))
+ (iss @ [SOME is]));
+
+fun string_of_tmode (Mode (predmode, termmode, param_modes)) =
+ "predmode: " ^ (string_of_mode predmode) ^
+ (if null param_modes then "" else
+ "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes))
+
+(* generation of case rules from user-given introduction rules *)
+
+fun mk_casesrule ctxt nparams introrules =
+ let
+ val ((_, intros_th), ctxt1) = Variable.import false introrules ctxt
+ val intros = map prop_of intros_th
+ val (pred, (params, args)) = strip_intro_concl nparams (hd intros)
+ val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
+ val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
+ val (argnames, ctxt3) = Variable.variant_fixes
+ (map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt2
+ val argvs = map2 (curry Free) argnames (map fastype_of args)
+ fun mk_case intro =
+ let
+ val (_, (_, args)) = strip_intro_concl nparams intro
+ val prems = Logic.strip_imp_prems intro
+ val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args)
+ val frees = (fold o fold_aterms)
+ (fn t as Free _ =>
+ if member (op aconv) params t then I else insert (op aconv) t
+ | _ => I) (args @ prems) []
+ in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
+ val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs))
+ val cases = map mk_case intros
+ in Logic.list_implies (assm :: cases, prop) end;
+
+
+datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
+ GeneratorPrem of term list * term | Generator of (string * typ);
+
+type moded_clause = term list * (indprem * tmode) list
+type 'a pred_mode_table = (string * (mode * 'a) list) list
+
+datatype predfun_data = PredfunData of {
+ name : string,
+ definition : thm,
+ intro : thm,
+ elim : thm
+};
+
+fun rep_predfun_data (PredfunData data) = data;
+fun mk_predfun_data (name, definition, intro, elim) =
+ PredfunData {name = name, definition = definition, intro = intro, elim = elim}
+
+datatype function_data = FunctionData of {
+ name : string,
+ equation : thm option (* is not used at all? *)
+};
+
+fun rep_function_data (FunctionData data) = data;
+fun mk_function_data (name, equation) =
+ FunctionData {name = name, equation = equation}
+
+datatype pred_data = PredData of {
+ intros : thm list,
+ elim : thm option,
+ nparams : int,
+ functions : (mode * predfun_data) list,
+ generators : (mode * function_data) list,
+ sizelim_functions : (mode * function_data) list
+};
+
+fun rep_pred_data (PredData data) = data;
+fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) =
+ PredData {intros = intros, elim = elim, nparams = nparams,
+ functions = functions, generators = generators, sizelim_functions = sizelim_functions}
+fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) =
+ mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_functions)))
+
+fun eq_option eq (NONE, NONE) = true
+ | eq_option eq (SOME x, SOME y) = eq (x, y)
+ | eq_option eq _ = false
+
+fun eq_pred_data (PredData d1, PredData d2) =
+ eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso
+ eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso
+ #nparams d1 = #nparams d2
+
+structure PredData = TheoryDataFun
+(
+ type T = pred_data Graph.T;
+ val empty = Graph.empty;
+ val copy = I;
+ val extend = I;
+ fun merge _ = Graph.merge eq_pred_data;
+);
+
+(* queries *)
+
+fun lookup_pred_data thy name =
+ Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name)
+
+fun the_pred_data thy name = case lookup_pred_data thy name
+ of NONE => error ("No such predicate " ^ quote name)
+ | SOME data => data;
+
+val is_registered = is_some oo lookup_pred_data
+
+val all_preds_of = Graph.keys o PredData.get
+
+fun intros_of thy = map (Thm.transfer thy) o #intros o the_pred_data thy
+
+fun the_elim_of thy name = case #elim (the_pred_data thy name)
+ of NONE => error ("No elimination rule for predicate " ^ quote name)
+ | SOME thm => Thm.transfer thy thm
+
+val has_elim = is_some o #elim oo the_pred_data;
+
+val nparams_of = #nparams oo the_pred_data
+
+val modes_of = (map fst) o #functions oo the_pred_data
+
+val sizelim_modes_of = (map fst) o #sizelim_functions oo the_pred_data
+
+val rpred_modes_of = (map fst) o #generators oo the_pred_data
+
+fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy)
+
+val is_compiled = not o null o #functions oo the_pred_data
+
+fun lookup_predfun_data thy name mode =
+ Option.map rep_predfun_data (AList.lookup (op =)
+ (#functions (the_pred_data thy name)) mode)
+
+fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode
+ of NONE => error ("No function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
+ | SOME data => data;
+
+val predfun_name_of = #name ooo the_predfun_data
+
+val predfun_definition_of = #definition ooo the_predfun_data
+
+val predfun_intro_of = #intro ooo the_predfun_data
+
+val predfun_elim_of = #elim ooo the_predfun_data
+
+fun lookup_generator_data thy name mode =
+ Option.map rep_function_data (AList.lookup (op =)
+ (#generators (the_pred_data thy name)) mode)
+
+fun the_generator_data thy name mode = case lookup_generator_data thy name mode
+ of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
+ | SOME data => data
+
+val generator_name_of = #name ooo the_generator_data
+
+val generator_modes_of = (map fst) o #generators oo the_pred_data
+
+fun all_generator_modes_of thy =
+ map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy)
+
+fun lookup_sizelim_function_data thy name mode =
+ Option.map rep_function_data (AList.lookup (op =)
+ (#sizelim_functions (the_pred_data thy name)) mode)
+
+fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode
+ of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode
+ ^ " of predicate " ^ name)
+ | SOME data => data
+
+val sizelim_function_name_of = #name ooo the_sizelim_function_data
+
+(*val generator_modes_of = (map fst) o #generators oo the_pred_data*)
+
+(* diagnostic display functions *)
+
+fun print_modes modes = Output.tracing ("Inferred modes:\n" ^
+ cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
+ string_of_mode ms)) modes));
+
+fun print_pred_mode_table string_of_entry thy pred_mode_table =
+ let
+ fun print_mode pred (mode, entry) = "mode : " ^ (string_of_mode mode)
+ ^ (string_of_entry pred mode entry)
+ fun print_pred (pred, modes) =
+ "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
+ val _ = Output.tracing (cat_lines (map print_pred pred_mode_table))
+ in () end;
+
+fun string_of_moded_prem thy (Prem (ts, p), tmode) =
+ (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
+ "(" ^ (string_of_tmode tmode) ^ ")"
+ | string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) =
+ (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
+ "(generator_mode: " ^ (string_of_mode predmode) ^ ")"
+ | string_of_moded_prem thy (Generator (v, T), _) =
+ "Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T)
+ | string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) =
+ (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
+ "(negative mode: " ^ string_of_smode is ^ ")"
+ | string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) =
+ (Syntax.string_of_term_global thy t) ^
+ "(sidecond mode: " ^ string_of_smode is ^ ")"
+ | string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented"
+
+fun print_moded_clauses thy =
+ let
+ fun string_of_clause pred mode clauses =
+ cat_lines (map (fn (ts, prems) => (space_implode " --> "
+ (map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " "
+ ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses)
+ in print_pred_mode_table string_of_clause thy end;
+
+fun print_compiled_terms thy =
+ print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy
+
+fun print_stored_rules thy =
+ let
+ val preds = (Graph.keys o PredData.get) thy
+ fun print pred () = let
+ val _ = writeln ("predicate: " ^ pred)
+ val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred))
+ val _ = writeln ("introrules: ")
+ val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm))
+ (rev (intros_of thy pred)) ()
+ in
+ if (has_elim thy pred) then
+ writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred))
+ else
+ writeln ("no elimrule defined")
+ end
+ in
+ fold print preds ()
+ end;
+
+fun print_all_modes thy =
+ let
+ val _ = writeln ("Inferred modes:")
+ fun print (pred, modes) u =
+ let
+ val _ = writeln ("predicate: " ^ pred)
+ val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
+ in u end
+ in
+ fold print (all_modes_of thy) ()
+ end
+
+(** preprocessing rules **)
+
+fun imp_prems_conv cv ct =
+ case Thm.term_of ct of
+ Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
+ | _ => Conv.all_conv ct
+
+fun Trueprop_conv cv ct =
+ case Thm.term_of ct of
+ Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct
+ | _ => error "Trueprop_conv"
+
+fun preprocess_intro thy rule =
+ Conv.fconv_rule
+ (imp_prems_conv
+ (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
+ (Thm.transfer thy rule)
+
+fun preprocess_elim thy nparams elimrule =
+ let
+ val _ = Output.tracing ("Preprocessing elimination rule "
+ ^ (Display.string_of_thm_global thy elimrule))
+ fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) =
+ HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)
+ | replace_eqs t = t
+ val prems = Thm.prems_of elimrule
+ val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams
+ fun preprocess_case t =
+ let
+ val params = Logic.strip_params t
+ val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t)
+ val assums_hyp' = assums1 @ (map replace_eqs assums2)
+ in
+ list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t))
+ end
+ val cases' = map preprocess_case (tl prems)
+ val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule)
+ (*val _ = Output.tracing ("elimrule': "^ (Syntax.string_of_term_global thy elimrule'))*)
+ val bigeq = (Thm.symmetric (Conv.implies_concl_conv
+ (MetaSimplifier.rewrite true [@{thm Predicate.eq_is_eq}])
+ (cterm_of thy elimrule')))
+ (*
+ val _ = Output.tracing ("bigeq:" ^ (Display.string_of_thm_global thy bigeq))
+ val res =
+ Thm.equal_elim bigeq elimrule
+ *)
+ (*
+ val t = (fn {...} => mycheat_tac thy 1)
+ val eq = Goal.prove (ProofContext.init thy) [] [] (Logic.mk_equals ((Thm.prop_of elimrule), elimrule')) t
+ *)
+ val _ = Output.tracing "Preprocessed elimination rule"
+ in
+ Thm.equal_elim bigeq elimrule
+ end;
+
+(* special case: predicate with no introduction rule *)
+fun noclause thy predname elim = let
+ val T = (Logic.unvarifyT o Sign.the_const_type thy) predname
+ val Ts = binder_types T
+ val names = Name.variant_list []
+ (map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts)))
+ val vs = map2 (curry Free) names Ts
+ val clausehd = HOLogic.mk_Trueprop (list_comb (Const (predname, T), vs))
+ val intro_t = Logic.mk_implies (@{prop False}, clausehd)
+ val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))
+ val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P)
+ val intro = Goal.prove (ProofContext.init thy) names [] intro_t
+ (fn {...} => etac @{thm FalseE} 1)
+ val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
+ (fn {...} => etac elim 1)
+in
+ ([intro], elim)
+end
+
+fun fetch_pred_data thy name =
+ case try (Inductive.the_inductive (ProofContext.init thy)) name of
+ SOME (info as (_, result)) =>
+ let
+ fun is_intro_of intro =
+ let
+ val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro))
+ in (fst (dest_Const const) = name) end;
+ val intros = ind_set_codegen_preproc thy ((map (preprocess_intro thy))
+ (filter is_intro_of (#intrs result)))
+ val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info)))
+ val nparams = length (Inductive.params_of (#raw_induct result))
+ val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
+ val (intros, elim) = if null intros then noclause thy name elim else (intros, elim)
+ in
+ mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
+ end
+ | NONE => error ("No such predicate: " ^ quote name)
+
+(* updaters *)
+
+fun apfst3 f (x, y, z) = (f x, y, z)
+fun apsnd3 f (x, y, z) = (x, f y, z)
+fun aptrd3 f (x, y, z) = (x, y, f z)
+
+fun add_predfun name mode data =
+ let
+ val add = (apsnd o apfst3 o cons) (mode, mk_predfun_data data)
+ in PredData.map (Graph.map_node name (map_pred_data add)) end
+
+fun is_inductive_predicate thy name =
+ is_some (try (Inductive.the_inductive (ProofContext.init thy)) name)
+
+fun depending_preds_of thy (key, value) =
+ let
+ val intros = (#intros o rep_pred_data) value
+ in
+ fold Term.add_const_names (map Thm.prop_of intros) []
+ |> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c))
+ end;
+
+
+(* code dependency graph *)
+(*
+fun dependencies_of thy name =
+ let
+ val (intros, elim, nparams) = fetch_pred_data thy name
+ val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
+ val keys = depending_preds_of thy intros
+ in
+ (data, keys)
+ end;
+*)
+(* guessing number of parameters *)
+fun find_indexes pred xs =
+ let
+ fun find is n [] = is
+ | find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs;
+ in rev (find [] 0 xs) end;
+
+fun guess_nparams T =
+ let
+ val argTs = binder_types T
+ val nparams = fold (curry Int.max)
+ (map (fn x => x + 1) (find_indexes is_predT argTs)) 0
+ in nparams end;
+
+fun add_intro thm thy = let
+ val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm)))
+ fun cons_intro gr =
+ case try (Graph.get_node gr) name of
+ SOME pred_data => Graph.map_node name (map_pred_data
+ (apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr
+ | NONE =>
+ let
+ val nparams = the_default (guess_nparams T) (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name)
+ in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), ([], [], []))) gr end;
+ in PredData.map cons_intro thy end
+
+fun set_elim thm = let
+ val (name, _) = dest_Const (fst
+ (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
+ fun set (intros, _, nparams) = (intros, SOME thm, nparams)
+ in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
+
+fun set_nparams name nparams = let
+ fun set (intros, elim, _ ) = (intros, elim, nparams)
+ in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
+
+fun register_predicate (pre_intros, pre_elim, nparams) thy =
+ let
+ val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros))))
+ (* preprocessing *)
+ val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros)
+ val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
+ in
+ if not (member (op =) (Graph.keys (PredData.get thy)) name) then
+ PredData.map
+ (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy
+ else thy
+ end
+
+fun register_intros pre_intros thy =
+ let
+ val (c, T) = dest_Const (fst (strip_intro_concl 0 (prop_of (hd pre_intros))))
+ val _ = Output.tracing ("Registering introduction rules of " ^ c)
+ val _ = Output.tracing (commas (map (Display.string_of_thm_global thy) pre_intros))
+ val nparams = guess_nparams T
+ val pre_elim =
+ (Drule.standard o (setmp quick_and_dirty true (SkipProof.make_thm thy)))
+ (mk_casesrule (ProofContext.init thy) nparams pre_intros)
+ in register_predicate (pre_intros, pre_elim, nparams) thy end
+
+fun set_generator_name pred mode name =
+ let
+ val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE))
+ in
+ PredData.map (Graph.map_node pred (map_pred_data set))
+ end
+
+fun set_sizelim_function_name pred mode name =
+ let
+ val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE))
+ in
+ PredData.map (Graph.map_node pred (map_pred_data set))
+ end
+
+(** data structures for generic compilation for different monads **)
+
+(* maybe rename functions more generic:
+ mk_predT -> mk_monadT; dest_predT -> dest_monadT
+ mk_single -> mk_return (?)
+*)
+datatype compilation_funs = CompilationFuns of {
+ mk_predT : typ -> typ,
+ dest_predT : typ -> typ,
+ mk_bot : typ -> term,
+ mk_single : term -> term,
+ mk_bind : term * term -> term,
+ mk_sup : term * term -> term,
+ mk_if : term -> term,
+ mk_not : term -> term,
+(* funT_of : mode -> typ -> typ, *)
+(* mk_fun_of : theory -> (string * typ) -> mode -> term, *)
+ mk_map : typ -> typ -> term -> term -> term,
+ lift_pred : term -> term
+};
+
+fun mk_predT (CompilationFuns funs) = #mk_predT funs
+fun dest_predT (CompilationFuns funs) = #dest_predT funs
+fun mk_bot (CompilationFuns funs) = #mk_bot funs
+fun mk_single (CompilationFuns funs) = #mk_single funs
+fun mk_bind (CompilationFuns funs) = #mk_bind funs
+fun mk_sup (CompilationFuns funs) = #mk_sup funs
+fun mk_if (CompilationFuns funs) = #mk_if funs
+fun mk_not (CompilationFuns funs) = #mk_not funs
+(*fun funT_of (CompilationFuns funs) = #funT_of funs*)
+(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*)
+fun mk_map (CompilationFuns funs) = #mk_map funs
+fun lift_pred (CompilationFuns funs) = #lift_pred funs
+
+fun funT_of compfuns (iss, is) T =
+ let
+ val Ts = binder_types T
+ val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
+ val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs
+ in
+ (paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs))
+ end;
+
+fun mk_fun_of compfuns thy (name, T) mode =
+ Const (predfun_name_of thy name mode, funT_of compfuns mode T)
+
+
+structure PredicateCompFuns =
+struct
+
+fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T])
+
+fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T
+ | dest_predT T = raise TYPE ("dest_predT", [T], []);
+
+fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T);
+
+fun mk_single t =
+ let val T = fastype_of t
+ in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end;
+
+fun mk_bind (x, f) =
+ let val T as Type ("fun", [_, U]) = fastype_of f
+ in
+ Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f
+ end;
+
+val mk_sup = HOLogic.mk_binop @{const_name sup};
+
+fun mk_if cond = Const (@{const_name Predicate.if_pred},
+ HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
+
+fun mk_not t = let val T = mk_predT HOLogic.unitT
+ in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
+
+fun mk_Enum f =
+ let val T as Type ("fun", [T', _]) = fastype_of f
+ in
+ Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f
+ end;
+
+fun mk_Eval (f, x) =
+ let
+ val T = fastype_of x
+ in
+ Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x
+ end;
+
+fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map},
+ (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp;
+
+val lift_pred = I
+
+val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
+ mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
+ mk_map = mk_map, lift_pred = lift_pred};
+
+end;
+
+structure RPredCompFuns =
+struct
+
+fun mk_rpredT T =
+ @{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"})
+
+fun dest_rpredT (Type ("fun", [_,
+ Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T
+ | dest_rpredT T = raise TYPE ("dest_rpredT", [T], []);
+
+fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T)
+
+fun mk_single t =
+ let
+ val T = fastype_of t
+ in
+ Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t
+ end;
+
+fun mk_bind (x, f) =
+ let
+ val T as (Type ("fun", [_, U])) = fastype_of f
+ in
+ Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f
+ end
+
+val mk_sup = HOLogic.mk_binop @{const_name RPred.supp}
+
+fun mk_if cond = Const (@{const_name RPred.if_rpred},
+ HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond;
+
+fun mk_not t = error "Negation is not defined for RPred"
+
+fun mk_map t = error "FIXME" (*FIXME*)
+
+fun lift_pred t =
+ let
+ val T = PredicateCompFuns.dest_predT (fastype_of t)
+ val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T
+ in
+ Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t
+ end;
+
+val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot,
+ mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
+ mk_map = mk_map, lift_pred = lift_pred};
+
+end;
+(* for external use with interactive mode *)
+val pred_compfuns = PredicateCompFuns.compfuns
+val rpred_compfuns = RPredCompFuns.compfuns;
+
+fun lift_random random =
+ let
+ val T = dest_randomT (fastype_of random)
+ in
+ Const (@{const_name lift_random}, (@{typ Random.seed} -->
+ HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
+ RPredCompFuns.mk_rpredT T) $ random
+ end;
+
+fun sizelim_funT_of compfuns (iss, is) T =
+ let
+ val Ts = binder_types T
+ val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
+ val paramTs' = map2 (fn SOME is => sizelim_funT_of PredicateCompFuns.compfuns ([], is) | NONE => I) iss paramTs
+ in
+ (paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs))
+ end;
+
+fun mk_sizelim_fun_of compfuns thy (name, T) mode =
+ Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T)
+
+fun mk_generator_of compfuns thy (name, T) mode =
+ Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T)
+
+(* Mode analysis *)
+
+(*** check if a term contains only constructor functions ***)
+fun is_constrt thy =
+ let
+ val cnstrs = flat (maps
+ (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
+ (Symtab.dest (Datatype.get_all thy)));
+ fun check t = (case strip_comb t of
+ (Free _, []) => true
+ | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
+ (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
+ | _ => false)
+ | _ => false)
+ in check end;
+
+(*** check if a type is an equality type (i.e. doesn't contain fun)
+ FIXME this is only an approximation ***)
+fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
+ | is_eqT _ = true;
+
+fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
+val terms_vs = distinct (op =) o maps term_vs;
+
+(** collect all Frees in a term (with duplicates!) **)
+fun term_vTs tm =
+ fold_aterms (fn Free xT => cons xT | _ => I) tm [];
+
+(*FIXME this function should not be named merge... make it local instead*)
+fun merge xs [] = xs
+ | merge [] ys = ys
+ | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
+ else y::merge (x::xs) ys;
+
+fun subsets i j = if i <= j then
+ let val is = subsets (i+1) j
+ in merge (map (fn ks => i::ks) is) is end
+ else [[]];
+
+(* FIXME: should be in library - cprod = map_prod I *)
+fun cprod ([], ys) = []
+ | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
+
+fun cprods xss = foldr (map op :: o cprod) [[]] xss;
+
+fun cprods_subset [] = [[]]
+ | cprods_subset (xs :: xss) =
+ let
+ val yss = (cprods_subset xss)
+ in maps (fn ys => map (fn x => cons x ys) xs) yss @ yss end
+
+(*TODO: cleanup function and put together with modes_of_term *)
+(*
+fun modes_of_param default modes t = let
+ val (vs, t') = strip_abs t
+ val b = length vs
+ fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
+ let
+ val (args1, args2) =
+ if length args < length iss then
+ error ("Too few arguments for inductive predicate " ^ name)
+ else chop (length iss) args;
+ val k = length args2;
+ val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1)
+ (1 upto b)
+ val partial_mode = (1 upto k) \\ perm
+ in
+ if not (partial_mode subset is) then [] else
+ let
+ val is' =
+ (fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm [])
+ |> fold (fn i => if i > k then cons (i - k + b) else I) is
+
+ val res = map (fn x => Mode (m, is', x)) (cprods (map
+ (fn (NONE, _) => [NONE]
+ | (SOME js, arg) => map SOME (filter
+ (fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
+ (iss ~~ args1)))
+ in res end
+ end)) (AList.lookup op = modes name)
+ in case strip_comb t' of
+ (Const (name, _), args) => the_default default (mk_modes name args)
+ | (Var ((name, _), _), args) => the (mk_modes name args)
+ | (Free (name, _), args) => the (mk_modes name args)
+ | _ => default end
+
+and
+*)
+fun modes_of_term modes t =
+ let
+ val ks = map_index (fn (i, T) => (i, NONE)) (binder_types (fastype_of t));
+ val default = [Mode (([], ks), ks, [])];
+ fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
+ let
+ val (args1, args2) =
+ if length args < length iss then
+ error ("Too few arguments for inductive predicate " ^ name)
+ else chop (length iss) args;
+ val k = length args2;
+ val prfx = map (rpair NONE) (1 upto k)
+ in
+ if not (is_prefix op = prfx is) then [] else
+ let val is' = List.drop (is, k)
+ in map (fn x => Mode (m, is', x)) (cprods (map
+ (fn (NONE, _) => [NONE]
+ | (SOME js, arg) => map SOME (filter
+ (fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
+ (iss ~~ args1)))
+ end
+ end)) (AList.lookup op = modes name)
+
+ in
+ case strip_comb (Envir.eta_contract t) of
+ (Const (name, _), args) => the_default default (mk_modes name args)
+ | (Var ((name, _), _), args) => the (mk_modes name args)
+ | (Free (name, _), args) => the (mk_modes name args)
+ | (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *)
+ | _ => default
+ end
+
+fun select_mode_prem thy modes vs ps =
+ find_first (is_some o snd) (ps ~~ map
+ (fn Prem (us, t) => find_first (fn Mode (_, is, _) =>
+ let
+ val (in_ts, out_ts) = split_smode is us;
+ val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
+ val vTs = maps term_vTs out_ts';
+ val dupTs = map snd (duplicates (op =) vTs) @
+ List.mapPartial (AList.lookup (op =) vTs) vs;
+ in
+ terms_vs (in_ts @ in_ts') subset vs andalso
+ forall (is_eqT o fastype_of) in_ts' andalso
+ term_vs t subset vs andalso
+ forall is_eqT dupTs
+ end)
+ (modes_of_term modes t handle Option =>
+ error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
+ | Negprem (us, t) => find_first (fn Mode (_, is, _) =>
+ length us = length is andalso
+ terms_vs us subset vs andalso
+ term_vs t subset vs)
+ (modes_of_term modes t handle Option =>
+ error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
+ | Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), [], []))
+ else NONE
+ ) ps);
+
+fun fold_prem f (Prem (args, _)) = fold f args
+ | fold_prem f (Negprem (args, _)) = fold f args
+ | fold_prem f (Sidecond t) = f t
+
+fun all_subsets [] = [[]]
+ | all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end
+
+fun generator vTs v =
+ let
+ val T = the (AList.lookup (op =) vTs v)
+ in
+ (Generator (v, T), Mode (([], []), [], []))
+ end;
+
+fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t)
+ | gen_prem (Negprem (us, t)) = error "it is a negated prem"
+ | gen_prem (Sidecond t) = error "it is a sidecond"
+ | gen_prem _ = error "gen_prem : invalid input for gen_prem"
+
+fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) =
+ if member (op =) param_vs v then
+ GeneratorPrem (us, t)
+ else p
+ | param_gen_prem param_vs p = p
+
+fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) =
+ let
+ (*
+ val _ = Output.tracing ("param_vs:" ^ commas param_vs)
+ val _ = Output.tracing ("iss:" ^
+ commas (map (fn is => case is of SOME is => string_of_smode is | NONE => "NONE") iss))
+ *)
+ val modes' = modes @ List.mapPartial
+ (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
+ (param_vs ~~ iss);
+ val gen_modes' = gen_modes @ List.mapPartial
+ (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
+ (param_vs ~~ iss);
+ val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts []))
+ val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps [])
+ fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs)
+ | check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of
+ NONE =>
+ (if with_generator then
+ (case select_mode_prem thy gen_modes' vs ps of
+ SOME (p as Prem _, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps)
+ (case p of Prem (us, _) => vs union terms_vs us | _ => vs)
+ (filter_out (equal p) ps)
+ | _ =>
+ let
+ val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length))
+ in
+ case (find_first (fn generator_vs => is_some
+ (select_mode_prem thy modes' (vs union generator_vs) ps)) all_generator_vs) of
+ SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps)
+ (vs union generator_vs) ps
+ | NONE => let
+ val _ = Output.tracing ("ps:" ^ (commas
+ (map (fn p => string_of_moded_prem thy (p, Mode (([], []), [], []))) ps)))
+ in (*error "mode analysis failed"*)NONE end
+ end)
+ else
+ NONE)
+ | SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps)
+ (case p of Prem (us, _) => vs union terms_vs us | _ => vs)
+ (filter_out (equal p) ps))
+ val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts));
+ val in_vs = terms_vs in_ts;
+ val concl_vs = terms_vs ts
+ in
+ if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
+ forall (is_eqT o fastype_of) in_ts' then
+ case check_mode_prems [] (param_vs union in_vs) ps of
+ NONE => NONE
+ | SOME (acc_ps, vs) =>
+ if with_generator then
+ SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs)))
+ else
+ if concl_vs subset vs then SOME (ts, rev acc_ps) else NONE
+ else NONE
+ end;
+
+fun check_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) =
+ let val SOME rs = AList.lookup (op =) clauses p
+ in (p, List.filter (fn m => case find_index
+ (is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of
+ ~1 => true
+ | i => (Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^
+ p ^ " violates mode " ^ string_of_mode m);
+ Output.tracing (commas (map (Syntax.string_of_term_global thy) (fst (nth rs i)))); false)) ms)
+ end;
+
+fun get_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) =
+ let
+ val SOME rs = AList.lookup (op =) clauses p
+ in
+ (p, map (fn m =>
+ (m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms)
+ end;
+
+fun fixp f (x : (string * mode list) list) =
+ let val y = f x
+ in if x = y then x else fixp f y end;
+
+fun infer_modes thy extra_modes all_modes param_vs clauses =
+ let
+ val modes =
+ fixp (fn modes =>
+ map (check_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes)
+ all_modes
+ in
+ map (get_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes
+ end;
+
+fun remove_from rem [] = []
+ | remove_from rem ((k, vs) :: xs) =
+ (case AList.lookup (op =) rem k of
+ NONE => (k, vs)
+ | SOME vs' => (k, vs \\ vs'))
+ :: remove_from rem xs
+
+fun infer_modes_with_generator thy extra_modes all_modes param_vs clauses =
+ let
+ val prednames = map fst clauses
+ val extra_modes = all_modes_of thy
+ val gen_modes = all_generator_modes_of thy
+ |> filter_out (fn (name, _) => member (op =) prednames name)
+ val starting_modes = remove_from extra_modes all_modes
+ val modes =
+ fixp (fn modes =>
+ map (check_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes)
+ starting_modes
+ in
+ map (get_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes
+ end;
+
+(* term construction *)
+
+fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of
+ NONE => (Free (s, T), (names, (s, [])::vs))
+ | SOME xs =>
+ let
+ val s' = Name.variant names s;
+ val v = Free (s', T)
+ in
+ (v, (s'::names, AList.update (op =) (s, v::xs) vs))
+ end);
+
+fun distinct_v (Free (s, T)) nvs = mk_v nvs s T
+ | distinct_v (t $ u) nvs =
+ let
+ val (t', nvs') = distinct_v t nvs;
+ val (u', nvs'') = distinct_v u nvs';
+ in (t' $ u', nvs'') end
+ | distinct_v x nvs = (x, nvs);
+
+fun compile_match thy compfuns eqs eqs' out_ts success_t =
+ let
+ val eqs'' = maps mk_eq eqs @ eqs'
+ val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) [];
+ val name = Name.variant names "x";
+ val name' = Name.variant (name :: names) "y";
+ val T = mk_tupleT (map fastype_of out_ts);
+ val U = fastype_of success_t;
+ val U' = dest_predT compfuns U;
+ val v = Free (name, T);
+ val v' = Free (name', T);
+ in
+ lambda v (fst (Datatype.make_case
+ (ProofContext.init thy) DatatypeCase.Quiet [] v
+ [(mk_tuple out_ts,
+ if null eqs'' then success_t
+ else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $
+ foldr1 HOLogic.mk_conj eqs'' $ success_t $
+ mk_bot compfuns U'),
+ (v', mk_bot compfuns U')]))
+ end;
+
+(*FIXME function can be removed*)
+fun mk_funcomp f t =
+ let
+ val names = Term.add_free_names t [];
+ val Ts = binder_types (fastype_of t);
+ val vs = map Free
+ (Name.variant_list names (replicate (length Ts) "x") ~~ Ts)
+ in
+ fold_rev lambda vs (f (list_comb (t, vs)))
+ end;
+(*
+fun compile_param_ext thy compfuns modes (NONE, t) = t
+ | compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
+ let
+ val (vs, u) = strip_abs t
+ val (ivs, ovs) = split_mode is vs
+ val (f, args) = strip_comb u
+ val (params, args') = chop (length ms) args
+ val (inargs, outargs) = split_mode is' args'
+ val b = length vs
+ val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b)
+ val outp_perm =
+ snd (split_mode is perm)
+ |> map (fn i => i - length (filter (fn x => x < i) is'))
+ val names = [] -- TODO
+ val out_names = Name.variant_list names (replicate (length outargs) "x")
+ val f' = case f of
+ Const (name, T) =>
+ if AList.defined op = modes name then
+ mk_predfun_of thy compfuns (name, T) (iss, is')
+ else error "compile param: Not an inductive predicate with correct mode"
+ | Free (name, T) => Free (name, param_funT_of compfuns T (SOME is'))
+ val outTs = dest_tupleT (dest_predT compfuns (body_type (fastype_of f')))
+ val out_vs = map Free (out_names ~~ outTs)
+ val params' = map (compile_param thy modes) (ms ~~ params)
+ val f_app = list_comb (f', params' @ inargs)
+ val single_t = (mk_single compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm)))
+ val match_t = compile_match thy compfuns [] [] out_vs single_t
+ in list_abs (ivs,
+ mk_bind compfuns (f_app, match_t))
+ end
+ | compile_param_ext _ _ _ _ = error "compile params"
+*)
+
+fun compile_param neg_in_sizelim size thy compfuns (NONE, t) = t
+ | compile_param neg_in_sizelim size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) =
+ let
+ val (f, args) = strip_comb (Envir.eta_contract t)
+ val (params, args') = chop (length ms) args
+ val params' = map (compile_param neg_in_sizelim size thy compfuns) (ms ~~ params)
+ val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
+ val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
+ val f' =
+ case f of
+ Const (name, T) =>
+ mk_fun_of compfuns thy (name, T) (iss, is')
+ | Free (name, T) =>
+ case neg_in_sizelim of
+ SOME _ => Free (name, sizelim_funT_of compfuns (iss, is') T)
+ | NONE => Free (name, funT_of compfuns (iss, is') T)
+
+ | _ => error ("PredicateCompiler: illegal parameter term")
+ in
+ (case neg_in_sizelim of SOME size_t =>
+ (fn t =>
+ let
+ val Ts = fst (split_last (binder_types (fastype_of t)))
+ val names = map (fn i => "x" ^ string_of_int i) (1 upto length Ts)
+ in
+ list_abs (names ~~ Ts, list_comb (t, (map Bound ((length Ts) - 1 downto 0)) @ [size_t]))
+ end)
+ | NONE => I)
+ (list_comb (f', params' @ args'))
+ end
+
+fun compile_expr neg_in_sizelim size thy ((Mode (mode, is, ms)), t) =
+ case strip_comb t of
+ (Const (name, T), params) =>
+ let
+ val params' = map (compile_param neg_in_sizelim size thy PredicateCompFuns.compfuns) (ms ~~ params)
+ val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
+ in
+ list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params')
+ end
+ | (Free (name, T), args) =>
+ let
+ val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
+ in
+ list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args)
+ end;
+
+fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) inargs =
+ case strip_comb t of
+ (Const (name, T), params) =>
+ let
+ val params' = map (compile_param NONE size thy PredicateCompFuns.compfuns) (ms ~~ params)
+ in
+ list_comb (mk_generator_of compfuns thy (name, T) mode, params' @ inargs)
+ end
+ | (Free (name, T), params) =>
+ lift_pred compfuns
+ (list_comb (Free (name, sizelim_funT_of PredicateCompFuns.compfuns ([], is) T), params @ inargs))
+
+
+(** specific rpred functions -- move them to the correct place in this file *)
+
+fun mk_Eval_of size ((x, T), NONE) names = (x, names)
+ | mk_Eval_of size ((x, T), SOME mode) names =
+ let
+ val Ts = binder_types T
+ (*val argnames = Name.variant_list names
+ (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
+ val args = map Free (argnames ~~ Ts)
+ val (inargs, outargs) = split_smode mode args*)
+ fun mk_split_lambda [] t = lambda (Free (Name.variant names "x", HOLogic.unitT)) t
+ | mk_split_lambda [x] t = lambda x t
+ | mk_split_lambda xs t =
+ let
+ fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
+ | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
+ in
+ mk_split_lambda' xs t
+ end;
+ fun mk_arg (i, T) =
+ let
+ val vname = Name.variant names ("x" ^ string_of_int i)
+ val default = Free (vname, T)
+ in
+ case AList.lookup (op =) mode i of
+ NONE => (([], [default]), [default])
+ | SOME NONE => (([default], []), [default])
+ | SOME (SOME pis) =>
+ case HOLogic.strip_tupleT T of
+ [] => error "pair mode but unit tuple" (*(([default], []), [default])*)
+ | [_] => error "pair mode but not a tuple" (*(([default], []), [default])*)
+ | Ts =>
+ let
+ val vnames = Name.variant_list names
+ (map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
+ (1 upto length Ts))
+ val args = map Free (vnames ~~ Ts)
+ fun split_args (i, arg) (ins, outs) =
+ if member (op =) pis i then
+ (arg::ins, outs)
+ else
+ (ins, arg::outs)
+ val (inargs, outargs) = fold_rev split_args ((1 upto length Ts) ~~ args) ([], [])
+ fun tuple args = if null args then [] else [HOLogic.mk_tuple args]
+ in ((tuple inargs, tuple outargs), args) end
+ end
+ val (inoutargs, args) = split_list (map mk_arg (1 upto (length Ts) ~~ Ts))
+ val (inargs, outargs) = pairself flat (split_list inoutargs)
+ val size_t = case size of NONE => [] | SOME size_t => [size_t]
+ val r = PredicateCompFuns.mk_Eval (list_comb (x, inargs @ size_t), mk_tuple outargs)
+ val t = fold_rev mk_split_lambda args r
+ in
+ (t, names)
+ end;
+
+fun compile_arg size thy param_vs iss arg =
+ let
+ val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
+ fun map_params (t as Free (f, T)) =
+ if member (op =) param_vs f then
+ case (the (AList.lookup (op =) (param_vs ~~ iss) f)) of
+ SOME is => let val T' = funT_of PredicateCompFuns.compfuns ([], is) T
+ in fst (mk_Eval_of size ((Free (f, T'), T), SOME is) []) end
+ | NONE => t
+ else t
+ | map_params t = t
+ in map_aterms map_params arg end
+
+fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) =
+ let
+ fun check_constrt t (names, eqs) =
+ if is_constrt thy t then (t, (names, eqs)) else
+ let
+ val s = Name.variant names "x";
+ val v = Free (s, fastype_of t)
+ in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;
+
+ val (in_ts, out_ts) = split_smode is ts;
+ val (in_ts', (all_vs', eqs)) =
+ fold_map check_constrt in_ts (all_vs, []);
+
+ fun compile_prems out_ts' vs names [] =
+ let
+ val (out_ts'', (names', eqs')) =
+ fold_map check_constrt out_ts' (names, []);
+ val (out_ts''', (names'', constr_vs)) = fold_map distinct_v
+ out_ts'' (names', map (rpair []) vs);
+ in
+ (* termify code:
+ compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
+ (mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts)))
+ *)
+ compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
+ (final_term out_ts)
+ end
+ | compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) =
+ let
+ val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
+ val (out_ts', (names', eqs)) =
+ fold_map check_constrt out_ts (names, [])
+ val (out_ts'', (names'', constr_vs')) = fold_map distinct_v
+ out_ts' ((names', map (rpair []) vs))
+ val (compiled_clause, rest) = case p of
+ Prem (us, t) =>
+ let
+ val (in_ts, out_ts''') = split_smode is us;
+ val in_ts = map (compile_arg size thy param_vs iss) in_ts
+ val args = case size of
+ NONE => in_ts
+ | SOME size_t => in_ts @ [size_t]
+ val u = lift_pred compfuns
+ (list_comb (compile_expr NONE size thy (mode, t), args))
+ val rest = compile_prems out_ts''' vs' names'' ps
+ in
+ (u, rest)
+ end
+ | Negprem (us, t) =>
+ let
+ val (in_ts, out_ts''') = split_smode is us
+ val u = lift_pred compfuns
+ (mk_not PredicateCompFuns.compfuns (list_comb (compile_expr size NONE thy (mode, t), in_ts)))
+ val rest = compile_prems out_ts''' vs' names'' ps
+ in
+ (u, rest)
+ end
+ | Sidecond t =>
+ let
+ val rest = compile_prems [] vs' names'' ps;
+ in
+ (mk_if compfuns t, rest)
+ end
+ | GeneratorPrem (us, t) =>
+ let
+ val (in_ts, out_ts''') = split_smode is us;
+ val args = case size of
+ NONE => in_ts
+ | SOME size_t => in_ts @ [size_t]
+ val u = compile_gen_expr size thy compfuns (mode, t) args
+ val rest = compile_prems out_ts''' vs' names'' ps
+ in
+ (u, rest)
+ end
+ | Generator (v, T) =>
+ let
+ val u = lift_random (HOLogic.mk_random T (the size))
+ val rest = compile_prems [Free (v, T)] vs' names'' ps;
+ in
+ (u, rest)
+ end
+ in
+ compile_match thy compfuns constr_vs' eqs out_ts''
+ (mk_bind compfuns (compiled_clause, rest))
+ end
+ val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps;
+ in
+ mk_bind compfuns (mk_single compfuns inp, prem_t)
+ end
+
+fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls =
+ let
+ val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T)
+ val (Us1, Us2) = split_smodeT (snd mode) Ts2
+ val funT_of = if use_size then sizelim_funT_of else funT_of
+ val Ts1' = map2 (fn NONE => I | SOME is => funT_of PredicateCompFuns.compfuns ([], is)) (fst mode) Ts1
+ val size_name = Name.variant (all_vs @ param_vs) "size"
+ fun mk_input_term (i, NONE) =
+ [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))]
+ | mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of
+ [] => error "strange unit input"
+ | [T] => [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))]
+ | Ts => let
+ val vnames = Name.variant_list (all_vs @ param_vs)
+ (map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
+ pis)
+ in if null pis then []
+ else [HOLogic.mk_tuple (map Free (vnames ~~ map (fn j => nth Ts (j - 1)) pis))] end
+ val in_ts = maps mk_input_term (snd mode)
+ val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1'
+ val size = Free (size_name, @{typ "code_numeral"})
+ val decr_size =
+ if use_size then
+ SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"})
+ $ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"}))
+ else
+ NONE
+ val cl_ts =
+ map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts))
+ thy all_vs param_vs mode (mk_tuple in_ts)) moded_cls;
+ val t = foldr1 (mk_sup compfuns) cl_ts
+ val T' = mk_predT compfuns (mk_tupleT Us2)
+ val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
+ $ HOLogic.mk_eq (size, @{term "0 :: code_numeral"})
+ $ mk_bot compfuns (dest_predT compfuns T') $ t
+ val fun_const = mk_fun_of compfuns thy (s, T) mode
+ val eq = if use_size then
+ (list_comb (fun_const, params @ in_ts @ [size]), size_t)
+ else
+ (list_comb (fun_const, params @ in_ts), t)
+ in
+ HOLogic.mk_Trueprop (HOLogic.mk_eq eq)
+ end;
+
+(* special setup for simpset *)
+val HOL_basic_ss' = HOL_basic_ss addsimps (@{thms "HOL.simp_thms"} @ [@{thm Pair_eq}])
+ setSolver (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
+ setSolver (mk_solver "True_solver" (fn _ => rtac @{thm TrueI}))
+
+(* Definition of executable functions and their intro and elim rules *)
+
+fun print_arities arities = tracing ("Arities:\n" ^
+ cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^
+ space_implode " -> " (map
+ (fn NONE => "X" | SOME k' => string_of_int k')
+ (ks @ [SOME k]))) arities));
+
+fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy =
+let
+ val Ts = binder_types (fastype_of pred)
+ val funtrm = Const (mode_id, funT)
+ val (Ts1, Ts2) = chop (length iss) Ts;
+ val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1
+ val param_names = Name.variant_list []
+ (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1)));
+ val params = map Free (param_names ~~ Ts1')
+ fun mk_args (i, T) argnames =
+ let
+ val vname = Name.variant (param_names @ argnames) ("x" ^ string_of_int (length Ts1' + i))
+ val default = (Free (vname, T), vname :: argnames)
+ in
+ case AList.lookup (op =) is i of
+ NONE => default
+ | SOME NONE => default
+ | SOME (SOME pis) =>
+ case HOLogic.strip_tupleT T of
+ [] => default
+ | [_] => default
+ | Ts =>
+ let
+ val vnames = Name.variant_list (param_names @ argnames)
+ (map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j)
+ (1 upto (length Ts)))
+ in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames @ argnames) end
+ end
+ val (args, argnames) = fold_map mk_args (1 upto (length Ts2) ~~ Ts2) []
+ val (inargs, outargs) = split_smode is args
+ val param_names' = Name.variant_list (param_names @ argnames)
+ (map (fn i => "p" ^ string_of_int i) (1 upto (length iss)))
+ val param_vs = map Free (param_names' ~~ Ts1)
+ val (params', names) = fold_map (mk_Eval_of NONE) ((params ~~ Ts1) ~~ iss) []
+ val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ args))
+ val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ args))
+ val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params')
+ val funargs = params @ inargs
+ val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
+ if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs))
+ val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
+ mk_tuple outargs))
+ val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)
+ val simprules = [defthm, @{thm eval_pred},
+ @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]
+ val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1
+ val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y"]) [] introtrm (fn {...} => unfolddef_tac)
+ val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
+ val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P)
+ val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac)
+in
+ (introthm, elimthm)
+end;
+
+fun create_constname_of_mode thy prefix name mode =
+ let
+ fun string_of_mode mode = if null mode then "0"
+ else space_implode "_" (map (fn (i, NONE) => string_of_int i | (i, SOME pis) => string_of_int i ^ "p"
+ ^ space_implode "p" (map string_of_int pis)) mode)
+ val HOmode = space_implode "_and_"
+ (fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) [])
+ in
+ (Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^
+ (if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode))
+ end;
+
+fun split_tupleT is T =
+ let
+ fun split_tuple' _ _ [] = ([], [])
+ | split_tuple' is i (T::Ts) =
+ (if i mem is then apfst else apsnd) (cons T)
+ (split_tuple' is (i+1) Ts)
+ in
+ split_tuple' is 1 (HOLogic.strip_tupleT T)
+ end
+
+fun mk_arg xin xout pis T =
+ let
+ val n = length (HOLogic.strip_tupleT T)
+ val ni = length pis
+ fun mk_proj i j t =
+ (if i = j then I else HOLogic.mk_fst)
+ (funpow (i - 1) HOLogic.mk_snd t)
+ fun mk_arg' i (si, so) = if i mem pis then
+ (mk_proj si ni xin, (si+1, so))
+ else
+ (mk_proj so (n - ni) xout, (si, so+1))
+ val (args, _) = fold_map mk_arg' (1 upto n) (1, 1)
+ in
+ HOLogic.mk_tuple args
+ end
+
+fun create_definitions preds (name, modes) thy =
+ let
+ val compfuns = PredicateCompFuns.compfuns
+ val T = AList.lookup (op =) preds name |> the
+ fun create_definition (mode as (iss, is)) thy = let
+ val mode_cname = create_constname_of_mode thy "" name mode
+ val mode_cbasename = Long_Name.base_name mode_cname
+ val Ts = binder_types T
+ val (Ts1, Ts2) = chop (length iss) Ts
+ val (Us1, Us2) = split_smodeT is Ts2
+ val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1
+ val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2))
+ val names = Name.variant_list []
+ (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
+ (* old *)
+ (*
+ val xs = map Free (names ~~ (Ts1' @ Ts2))
+ val (xparams, xargs) = chop (length iss) xs
+ val (xins, xouts) = split_smode is xargs
+ *)
+ (* new *)
+ val param_names = Name.variant_list []
+ (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1')))
+ val xparams = map Free (param_names ~~ Ts1')
+ fun mk_vars (i, T) names =
+ let
+ val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i))
+ in
+ case AList.lookup (op =) is i of
+ NONE => ((([], [Free (vname, T)]), Free (vname, T)), vname :: names)
+ | SOME NONE => ((([Free (vname, T)], []), Free (vname, T)), vname :: names)
+ | SOME (SOME pis) =>
+ let
+ val (Tins, Touts) = split_tupleT pis T
+ val name_in = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "in")
+ val name_out = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "out")
+ val xin = Free (name_in, HOLogic.mk_tupleT Tins)
+ val xout = Free (name_out, HOLogic.mk_tupleT Touts)
+ val xarg = mk_arg xin xout pis T
+ in (((if null Tins then [] else [xin], if null Touts then [] else [xout]), xarg), name_in :: name_out :: names) end
+ end
+ val (xinoutargs, names) = fold_map mk_vars ((1 upto (length Ts2)) ~~ Ts2) param_names
+ val (xinout, xargs) = split_list xinoutargs
+ val (xins, xouts) = pairself flat (split_list xinout)
+ val (xparams', names') = fold_map (mk_Eval_of NONE) ((xparams ~~ Ts1) ~~ iss) names
+ fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t
+ | mk_split_lambda [x] t = lambda x t
+ | mk_split_lambda xs t =
+ let
+ fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
+ | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
+ in
+ mk_split_lambda' xs t
+ end;
+ val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts
+ (list_comb (Const (name, T), xparams' @ xargs)))
+ val lhs = list_comb (Const (mode_cname, funT), xparams @ xins)
+ val def = Logic.mk_equals (lhs, predterm)
+ val ([definition], thy') = thy |>
+ Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |>
+ PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])]
+ val (intro, elim) =
+ create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy'
+ in thy'
+ |> add_predfun name mode (mode_cname, definition, intro, elim)
+ |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd
+ |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim) |> snd
+ |> Theory.checkpoint
+ end;
+ in
+ fold create_definition modes thy
+ end;
+
+fun sizelim_create_definitions preds (name, modes) thy =
+ let
+ val T = AList.lookup (op =) preds name |> the
+ fun create_definition mode thy =
+ let
+ val mode_cname = create_constname_of_mode thy "sizelim_" name mode
+ val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T
+ in
+ thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
+ |> set_sizelim_function_name name mode mode_cname
+ end;
+ in
+ fold create_definition modes thy
+ end;
+
+fun generator_funT_of (iss, is) T =
+ let
+ val Ts = binder_types T
+ val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
+ val paramTs' = map2 (fn SOME is => sizelim_funT_of PredicateCompFuns.compfuns ([], is) | NONE => I) iss paramTs
+ in
+ (paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT RPredCompFuns.compfuns (mk_tupleT outargTs))
+ end
+
+fun rpred_create_definitions preds (name, modes) thy =
+ let
+ val T = AList.lookup (op =) preds name |> the
+ fun create_definition mode thy =
+ let
+ val mode_cname = create_constname_of_mode thy "gen_" name mode
+ val funT = generator_funT_of mode T
+ in
+ thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
+ |> set_generator_name name mode mode_cname
+ end;
+ in
+ fold create_definition modes thy
+ end;
+
+(* Proving equivalence of term *)
+
+fun is_Type (Type _) = true
+ | is_Type _ = false
+
+(* returns true if t is an application of an datatype constructor *)
+(* which then consequently would be splitted *)
+(* else false *)
+fun is_constructor thy t =
+ if (is_Type (fastype_of t)) then
+ (case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of
+ NONE => false
+ | SOME info => (let
+ val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
+ val (c, _) = strip_comb t
+ in (case c of
+ Const (name, _) => name mem_string constr_consts
+ | _ => false) end))
+ else false
+
+(* MAJOR FIXME: prove_params should be simple
+ - different form of introrule for parameters ? *)
+fun prove_param thy (NONE, t) = TRY (rtac @{thm refl} 1)
+ | prove_param thy (m as SOME (Mode (mode, is, ms)), t) =
+ let
+ val (f, args) = strip_comb (Envir.eta_contract t)
+ val (params, _) = chop (length ms) args
+ val f_tac = case f of
+ Const (name, T) => simp_tac (HOL_basic_ss addsimps
+ ([@{thm eval_pred}, (predfun_definition_of thy name mode),
+ @{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
+ @{thm "snd_conv"}, @{thm pair_collapse}, @{thm "Product_Type.split_conv"}])) 1
+ | Free _ => TRY (rtac @{thm refl} 1)
+ | Abs _ => error "prove_param: No valid parameter term"
+ in
+ REPEAT_DETERM (etac @{thm thin_rl} 1)
+ THEN REPEAT_DETERM (rtac @{thm ext} 1)
+ THEN print_tac "prove_param"
+ THEN f_tac
+ THEN print_tac "after simplification in prove_args"
+ THEN (EVERY (map (prove_param thy) (ms ~~ params)))
+ THEN (REPEAT_DETERM (atac 1))
+ end
+
+fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) =
+ case strip_comb t of
+ (Const (name, T), args) =>
+ let
+ val introrule = predfun_intro_of thy name mode
+ val (args1, args2) = chop (length ms) args
+ in
+ rtac @{thm bindI} 1
+ THEN print_tac "before intro rule:"
+ (* for the right assumption in first position *)
+ THEN rotate_tac premposition 1
+ THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule)
+ THEN rtac introrule 1
+ THEN print_tac "after intro rule"
+ (* work with parameter arguments *)
+ THEN (atac 1)
+ THEN (print_tac "parameter goal")
+ THEN (EVERY (map (prove_param thy) (ms ~~ args1)))
+ THEN (REPEAT_DETERM (atac 1))
+ end
+ | _ => rtac @{thm bindI} 1
+ THEN asm_full_simp_tac
+ (HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
+ @{thm "snd_conv"}, @{thm pair_collapse}]) 1
+ THEN (atac 1)
+ THEN print_tac "after prove parameter call"
+
+
+fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st;
+
+fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st
+
+fun prove_match thy (out_ts : term list) = let
+ fun get_case_rewrite t =
+ if (is_constructor thy t) then let
+ val case_rewrites = (#case_rewrites (Datatype.the_info thy
+ ((fst o dest_Type o fastype_of) t)))
+ in case_rewrites @ (flat (map get_case_rewrite (snd (strip_comb t)))) end
+ else []
+ val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: (flat (map get_case_rewrite out_ts))
+(* replace TRY by determining if it necessary - are there equations when calling compile match? *)
+in
+ (* make this simpset better! *)
+ asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1
+ THEN print_tac "after prove_match:"
+ THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1
+ THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))
+ THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))))
+ THEN print_tac "after if simplification"
+end;
+
+(* corresponds to compile_fun -- maybe call that also compile_sidecond? *)
+
+fun prove_sidecond thy modes t =
+ let
+ fun preds_of t nameTs = case strip_comb t of
+ (f as Const (name, T), args) =>
+ if AList.defined (op =) modes name then (name, T) :: nameTs
+ else fold preds_of args nameTs
+ | _ => nameTs
+ val preds = preds_of t []
+ val defs = map
+ (fn (pred, T) => predfun_definition_of thy pred
+ ([], map (rpair NONE) (1 upto (length (binder_types T)))))
+ preds
+ in
+ (* remove not_False_eq_True when simpset in prove_match is better *)
+ simp_tac (HOL_basic_ss addsimps
+ (@{thms "HOL.simp_thms"} @ (@{thm not_False_eq_True} :: @{thm eval_pred} :: defs))) 1
+ (* need better control here! *)
+ end
+
+fun prove_clause thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) =
+ let
+ val (in_ts, clause_out_ts) = split_smode is ts;
+ fun prove_prems out_ts [] =
+ (prove_match thy out_ts)
+ THEN print_tac "before simplifying assumptions"
+ THEN asm_full_simp_tac HOL_basic_ss' 1
+ THEN print_tac "before single intro rule"
+ THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
+ | prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
+ let
+ val premposition = (find_index (equal p) clauses) + nargs
+ val rest_tac = (case p of Prem (us, t) =>
+ let
+ val (_, out_ts''') = split_smode is us
+ val rec_tac = prove_prems out_ts''' ps
+ in
+ print_tac "before clause:"
+ THEN asm_simp_tac HOL_basic_ss 1
+ THEN print_tac "before prove_expr:"
+ THEN prove_expr thy (mode, t, us) premposition
+ THEN print_tac "after prove_expr:"
+ THEN rec_tac
+ end
+ | Negprem (us, t) =>
+ let
+ val (_, out_ts''') = split_smode is us
+ val rec_tac = prove_prems out_ts''' ps
+ val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
+ val (_, params) = strip_comb t
+ in
+ rtac @{thm bindI} 1
+ THEN (if (is_some name) then
+ simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1
+ THEN rtac @{thm not_predI} 1
+ THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
+ THEN (REPEAT_DETERM (atac 1))
+ (* FIXME: work with parameter arguments *)
+ THEN (EVERY (map (prove_param thy) (param_modes ~~ params)))
+ else
+ rtac @{thm not_predI'} 1)
+ THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
+ THEN rec_tac
+ end
+ | Sidecond t =>
+ rtac @{thm bindI} 1
+ THEN rtac @{thm if_predI} 1
+ THEN print_tac "before sidecond:"
+ THEN prove_sidecond thy modes t
+ THEN print_tac "after sidecond:"
+ THEN prove_prems [] ps)
+ in (prove_match thy out_ts)
+ THEN rest_tac
+ end;
+ val prems_tac = prove_prems in_ts moded_ps
+ in
+ rtac @{thm bindI} 1
+ THEN rtac @{thm singleI} 1
+ THEN prems_tac
+ end;
+
+fun select_sup 1 1 = []
+ | select_sup _ 1 = [rtac @{thm supI1}]
+ | select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1));
+
+fun prove_one_direction thy clauses preds modes pred mode moded_clauses =
+ let
+ val T = the (AList.lookup (op =) preds pred)
+ val nargs = length (binder_types T) - nparams_of thy pred
+ val pred_case_rule = the_elim_of thy pred
+ in
+ REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
+ THEN print_tac "before applying elim rule"
+ THEN etac (predfun_elim_of thy pred mode) 1
+ THEN etac pred_case_rule 1
+ THEN (EVERY (map
+ (fn i => EVERY' (select_sup (length moded_clauses) i) i)
+ (1 upto (length moded_clauses))))
+ THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses))
+ THEN print_tac "proved one direction"
+ end;
+
+(** Proof in the other direction **)
+
+fun prove_match2 thy out_ts = let
+ fun split_term_tac (Free _) = all_tac
+ | split_term_tac t =
+ if (is_constructor thy t) then let
+ val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t)
+ val num_of_constrs = length (#case_rewrites info)
+ (* special treatment of pairs -- because of fishing *)
+ val split_rules = case (fst o dest_Type o fastype_of) t of
+ "*" => [@{thm prod.split_asm}]
+ | _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm")
+ val (_, ts) = strip_comb t
+ in
+ (Splitter.split_asm_tac split_rules 1)
+(* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1)
+ THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *)
+ THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2))
+ THEN (EVERY (map split_term_tac ts))
+ end
+ else all_tac
+ in
+ split_term_tac (mk_tuple out_ts)
+ THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2))))
+ end
+
+(* VERY LARGE SIMILIRATIY to function prove_param
+-- join both functions
+*)
+(* TODO: remove function *)
+
+fun prove_param2 thy (NONE, t) = all_tac
+ | prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let
+ val (f, args) = strip_comb (Envir.eta_contract t)
+ val (params, _) = chop (length ms) args
+ val f_tac = case f of
+ Const (name, T) => full_simp_tac (HOL_basic_ss addsimps
+ (@{thm eval_pred}::(predfun_definition_of thy name mode)
+ :: @{thm "Product_Type.split_conv"}::[])) 1
+ | Free _ => all_tac
+ | _ => error "prove_param2: illegal parameter term"
+ in
+ print_tac "before simplification in prove_args:"
+ THEN f_tac
+ THEN print_tac "after simplification in prove_args"
+ THEN (EVERY (map (prove_param2 thy) (ms ~~ params)))
+ end
+
+
+fun prove_expr2 thy (Mode (mode, is, ms), t) =
+ (case strip_comb t of
+ (Const (name, T), args) =>
+ etac @{thm bindE} 1
+ THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
+ THEN print_tac "prove_expr2-before"
+ THEN (debug_tac (Syntax.string_of_term_global thy
+ (prop_of (predfun_elim_of thy name mode))))
+ THEN (etac (predfun_elim_of thy name mode) 1)
+ THEN print_tac "prove_expr2"
+ THEN (EVERY (map (prove_param2 thy) (ms ~~ args)))
+ THEN print_tac "finished prove_expr2"
+ | _ => etac @{thm bindE} 1)
+
+(* FIXME: what is this for? *)
+(* replace defined by has_mode thy pred *)
+(* TODO: rewrite function *)
+fun prove_sidecond2 thy modes t = let
+ fun preds_of t nameTs = case strip_comb t of
+ (f as Const (name, T), args) =>
+ if AList.defined (op =) modes name then (name, T) :: nameTs
+ else fold preds_of args nameTs
+ | _ => nameTs
+ val preds = preds_of t []
+ val defs = map
+ (fn (pred, T) => predfun_definition_of thy pred
+ ([], map (rpair NONE) (1 upto (length (binder_types T)))))
+ preds
+ in
+ (* only simplify the one assumption *)
+ full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1
+ (* need better control here! *)
+ THEN print_tac "after sidecond2 simplification"
+ end
+
+fun prove_clause2 thy modes pred (iss, is) (ts, ps) i =
+ let
+ val pred_intro_rule = nth (intros_of thy pred) (i - 1)
+ val (in_ts, clause_out_ts) = split_smode is ts;
+ fun prove_prems2 out_ts [] =
+ print_tac "before prove_match2 - last call:"
+ THEN prove_match2 thy out_ts
+ THEN print_tac "after prove_match2 - last call:"
+ THEN (etac @{thm singleE} 1)
+ THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
+ THEN (asm_full_simp_tac HOL_basic_ss' 1)
+ THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
+ THEN (asm_full_simp_tac HOL_basic_ss' 1)
+ THEN SOLVED (print_tac "state before applying intro rule:"
+ THEN (rtac pred_intro_rule 1)
+ (* How to handle equality correctly? *)
+ THEN (print_tac "state before assumption matching")
+ THEN (REPEAT (atac 1 ORELSE
+ (CHANGED (asm_full_simp_tac (HOL_basic_ss' addsimps
+ [@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]) 1)
+ THEN print_tac "state after simp_tac:"))))
+ | prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
+ let
+ val rest_tac = (case p of
+ Prem (us, t) =>
+ let
+ val (_, out_ts''') = split_smode is us
+ val rec_tac = prove_prems2 out_ts''' ps
+ in
+ (prove_expr2 thy (mode, t)) THEN rec_tac
+ end
+ | Negprem (us, t) =>
+ let
+ val (_, out_ts''') = split_smode is us
+ val rec_tac = prove_prems2 out_ts''' ps
+ val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
+ val (_, params) = strip_comb t
+ in
+ print_tac "before neg prem 2"
+ THEN etac @{thm bindE} 1
+ THEN (if is_some name then
+ full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1
+ THEN etac @{thm not_predE} 1
+ THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
+ THEN (EVERY (map (prove_param2 thy) (param_modes ~~ params)))
+ else
+ etac @{thm not_predE'} 1)
+ THEN rec_tac
+ end
+ | Sidecond t =>
+ etac @{thm bindE} 1
+ THEN etac @{thm if_predE} 1
+ THEN prove_sidecond2 thy modes t
+ THEN prove_prems2 [] ps)
+ in print_tac "before prove_match2:"
+ THEN prove_match2 thy out_ts
+ THEN print_tac "after prove_match2:"
+ THEN rest_tac
+ end;
+ val prems_tac = prove_prems2 in_ts ps
+ in
+ print_tac "starting prove_clause2"
+ THEN etac @{thm bindE} 1
+ THEN (etac @{thm singleE'} 1)
+ THEN (TRY (etac @{thm Pair_inject} 1))
+ THEN print_tac "after singleE':"
+ THEN prems_tac
+ end;
+
+fun prove_other_direction thy modes pred mode moded_clauses =
+ let
+ fun prove_clause clause i =
+ (if i < length moded_clauses then etac @{thm supE} 1 else all_tac)
+ THEN (prove_clause2 thy modes pred mode clause i)
+ in
+ (DETERM (TRY (rtac @{thm unit.induct} 1)))
+ THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all})))
+ THEN (rtac (predfun_intro_of thy pred mode) 1)
+ THEN (REPEAT_DETERM (rtac @{thm refl} 2))
+ THEN (EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses))))
+ end;
+
+(** proof procedure **)
+
+fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) =
+ let
+ val ctxt = ProofContext.init thy
+ val clauses = the (AList.lookup (op =) clauses pred)
+ in
+ Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term
+ (if !do_proofs then
+ (fn _ =>
+ rtac @{thm pred_iffI} 1
+ THEN print_tac "after pred_iffI"
+ THEN prove_one_direction thy clauses preds modes pred mode moded_clauses
+ THEN print_tac "proved one direction"
+ THEN prove_other_direction thy modes pred mode moded_clauses
+ THEN print_tac "proved other direction")
+ else (fn _ => setmp quick_and_dirty true SkipProof.cheat_tac thy))
+ end;
+
+(* composition of mode inference, definition, compilation and proof *)
+
+(** auxillary combinators for table of preds and modes **)
+
+fun map_preds_modes f preds_modes_table =
+ map (fn (pred, modes) =>
+ (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table
+
+fun join_preds_modes table1 table2 =
+ map_preds_modes (fn pred => fn mode => fn value =>
+ (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1
+
+fun maps_modes preds_modes_table =
+ map (fn (pred, modes) =>
+ (pred, map (fn (mode, value) => value) modes)) preds_modes_table
+
+fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses =
+ map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred
+ (the (AList.lookup (op =) preds pred))) moded_clauses
+
+fun prove thy clauses preds modes moded_clauses compiled_terms =
+ map_preds_modes (prove_pred thy clauses preds modes)
+ (join_preds_modes moded_clauses compiled_terms)
+
+fun prove_by_skip thy _ _ _ _ compiled_terms =
+ map_preds_modes (fn pred => fn mode => fn t => Drule.standard (setmp quick_and_dirty true (SkipProof.make_thm thy) t))
+ compiled_terms
+
+fun prepare_intrs thy prednames =
+ let
+ val intrs = maps (intros_of thy) prednames
+ |> map (Logic.unvarify o prop_of)
+ val nparams = nparams_of thy (hd prednames)
+ val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name)
+ val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs)
+ val _ $ u = Logic.strip_imp_concl (hd intrs);
+ val params = List.take (snd (strip_comb u), nparams);
+ val param_vs = maps term_vs params
+ val all_vs = terms_vs intrs
+ fun dest_prem t =
+ (case strip_comb t of
+ (v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t
+ | (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of
+ Prem (ts, t) => Negprem (ts, t)
+ | Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t)))
+ | Sidecond t => Sidecond (c $ t))
+ | (c as Const (s, _), ts) =>
+ if is_registered thy s then
+ let val (ts1, ts2) = chop (nparams_of thy s) ts
+ in Prem (ts2, list_comb (c, ts1)) end
+ else Sidecond t
+ | _ => Sidecond t)
+ fun add_clause intr (clauses, arities) =
+ let
+ val _ $ t = Logic.strip_imp_concl intr;
+ val (Const (name, T), ts) = strip_comb t;
+ val (ts1, ts2) = chop nparams ts;
+ val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr);
+ val (Ts, Us) = chop nparams (binder_types T)
+ in
+ (AList.update op = (name, these (AList.lookup op = clauses name) @
+ [(ts2, prems)]) clauses,
+ AList.update op = (name, (map (fn U => (case strip_type U of
+ (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs)
+ | _ => NONE)) Ts,
+ length Us)) arities)
+ end;
+ val (clauses, arities) = fold add_clause intrs ([], []);
+ fun modes_of_arities arities =
+ (map (fn (s, (ks, k)) => (s, cprod (cprods (map
+ (fn NONE => [NONE]
+ | SOME k' => map SOME (map (map (rpair NONE)) (subsets 1 k'))) ks),
+ map (map (rpair NONE)) (subsets 1 k)))) arities)
+ fun modes_of_typ T =
+ let
+ val (Ts, Us) = chop nparams (binder_types T)
+ fun all_smodes_of_typs Ts = cprods_subset (
+ map_index (fn (i, U) =>
+ case HOLogic.strip_tupleT U of
+ [] => [(i + 1, NONE)]
+ | [U] => [(i + 1, NONE)]
+ | Us => (i + 1, NONE) ::
+ (map (pair (i + 1) o SOME) ((subsets 1 (length Us)) \\ [[], 1 upto (length Us)])))
+ Ts)
+ in
+ cprod (cprods (map (fn T => case strip_type T of
+ (Rs as _ :: _, Type ("bool", [])) => map SOME (all_smodes_of_typs Rs) | _ => [NONE]) Ts),
+ all_smodes_of_typs Us)
+ end
+ val all_modes = map (fn (s, T) => (s, modes_of_typ T)) preds
+ in (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) end;
+
+(** main function of predicate compiler **)
+
+fun add_equations_of steps prednames thy =
+ let
+ val _ = Output.tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...")
+ val _ = Output.tracing (commas (map (Display.string_of_thm_global thy) (maps (intros_of thy) prednames)))
+ val (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) =
+ prepare_intrs thy prednames
+ val _ = Output.tracing "Infering modes..."
+ val moded_clauses = #infer_modes steps thy extra_modes all_modes param_vs clauses
+ val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
+ val _ = print_modes modes
+ val _ = print_moded_clauses thy moded_clauses
+ val _ = Output.tracing "Defining executable functions..."
+ val thy' = fold (#create_definitions steps preds) modes thy
+ |> Theory.checkpoint
+ val _ = Output.tracing "Compiling equations..."
+ val compiled_terms =
+ (#compile_preds steps) thy' all_vs param_vs preds moded_clauses
+ val _ = print_compiled_terms thy' compiled_terms
+ val _ = Output.tracing "Proving equations..."
+ val result_thms = #prove steps thy' clauses preds (extra_modes @ modes)
+ moded_clauses compiled_terms
+ val qname = #qname steps
+ (* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *)
+ val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute
+ (fn thm => Context.mapping (Code.add_eqn thm) I))))
+ val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
+ [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),
+ [attrib thy ])] thy))
+ (maps_modes result_thms) thy'
+ |> Theory.checkpoint
+ in
+ thy''
+ end
+
+fun extend' value_of edges_of key (G, visited) =
+ let
+ val (G', v) = case try (Graph.get_node G) key of
+ SOME v => (G, v)
+ | NONE => (Graph.new_node (key, value_of key) G, value_of key)
+ val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited)
+ (G', key :: visited)
+ in
+ (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited')
+ end;
+
+fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, []))
+
+fun gen_add_equations steps names thy =
+ let
+ val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy
+ |> Theory.checkpoint;
+ fun strong_conn_of gr keys =
+ Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr)
+ val scc = strong_conn_of (PredData.get thy') names
+ val thy'' = fold_rev
+ (fn preds => fn thy =>
+ if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy)
+ scc thy' |> Theory.checkpoint
+ in thy'' end
+
+(* different instantiantions of the predicate compiler *)
+
+val add_equations = gen_add_equations
+ {infer_modes = infer_modes,
+ create_definitions = create_definitions,
+ compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false,
+ prove = prove,
+ are_not_defined = fn thy => forall (null o modes_of thy),
+ qname = "equation"}
+
+val add_sizelim_equations = gen_add_equations
+ {infer_modes = infer_modes,
+ create_definitions = sizelim_create_definitions,
+ compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true,
+ prove = prove_by_skip,
+ are_not_defined = fn thy => forall (null o sizelim_modes_of thy),
+ qname = "sizelim_equation"
+ }
+
+val add_quickcheck_equations = gen_add_equations
+ {infer_modes = infer_modes_with_generator,
+ create_definitions = rpred_create_definitions,
+ compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true,
+ prove = prove_by_skip,
+ are_not_defined = fn thy => forall (null o rpred_modes_of thy),
+ qname = "rpred_equation"}
+
+(** user interface **)
+
+(* code_pred_intro attribute *)
+
+fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
+
+val code_pred_intros_attrib = attrib add_intro;
+
+
+(*FIXME
+- Naming of auxiliary rules necessary?
+- add default code equations P x y z = P_i_i_i x y z
+*)
+
+val setup = PredData.put (Graph.empty) #>
+ Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro))
+ "adding alternative introduction rules for code generation of inductive predicates"
+(* Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib)
+ "adding alternative elimination rules for code generation of inductive predicates";
+ *)
+ (*FIXME name discrepancy in attribs and ML code*)
+ (*FIXME intros should be better named intro*)
+ (*FIXME why distinguished attribute for cases?*)
+
+(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *)
+fun generic_code_pred prep_const rpred raw_const lthy =
+ let
+ val thy = ProofContext.theory_of lthy
+ val const = prep_const thy raw_const
+ val lthy' = LocalTheory.theory (PredData.map
+ (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy
+ |> LocalTheory.checkpoint
+ val thy' = ProofContext.theory_of lthy'
+ val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy')
+ fun mk_cases const =
+ let
+ val nparams = nparams_of thy' const
+ val intros = intros_of thy' const
+ in mk_casesrule lthy' nparams intros end
+ val cases_rules = map mk_cases preds
+ val cases =
+ map (fn case_rule => RuleCases.Case {fixes = [],
+ assumes = [("", Logic.strip_imp_prems case_rule)],
+ binds = [], cases = []}) cases_rules
+ val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases
+ val lthy'' = lthy'
+ |> fold Variable.auto_fixes cases_rules
+ |> ProofContext.add_cases true case_env
+ fun after_qed thms goal_ctxt =
+ let
+ val global_thms = ProofContext.export goal_ctxt
+ (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms)
+ in
+ goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #>
+ (if rpred then
+ (add_equations [const] #>
+ add_sizelim_equations [const] #> add_quickcheck_equations [const])
+ else add_equations [const]))
+ end
+ in
+ Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''
+ end;
+
+val code_pred = generic_code_pred (K I);
+val code_pred_cmd = generic_code_pred Code.read_const
+
+(* transformation for code generation *)
+
+val eval_ref = ref (NONE : (unit -> term Predicate.pred) option);
+
+(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
+fun analyze_compr thy t_compr =
+ let
+ val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t
+ | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr);
+ val (body, Ts, fp) = HOLogic.strip_psplits split;
+ val (pred as Const (name, T), all_args) = strip_comb body;
+ val (params, args) = chop (nparams_of thy name) all_args;
+ val user_mode = map_filter I (map_index
+ (fn (i, t) => case t of Bound j => if j < length Ts then NONE
+ else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*)
+ val user_mode' = map (rpair NONE) user_mode
+ val modes = filter (fn Mode (_, is, _) => is = user_mode')
+ (modes_of_term (all_modes_of thy) (list_comb (pred, params)));
+ val m = case modes
+ of [] => error ("No mode possible for comprehension "
+ ^ Syntax.string_of_term_global thy t_compr)
+ | [m] => m
+ | m :: _ :: _ => (warning ("Multiple modes possible for comprehension "
+ ^ Syntax.string_of_term_global thy t_compr); m);
+ val (inargs, outargs) = split_smode user_mode' args;
+ val t_pred = list_comb (compile_expr NONE NONE thy (m, list_comb (pred, params)), inargs);
+ val t_eval = if null outargs then t_pred else
+ let
+ val outargs_bounds = map (fn Bound i => i) outargs;
+ val outargsTs = map (nth Ts) outargs_bounds;
+ val T_pred = HOLogic.mk_tupleT outargsTs;
+ val T_compr = HOLogic.mk_ptupleT fp Ts;
+ val arrange_bounds = map_index I outargs_bounds
+ |> sort (prod_ord (K EQUAL) int_ord)
+ |> map fst;
+ val arrange = funpow (length outargs_bounds - 1) HOLogic.mk_split
+ (Term.list_abs (map (pair "") outargsTs,
+ HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds)))
+ in mk_map PredicateCompFuns.compfuns T_pred T_compr arrange t_pred end
+ in t_eval end;
+
+fun eval thy t_compr =
+ let
+ val t = analyze_compr thy t_compr;
+ val T = dest_predT PredicateCompFuns.compfuns (fastype_of t);
+ val t' = mk_map PredicateCompFuns.compfuns T HOLogic.termT (HOLogic.term_of_const T) t;
+ in (T, Code_ML.eval NONE ("Predicate_Compile_Core.eval_ref", eval_ref) Predicate.map thy t' []) end;
+
+fun values ctxt k t_compr =
+ let
+ val thy = ProofContext.theory_of ctxt;
+ val (T, t) = eval thy t_compr;
+ val setT = HOLogic.mk_setT T;
+ val (ts, _) = Predicate.yieldn k t;
+ val elemsT = HOLogic.mk_set T ts;
+ in if k = ~1 orelse length ts < k then elemsT
+ else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ t_compr
+ end;
+ (*
+fun random_values ctxt k t =
+ let
+ val thy = ProofContext.theory_of ctxt
+ val _ =
+ in
+ end;
+ *)
+fun values_cmd modes k raw_t state =
+ let
+ val ctxt = Toplevel.context_of state;
+ val t = Syntax.read_term ctxt raw_t;
+ val t' = values ctxt k t;
+ val ty' = Term.type_of t';
+ val ctxt' = Variable.auto_fixes t' ctxt;
+ val p = PrintMode.with_modes modes (fn () =>
+ Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,
+ Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();
+ in Pretty.writeln p end;
+
+
+local structure P = OuterParse in
+
+val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) [];
+
+val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag
+ (opt_modes -- Scan.optional P.nat ~1 -- P.term
+ >> (fn ((modes, k), t) => Toplevel.no_timing o Toplevel.keep
+ (values_cmd modes k t)));
+
+end;
+
+end;
--- a/src/HOL/Tools/hologic.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Tools/hologic.ML Thu Sep 24 17:26:05 2009 +0200
@@ -613,17 +613,17 @@
| mk_typerep (T as TFree _) = Const ("Typerep.typerep_class.typerep",
Term.itselfT T --> typerepT) $ Logic.mk_type T;
-val termT = Type ("Code_Eval.term", []);
+val termT = Type ("Code_Evaluation.term", []);
-fun term_of_const T = Const ("Code_Eval.term_of_class.term_of", T --> termT);
+fun term_of_const T = Const ("Code_Evaluation.term_of_class.term_of", T --> termT);
fun mk_term_of T t = term_of_const T $ t;
fun reflect_term (Const (c, T)) =
- Const ("Code_Eval.Const", literalT --> typerepT --> termT)
+ Const ("Code_Evaluation.Const", literalT --> typerepT --> termT)
$ mk_literal c $ mk_typerep T
| reflect_term (t1 $ t2) =
- Const ("Code_Eval.App", termT --> termT --> termT)
+ Const ("Code_Evaluation.App", termT --> termT --> termT)
$ reflect_term t1 $ reflect_term t2
| reflect_term (Abs (v, _, t)) = Abs (v, termT, reflect_term t)
| reflect_term t = t;
@@ -631,7 +631,7 @@
fun mk_valtermify_app c vs T =
let
fun termifyT T = mk_prodT (T, unitT --> termT);
- fun valapp T T' = Const ("Code_Eval.valapp",
+ fun valapp T T' = Const ("Code_Evaluation.valapp",
termifyT (T --> T') --> termifyT T --> termifyT T');
fun mk_fTs [] _ = []
| mk_fTs (_ :: Ts) T = (Ts ---> T) :: mk_fTs Ts T;
--- a/src/HOL/Tools/inductive.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Tools/inductive.ML Thu Sep 24 17:26:05 2009 +0200
@@ -103,7 +103,10 @@
"(P & True) = P" "(True & P) = P"
by (fact simp_thms)+};
-val simp_thms'' = inf_fun_eq :: inf_bool_eq :: simp_thms';
+val simp_thms'' = map mk_meta_eq [@{thm inf_fun_eq}, @{thm inf_bool_eq}] @ simp_thms';
+
+val simp_thms''' = map mk_meta_eq
+ [@{thm le_fun_def}, @{thm le_bool_def}, @{thm sup_fun_eq}, @{thm sup_bool_eq}];
(** context data **)
@@ -171,15 +174,15 @@
(case concl of
(_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
| _ => [thm' RS (thm' RS eq_to_mono2)]);
- fun dest_less_concl thm = dest_less_concl (thm RS le_funD)
- handle THM _ => thm RS le_boolD
+ fun dest_less_concl thm = dest_less_concl (thm RS @{thm le_funD})
+ handle THM _ => thm RS @{thm le_boolD}
in
case concl of
Const ("==", _) $ _ $ _ => eq2mono (thm RS meta_eq_to_obj_eq)
| _ $ (Const ("op =", _) $ _ $ _) => eq2mono thm
| _ $ (Const (@{const_name HOL.less_eq}, _) $ _ $ _) =>
[dest_less_concl (Seq.hd (REPEAT (FIRSTGOAL
- (resolve_tac [le_funI, le_boolI'])) thm))]
+ (resolve_tac [@{thm le_funI}, @{thm le_boolI'}])) thm))]
| _ => [thm]
end handle THM _ =>
error ("Bad monotonicity theorem:\n" ^ Display.string_of_thm_without_context thm);
@@ -323,11 +326,11 @@
(HOLogic.mk_Trueprop
(Const (@{const_name Orderings.mono}, (predT --> predT) --> HOLogic.boolT) $ fp_fun))
(fn _ => EVERY [rtac @{thm monoI} 1,
- REPEAT (resolve_tac [le_funI, le_boolI'] 1),
+ REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI'}] 1),
REPEAT (FIRST
[atac 1,
resolve_tac (List.concat (map mk_mono monos) @ get_monos ctxt) 1,
- etac le_funE 1, dtac le_boolD 1])]));
+ etac @{thm le_funE} 1, dtac @{thm le_boolD} 1])]));
(* prove introduction rules *)
@@ -338,7 +341,7 @@
val unfold = funpow k (fn th => th RS fun_cong)
(mono RS (fp_def RS
- (if coind then def_gfp_unfold else def_lfp_unfold)));
+ (if coind then @{thm def_gfp_unfold} else @{thm def_lfp_unfold})));
fun select_disj 1 1 = []
| select_disj _ 1 = [rtac disjI1]
@@ -553,13 +556,13 @@
val ind_concl = HOLogic.mk_Trueprop
(HOLogic.mk_binrel "HOL.ord_class.less_eq" (rec_const, ind_pred));
- val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
+ val raw_fp_induct = (mono RS (fp_def RS @{thm def_lfp_induct}));
val induct = SkipProof.prove ctxt'' [] ind_prems ind_concl
(fn {prems, ...} => EVERY
[rewrite_goals_tac [inductive_conj_def],
DETERM (rtac raw_fp_induct 1),
- REPEAT (resolve_tac [le_funI, le_boolI] 1),
+ REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI}] 1),
rewrite_goals_tac simp_thms'',
(*This disjE separates out the introduction rules*)
REPEAT (FIRSTGOAL (eresolve_tac [disjE, exE, FalseE])),
@@ -577,7 +580,7 @@
[rewrite_goals_tac rec_preds_defs,
REPEAT (EVERY
[REPEAT (resolve_tac [conjI, impI] 1),
- REPEAT (eresolve_tac [le_funE, le_boolE] 1),
+ REPEAT (eresolve_tac [@{thm le_funE}, @{thm le_boolE}] 1),
atac 1,
rewrite_goals_tac simp_thms',
atac 1])])
@@ -763,8 +766,8 @@
(snd (Variable.add_fixes (map (fst o dest_Free) params) ctxt1)) ctxt1)
(rotate_prems ~1 (ObjectLogic.rulify
(fold_rule rec_preds_defs
- (rewrite_rule [le_fun_def, le_bool_def, sup_fun_eq, sup_bool_eq]
- (mono RS (fp_def RS def_coinduct))))))
+ (rewrite_rule simp_thms'''
+ (mono RS (fp_def RS @{thm def_coinduct}))))))
else
prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono fp_def
rec_preds_defs ctxt1);
--- a/src/HOL/Tools/quickcheck_generators.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Tools/quickcheck_generators.ML Thu Sep 24 17:26:05 2009 +0200
@@ -76,7 +76,7 @@
val lhs = HOLogic.mk_random T size;
val rhs = HOLogic.mk_ST [((HOLogic.mk_random T' size, @{typ Random.seed}), SOME (v, Tm'))]
(HOLogic.mk_return Tm @{typ Random.seed}
- (mk_const "Code_Eval.valapp" [T', T]
+ (mk_const "Code_Evaluation.valapp" [T', T]
$ HOLogic.mk_prod (t_constr, Abs ("u", @{typ unit}, HOLogic.reflect_term t_constr)) $ t_v))
@{typ Random.seed} (SOME Tm, @{typ Random.seed});
val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
--- a/src/HOL/UNITY/Simple/Common.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/UNITY/Simple/Common.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1,5 +1,4 @@
(* Title: HOL/UNITY/Common
- ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
@@ -10,7 +9,9 @@
From Misra, "A Logic for Concurrent Programming" (1994), sections 5.1 and 13.1.
*)
-theory Common imports "../UNITY_Main" begin
+theory Common
+imports "../UNITY_Main"
+begin
consts
ftime :: "nat=>nat"
@@ -65,7 +66,7 @@
lemma "mk_total_program (UNIV, {range(%t.(t, max (ftime t) (gtime t)))}, UNIV)
\<in> {m} co (maxfg m)"
apply (simp add: mk_total_program_def)
-apply (simp add: constrains_def maxfg_def gasc)
+apply (simp add: constrains_def maxfg_def gasc min_max.sup_absorb2)
done
(*This one is t := t+1 if t <max (ftime t) (gtime t) *)
@@ -73,7 +74,7 @@
(UNIV, { {(t, Suc t) | t. t < max (ftime t) (gtime t)} }, UNIV)
\<in> {m} co (maxfg m)"
apply (simp add: mk_total_program_def)
-apply (simp add: constrains_def maxfg_def gasc)
+apply (simp add: constrains_def maxfg_def gasc min_max.sup_absorb2)
done
--- a/src/HOL/Word/BinBoolList.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Word/BinBoolList.thy Thu Sep 24 17:26:05 2009 +0200
@@ -919,7 +919,7 @@
apply (drule spec)
apply (erule trans)
apply (drule_tac x = "bin_cat y n a" in spec)
- apply (simp add : bin_cat_assoc_sym)
+ apply (simp add : bin_cat_assoc_sym min_max.inf_absorb2)
done
lemma bin_rcat_bl:
--- a/src/HOL/Word/BinGeneral.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Word/BinGeneral.thy Thu Sep 24 17:26:05 2009 +0200
@@ -508,7 +508,7 @@
lemma sbintrunc_sbintrunc_min [simp]:
"sbintrunc m (sbintrunc n w) = sbintrunc (min m n) w"
apply (rule bin_eqI)
- apply (auto simp: nth_sbintr)
+ apply (auto simp: nth_sbintr min_max.inf_absorb1 min_max.inf_absorb2)
done
lemmas bintrunc_Pls =
--- a/src/HOL/Word/WordDefinition.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Word/WordDefinition.thy Thu Sep 24 17:26:05 2009 +0200
@@ -381,14 +381,14 @@
apply (unfold word_size)
apply (subst word_ubin.norm_Rep [symmetric])
apply (simp only: bintrunc_bintrunc_min word_size)
- apply simp
+ apply (simp add: min_max.inf_absorb2)
done
lemma wi_bintr':
"wb = word_of_int bin ==> n >= size wb ==>
word_of_int (bintrunc n bin) = wb"
unfolding word_size
- by (clarsimp simp add : word_ubin.norm_eq_iff [symmetric])
+ by (clarsimp simp add: word_ubin.norm_eq_iff [symmetric] min_max.inf_absorb1)
lemmas bintr_uint = bintr_uint' [unfolded word_size]
lemmas wi_bintr = wi_bintr' [unfolded word_size]
--- a/src/HOL/Word/WordShift.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/Word/WordShift.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1017,8 +1017,8 @@
(word_cat (word_of_int w :: 'b word) (b :: 'c word) :: 'a word) =
word_of_int (bin_cat w (size b) (uint b))"
apply (unfold word_cat_def word_size)
- apply (clarsimp simp add : word_ubin.norm_eq_iff [symmetric]
- word_ubin.eq_norm bintr_cat)
+ apply (clarsimp simp add: word_ubin.norm_eq_iff [symmetric]
+ word_ubin.eq_norm bintr_cat min_max.inf_absorb1)
done
lemma word_cat_split_alt:
--- a/src/HOL/ex/Predicate_Compile.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/ex/Predicate_Compile.thy Thu Sep 24 17:26:05 2009 +0200
@@ -1,8 +1,17 @@
theory Predicate_Compile
imports Complex_Main RPred
-uses "predicate_compile.ML"
+uses
+ "../Tools/Predicate_Compile/pred_compile_aux.ML"
+ "../Tools/Predicate_Compile/predicate_compile_core.ML"
+ "../Tools/Predicate_Compile/pred_compile_set.ML"
+ "../Tools/Predicate_Compile/pred_compile_data.ML"
+ "../Tools/Predicate_Compile/pred_compile_fun.ML"
+ "../Tools/Predicate_Compile/pred_compile_pred.ML"
+ "../Tools/Predicate_Compile/predicate_compile.ML"
+ "../Tools/Predicate_Compile/pred_compile_quickcheck.ML"
begin
setup {* Predicate_Compile.setup *}
+setup {* Quickcheck.add_generator ("pred_compile", Pred_Compile_Quickcheck.quickcheck) *}
end
\ No newline at end of file
--- a/src/HOL/ex/Predicate_Compile_ex.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/ex/Predicate_Compile_ex.thy Thu Sep 24 17:26:05 2009 +0200
@@ -22,8 +22,10 @@
| "append xs ys zs \<Longrightarrow> append (x # xs) ys (x # zs)"
code_pred append .
+code_pred (inductify_all) (rpred) append .
thm append.equation
+thm append.rpred_equation
values "{(ys, xs). append xs ys [0, Suc 0, 2]}"
values "{zs. append [0, Suc 0, 2] [17, 8] zs}"
@@ -49,6 +51,22 @@
thm partition.equation
+
+inductive member
+for xs
+where "x \<in> set xs ==> member xs x"
+
+lemma [code_pred_intros]:
+ "member (x#xs') x"
+by (auto intro: member.intros)
+
+lemma [code_pred_intros]:
+"member xs x ==> member (x'#xs) x"
+by (auto intro: member.intros elim!: member.cases)
+(* strange bug must be repaired! *)
+(*
+code_pred member sorry
+*)
inductive is_even :: "nat \<Rightarrow> bool"
where
"n mod 2 = 0 \<Longrightarrow> is_even n"
@@ -70,15 +88,11 @@
case tranclp
from this converse_tranclpE[OF this(1)] show thesis by metis
qed
-
+(*
+code_pred (inductify_all) (rpred) tranclp .
thm tranclp.equation
-(*
-setup {* Predicate_Compile.add_sizelim_equations [@{const_name tranclp}] *}
-setup {* fn thy => exception_trace (fn () => Predicate_Compile.add_quickcheck_equations [@{const_name tranclp}] thy) *}
-
thm tranclp.rpred_equation
*)
-
inductive succ :: "nat \<Rightarrow> nat \<Rightarrow> bool" where
"succ 0 1"
| "succ m n \<Longrightarrow> succ (Suc m) (Suc n)"
@@ -157,6 +171,7 @@
values 3 "{(a,q). step (par nil nil) a q}"
*)
+subsection {* divmod *}
inductive divmod_rel :: "nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" where
"k < l \<Longrightarrow> divmod_rel k l 0 k"
@@ -166,4 +181,261 @@
value [code] "Predicate.singleton (divmod_rel_1_2 1705 42)"
+section {* Executing definitions *}
+
+definition Min
+where "Min s r x \<equiv> s x \<and> (\<forall>y. r x y \<longrightarrow> x = y)"
+
+code_pred (inductify_all) Min .
+
+subsection {* Examples with lists *}
+
+inductive filterP for Pa where
+"(filterP::('a => bool) => 'a list => 'a list => bool) (Pa::'a => bool) [] []"
+| "[| (res::'a list) = (y::'a) # (resa::'a list); (filterP::('a => bool) => 'a list => 'a list => bool) (Pa::'a => bool) (xt::'a list) resa; Pa y |]
+==> filterP Pa (y # xt) res"
+| "[| (filterP::('a => bool) => 'a list => 'a list => bool) (Pa::'a => bool) (xt::'a list) (res::'a list); ~ Pa (y::'a) |] ==> filterP Pa (y # xt) res"
+
+(*
+code_pred (inductify_all) (rpred) filterP .
+thm filterP.rpred_equation
+*)
+
+code_pred (inductify_all) lexord .
+
+thm lexord.equation
+
+lemma "(u, v) : lexord r ==> (x @ u, y @ v) : lexord r"
+(*quickcheck[generator=pred_compile]*)
+oops
+
+lemmas [code_pred_def] = lexn_conv lex_conv lenlex_conv
+
+code_pred (inductify_all) lexn .
+thm lexn.equation
+
+code_pred (inductify_all) lenlex .
+thm lenlex.equation
+(*
+code_pred (inductify_all) (rpred) lenlex .
+thm lenlex.rpred_equation
+*)
+thm lists.intros
+code_pred (inductify_all) lists .
+
+thm lists.equation
+
+datatype 'a tree = ET | MKT 'a "'a tree" "'a tree" nat
+fun height :: "'a tree => nat" where
+"height ET = 0"
+| "height (MKT x l r h) = max (height l) (height r) + 1"
+
+consts avl :: "'a tree => bool"
+primrec
+ "avl ET = True"
+ "avl (MKT x l r h) = ((height l = height r \<or> height l = 1 + height r \<or> height r = 1+height l) \<and>
+ h = max (height l) (height r) + 1 \<and> avl l \<and> avl r)"
+
+code_pred (inductify_all) avl .
+thm avl.equation
+
+lemma [code_pred_inline]: "bot_fun_inst.bot_fun == (\<lambda>(y::'a::type). False)"
+unfolding bot_fun_inst.bot_fun[symmetric] bot_bool_eq[symmetric] bot_fun_eq by simp
+
+fun set_of
+where
+"set_of ET = {}"
+| "set_of (MKT n l r h) = insert n (set_of l \<union> set_of r)"
+
+fun is_ord
+where
+"is_ord ET = True"
+| "is_ord (MKT n l r h) =
+ ((\<forall>n' \<in> set_of l. n' < n) \<and> (\<forall>n' \<in> set_of r. n < n') \<and> is_ord l \<and> is_ord r)"
+
+declare Un_def[code_pred_def]
+
+code_pred (inductify_all) set_of .
+thm set_of.equation
+(* FIXME *)
+(*
+code_pred (inductify_all) is_ord .
+thm is_ord.equation
+*)
+section {* Definitions about Relations *}
+
+code_pred (inductify_all) converse .
+thm converse.equation
+
+code_pred (inductify_all) Domain .
+thm Domain.equation
+
+
+section {* Context Free Grammar *}
+
+datatype alphabet = a | b
+
+inductive_set S\<^isub>1 and A\<^isub>1 and B\<^isub>1 where
+ "[] \<in> S\<^isub>1"
+| "w \<in> A\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1"
+| "w \<in> B\<^isub>1 \<Longrightarrow> a # w \<in> S\<^isub>1"
+| "w \<in> S\<^isub>1 \<Longrightarrow> a # w \<in> A\<^isub>1"
+| "w \<in> S\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1"
+| "\<lbrakk>v \<in> B\<^isub>1; v \<in> B\<^isub>1\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>1"
+
+code_pred (inductify_all) S\<^isub>1p .
+
+thm S\<^isub>1p.equation
+
+theorem S\<^isub>1_sound:
+"w \<in> S\<^isub>1 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
+quickcheck[generator=pred_compile]
+oops
+
+inductive_set S\<^isub>2 and A\<^isub>2 and B\<^isub>2 where
+ "[] \<in> S\<^isub>2"
+| "w \<in> A\<^isub>2 \<Longrightarrow> b # w \<in> S\<^isub>2"
+| "w \<in> B\<^isub>2 \<Longrightarrow> a # w \<in> S\<^isub>2"
+| "w \<in> S\<^isub>2 \<Longrightarrow> a # w \<in> A\<^isub>2"
+| "w \<in> S\<^isub>2 \<Longrightarrow> b # w \<in> B\<^isub>2"
+| "\<lbrakk>v \<in> B\<^isub>2; v \<in> B\<^isub>2\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>2"
+(*
+code_pred (inductify_all) (rpred) S\<^isub>2 .
+ML {* Predicate_Compile_Core.intros_of @{theory} @{const_name "B\<^isub>2"} *}
+*)
+theorem S\<^isub>2_sound:
+"w \<in> S\<^isub>2 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
+(*quickcheck[generator=SML]*)
+quickcheck[generator=pred_compile, size=15, iterations=100]
+oops
+
+inductive_set S\<^isub>3 and A\<^isub>3 and B\<^isub>3 where
+ "[] \<in> S\<^isub>3"
+| "w \<in> A\<^isub>3 \<Longrightarrow> b # w \<in> S\<^isub>3"
+| "w \<in> B\<^isub>3 \<Longrightarrow> a # w \<in> S\<^isub>3"
+| "w \<in> S\<^isub>3 \<Longrightarrow> a # w \<in> A\<^isub>3"
+| "w \<in> S\<^isub>3 \<Longrightarrow> b # w \<in> B\<^isub>3"
+| "\<lbrakk>v \<in> B\<^isub>3; w \<in> B\<^isub>3\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>3"
+
+(*
+code_pred (inductify_all) S\<^isub>3 .
+*)
+theorem S\<^isub>3_sound:
+"w \<in> S\<^isub>3 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
+quickcheck[generator=pred_compile, size=10, iterations=1]
+oops
+
+lemma "\<not> (length w > 2) \<or> \<not> (length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b])"
+quickcheck[size=10, generator = pred_compile]
+oops
+
+theorem S\<^isub>3_complete:
+"length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b] \<longrightarrow> w \<in> S\<^isub>3"
+(*quickcheck[generator=SML]*)
+quickcheck[generator=pred_compile, size=10, iterations=100]
+oops
+
+inductive_set S\<^isub>4 and A\<^isub>4 and B\<^isub>4 where
+ "[] \<in> S\<^isub>4"
+| "w \<in> A\<^isub>4 \<Longrightarrow> b # w \<in> S\<^isub>4"
+| "w \<in> B\<^isub>4 \<Longrightarrow> a # w \<in> S\<^isub>4"
+| "w \<in> S\<^isub>4 \<Longrightarrow> a # w \<in> A\<^isub>4"
+| "\<lbrakk>v \<in> A\<^isub>4; w \<in> A\<^isub>4\<rbrakk> \<Longrightarrow> b # v @ w \<in> A\<^isub>4"
+| "w \<in> S\<^isub>4 \<Longrightarrow> b # w \<in> B\<^isub>4"
+| "\<lbrakk>v \<in> B\<^isub>4; w \<in> B\<^isub>4\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>4"
+
+theorem S\<^isub>4_sound:
+"w \<in> S\<^isub>4 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
+quickcheck[generator = pred_compile, size=2, iterations=1]
+oops
+
+theorem S\<^isub>4_complete:
+"length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b] \<longrightarrow> w \<in> S\<^isub>4"
+quickcheck[generator = pred_compile, size=5, iterations=1]
+oops
+
+theorem S\<^isub>4_A\<^isub>4_B\<^isub>4_sound_and_complete:
+"w \<in> S\<^isub>4 \<longleftrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
+"w \<in> A\<^isub>4 \<longleftrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b] + 1"
+"w \<in> B\<^isub>4 \<longleftrightarrow> length [x \<leftarrow> w. x = b] = length [x \<leftarrow> w. x = a] + 1"
+(*quickcheck[generator = pred_compile, size=5, iterations=1]*)
+oops
+
+
+section {* Lambda *}
+datatype type =
+ Atom nat
+ | Fun type type (infixr "\<Rightarrow>" 200)
+
+datatype dB =
+ Var nat
+ | App dB dB (infixl "\<degree>" 200)
+ | Abs type dB
+
+primrec
+ nth_el :: "'a list \<Rightarrow> nat \<Rightarrow> 'a option" ("_\<langle>_\<rangle>" [90, 0] 91)
+where
+ "[]\<langle>i\<rangle> = None"
+| "(x # xs)\<langle>i\<rangle> = (case i of 0 \<Rightarrow> Some x | Suc j \<Rightarrow> xs \<langle>j\<rangle>)"
+
+(*
+inductive nth_el' :: "'a list \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> bool"
+where
+ "nth_el' (x # xs) 0 x"
+| "nth_el' xs i y \<Longrightarrow> nth_el' (x # xs) (Suc i) y"
+*)
+inductive typing :: "type list \<Rightarrow> dB \<Rightarrow> type \<Rightarrow> bool" ("_ \<turnstile> _ : _" [50, 50, 50] 50)
+ where
+ Var [intro!]: "nth_el env x = Some T \<Longrightarrow> env \<turnstile> Var x : T"
+ | Abs [intro!]: "T # env \<turnstile> t : U \<Longrightarrow> env \<turnstile> Abs T t : (T \<Rightarrow> U)"
+(* | App [intro!]: "env \<turnstile> s : T \<Rightarrow> U \<Longrightarrow> env \<turnstile> t : T \<Longrightarrow> env \<turnstile> (s \<degree> t) : U" *)
+ | App [intro!]: "env \<turnstile> s : U \<Rightarrow> T \<Longrightarrow> env \<turnstile> t : T \<Longrightarrow> env \<turnstile> (s \<degree> t) : U"
+
+primrec
+ lift :: "[dB, nat] => dB"
+where
+ "lift (Var i) k = (if i < k then Var i else Var (i + 1))"
+ | "lift (s \<degree> t) k = lift s k \<degree> lift t k"
+ | "lift (Abs T s) k = Abs T (lift s (k + 1))"
+
+primrec
+ subst :: "[dB, dB, nat] => dB" ("_[_'/_]" [300, 0, 0] 300)
+where
+ subst_Var: "(Var i)[s/k] =
+ (if k < i then Var (i - 1) else if i = k then s else Var i)"
+ | subst_App: "(t \<degree> u)[s/k] = t[s/k] \<degree> u[s/k]"
+ | subst_Abs: "(Abs T t)[s/k] = Abs T (t[lift s 0 / k+1])"
+
+inductive beta :: "[dB, dB] => bool" (infixl "\<rightarrow>\<^sub>\<beta>" 50)
+ where
+ beta [simp, intro!]: "Abs T s \<degree> t \<rightarrow>\<^sub>\<beta> s[t/0]"
+ | appL [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> s \<degree> u \<rightarrow>\<^sub>\<beta> t \<degree> u"
+ | appR [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> u \<degree> s \<rightarrow>\<^sub>\<beta> u \<degree> t"
+ | abs [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> Abs T s \<rightarrow>\<^sub>\<beta> Abs T t"
+
+lemma "Gamma \<turnstile> t : T \<Longrightarrow> t \<rightarrow>\<^sub>\<beta> t' \<Longrightarrow> Gamma \<turnstile> t' : T"
+quickcheck[generator = pred_compile, size = 10, iterations = 1000]
+oops
+(* FIXME *)
+(*
+inductive test for P where
+"[| filter P vs = res |]
+==> test P vs res"
+
+code_pred test .
+*)
+(*
+export_code test_for_1_yields_1_2 in SML file -
+code_pred (inductify_all) (rpred) test .
+
+thm test.equation
+*)
+
+lemma filter_eq_ConsD:
+ "filter P ys = x#xs \<Longrightarrow>
+ \<exists>us vs. ys = ts @ x # vs \<and> (\<forall>u\<in>set us. \<not> P u) \<and> P x \<and> xs = filter P vs"
+(*quickcheck[generator = pred_compile]*)
+oops
+
+
end
\ No newline at end of file
--- a/src/HOL/ex/RPred.thy Thu Sep 24 17:25:42 2009 +0200
+++ b/src/HOL/ex/RPred.thy Thu Sep 24 17:26:05 2009 +0200
@@ -14,13 +14,15 @@
definition return :: "'a => 'a rpred"
where "return x = Pair (Predicate.single x)"
-definition bind :: "'a rpred \<Rightarrow> ('a \<Rightarrow> 'b rpred) \<Rightarrow> 'b rpred" (infixl "\<guillemotright>=" 60)
+definition bind :: "'a rpred \<Rightarrow> ('a \<Rightarrow> 'b rpred) \<Rightarrow> 'b rpred"
+(* (infixl "\<guillemotright>=" 60) *)
where "bind RP f =
(\<lambda>s. let (P, s') = RP s;
(s1, s2) = Random.split_seed s'
in (Predicate.bind P (%a. fst (f a s1)), s2))"
-definition supp :: "'a rpred \<Rightarrow> 'a rpred \<Rightarrow> 'a rpred" (infixl "\<squnion>" 80)
+definition supp :: "'a rpred \<Rightarrow> 'a rpred \<Rightarrow> 'a rpred"
+(* (infixl "\<squnion>" 80) *)
where
"supp RP1 RP2 = (\<lambda>s. let (P1, s') = RP1 s; (P2, s'') = RP2 s'
in (upper_semilattice_class.sup P1 P2, s''))"
@@ -43,6 +45,8 @@
where "lift_random g = scomp g (Pair o (Predicate.single o fst))"
definition map_rpred :: "('a \<Rightarrow> 'b) \<Rightarrow> ('a rpred \<Rightarrow> 'b rpred)"
-where "map_rpred f P = P \<guillemotright>= (return o f)"
+where "map_rpred f P = bind P (return o f)"
+
+hide (open) const return bind supp
end
\ No newline at end of file
--- a/src/HOL/ex/predicate_compile.ML Thu Sep 24 17:25:42 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,2182 +0,0 @@
-(* Author: Lukas Bulwahn, TU Muenchen
-
-(Prototype of) A compiler from predicates specified by intro/elim rules
-to equations.
-*)
-
-signature PREDICATE_COMPILE =
-sig
- type mode = int list option list * int list
- (*val add_equations_of: bool -> string list -> theory -> theory *)
- val register_predicate : (thm list * thm * int) -> theory -> theory
- val is_registered : theory -> string -> bool
- (* val fetch_pred_data : theory -> string -> (thm list * thm * int) *)
- val predfun_intro_of: theory -> string -> mode -> thm
- val predfun_elim_of: theory -> string -> mode -> thm
- val strip_intro_concl: int -> term -> term * (term list * term list)
- val predfun_name_of: theory -> string -> mode -> string
- val all_preds_of : theory -> string list
- val modes_of: theory -> string -> mode list
- val string_of_mode : mode -> string
- val intros_of: theory -> string -> thm list
- val nparams_of: theory -> string -> int
- val add_intro: thm -> theory -> theory
- val set_elim: thm -> theory -> theory
- val setup: theory -> theory
- val code_pred: string -> Proof.context -> Proof.state
- val code_pred_cmd: string -> Proof.context -> Proof.state
- val print_stored_rules: theory -> unit
- val print_all_modes: theory -> unit
- val do_proofs: bool ref
- val mk_casesrule : Proof.context -> int -> thm list -> term
- val analyze_compr: theory -> term -> term
- val eval_ref: (unit -> term Predicate.pred) option ref
- val add_equations : string list -> theory -> theory
- val code_pred_intros_attrib : attribute
- (* used by Quickcheck_Generator *)
- (*val funT_of : mode -> typ -> typ
- val mk_if_pred : term -> term
- val mk_Eval : term * term -> term*)
- val mk_tupleT : typ list -> typ
-(* val mk_predT : typ -> typ *)
- (* temporary for testing of the compilation *)
- datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
- GeneratorPrem of term list * term | Generator of (string * typ);
- val prepare_intrs: theory -> string list ->
- (string * typ) list * int * string list * string list * (string * mode list) list *
- (string * (term list * indprem list) list) list * (string * (int option list * int)) list
- datatype compilation_funs = CompilationFuns of {
- mk_predT : typ -> typ,
- dest_predT : typ -> typ,
- mk_bot : typ -> term,
- mk_single : term -> term,
- mk_bind : term * term -> term,
- mk_sup : term * term -> term,
- mk_if : term -> term,
- mk_not : term -> term,
- mk_map : typ -> typ -> term -> term -> term,
- lift_pred : term -> term
- };
- datatype tmode = Mode of mode * int list * tmode option list;
- type moded_clause = term list * (indprem * tmode) list
- type 'a pred_mode_table = (string * (mode * 'a) list) list
- val infer_modes : bool -> theory -> (string * (int list option list * int list) list) list
- -> (string * (int option list * int)) list -> string list
- -> (string * (term list * indprem list) list) list
- -> (moded_clause list) pred_mode_table
- val infer_modes_with_generator : theory -> (string * (int list option list * int list) list) list
- -> (string * (int option list * int)) list -> string list
- -> (string * (term list * indprem list) list) list
- -> (moded_clause list) pred_mode_table
- (*val compile_preds : theory -> compilation_funs -> string list -> string list
- -> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table
- val rpred_create_definitions :(string * typ) list -> string * mode list
- -> theory -> theory
- val split_smode : int list -> term list -> (term list * term list) *)
- val print_moded_clauses :
- theory -> (moded_clause list) pred_mode_table -> unit
- val print_compiled_terms : theory -> term pred_mode_table -> unit
- (*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*)
- val rpred_compfuns : compilation_funs
- val dest_funT : typ -> typ * typ
- (* val depending_preds_of : theory -> thm list -> string list *)
- val add_quickcheck_equations : string list -> theory -> theory
- val add_sizelim_equations : string list -> theory -> theory
- val is_inductive_predicate : theory -> string -> bool
- val terms_vs : term list -> string list
- val subsets : int -> int -> int list list
- val check_mode_clause : bool -> theory -> string list ->
- (string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list)
- -> (term list * (indprem * tmode) list) option
- val string_of_moded_prem : theory -> (indprem * tmode) -> string
- val all_modes_of : theory -> (string * mode list) list
- val all_generator_modes_of : theory -> (string * mode list) list
- val compile_clause : compilation_funs -> term option -> (term list -> term) ->
- theory -> string list -> string list -> mode -> term -> moded_clause -> term
- val preprocess_intro : theory -> thm -> thm
- val is_constrt : theory -> term -> bool
- val is_predT : typ -> bool
- val guess_nparams : typ -> int
-end;
-
-structure Predicate_Compile : PREDICATE_COMPILE =
-struct
-
-(** auxiliary **)
-
-(* debug stuff *)
-
-fun tracing s = (if ! Toplevel.debug then Output.tracing s else ());
-
-fun print_tac s = Seq.single; (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *)
-fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *)
-
-val do_proofs = ref true;
-
-fun mycheat_tac thy i st =
- (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
-
-fun remove_last_goal thy st =
- (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) (nprems_of st)) st
-
-(* reference to preprocessing of InductiveSet package *)
-
-val ind_set_codegen_preproc = Inductive_Set.codegen_preproc;
-
-(** fundamentals **)
-
-(* syntactic operations *)
-
-fun mk_eq (x, xs) =
- let fun mk_eqs _ [] = []
- | mk_eqs a (b::cs) =
- HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs
- in mk_eqs x xs end;
-
-fun mk_tupleT [] = HOLogic.unitT
- | mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts;
-
-fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = []
- | dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2)
- | dest_tupleT t = [t]
-
-fun mk_tuple [] = HOLogic.unit
- | mk_tuple ts = foldr1 HOLogic.mk_prod ts;
-
-fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = []
- | dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2)
- | dest_tuple t = [t]
-
-fun mk_scomp (t, u) =
- let
- val T = fastype_of t
- val U = fastype_of u
- val [A] = binder_types T
- val D = body_type U
- in
- Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u
- end;
-
-fun dest_funT (Type ("fun",[S, T])) = (S, T)
- | dest_funT T = raise TYPE ("dest_funT", [T], [])
-
-fun mk_fun_comp (t, u) =
- let
- val (_, B) = dest_funT (fastype_of t)
- val (C, A) = dest_funT (fastype_of u)
- in
- Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u
- end;
-
-fun dest_randomT (Type ("fun", [@{typ Random.seed},
- Type ("*", [Type ("*", [T, @{typ "unit => Code_Eval.term"}]) ,@{typ Random.seed}])])) = T
- | dest_randomT T = raise TYPE ("dest_randomT", [T], [])
-
-(* destruction of intro rules *)
-
-(* FIXME: look for other place where this functionality was used before *)
-fun strip_intro_concl nparams intro = let
- val _ $ u = Logic.strip_imp_concl intro
- val (pred, all_args) = strip_comb u
- val (params, args) = chop nparams all_args
-in (pred, (params, args)) end
-
-(** data structures **)
-
-type smode = int list;
-type mode = smode option list * smode;
-datatype tmode = Mode of mode * int list * tmode option list;
-
-fun split_smode is ts =
- let
- fun split_smode' _ _ [] = ([], [])
- | split_smode' is i (t::ts) = (if i mem is then apfst else apsnd) (cons t)
- (split_smode' is (i+1) ts)
- in split_smode' is 1 ts end
-
-fun split_mode (iss, is) ts =
- let
- val (t1, t2) = chop (length iss) ts
- in (t1, split_smode is t2) end
-
-fun string_of_mode (iss, is) = space_implode " -> " (map
- (fn NONE => "X"
- | SOME js => enclose "[" "]" (commas (map string_of_int js)))
- (iss @ [SOME is]));
-
-fun string_of_tmode (Mode (predmode, termmode, param_modes)) =
- "predmode: " ^ (string_of_mode predmode) ^
- (if null param_modes then "" else
- "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes))
-
-datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
- GeneratorPrem of term list * term | Generator of (string * typ);
-
-type moded_clause = term list * (indprem * tmode) list
-type 'a pred_mode_table = (string * (mode * 'a) list) list
-
-datatype predfun_data = PredfunData of {
- name : string,
- definition : thm,
- intro : thm,
- elim : thm
-};
-
-fun rep_predfun_data (PredfunData data) = data;
-fun mk_predfun_data (name, definition, intro, elim) =
- PredfunData {name = name, definition = definition, intro = intro, elim = elim}
-
-datatype function_data = FunctionData of {
- name : string,
- equation : thm option (* is not used at all? *)
-};
-
-fun rep_function_data (FunctionData data) = data;
-fun mk_function_data (name, equation) =
- FunctionData {name = name, equation = equation}
-
-datatype pred_data = PredData of {
- intros : thm list,
- elim : thm option,
- nparams : int,
- functions : (mode * predfun_data) list,
- generators : (mode * function_data) list,
- sizelim_functions : (mode * function_data) list
-};
-
-fun rep_pred_data (PredData data) = data;
-fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) =
- PredData {intros = intros, elim = elim, nparams = nparams,
- functions = functions, generators = generators, sizelim_functions = sizelim_functions}
-fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) =
- mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_functions)))
-
-fun eq_option eq (NONE, NONE) = true
- | eq_option eq (SOME x, SOME y) = eq (x, y)
- | eq_option eq _ = false
-
-fun eq_pred_data (PredData d1, PredData d2) =
- eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso
- eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso
- #nparams d1 = #nparams d2
-
-structure PredData = TheoryDataFun
-(
- type T = pred_data Graph.T;
- val empty = Graph.empty;
- val copy = I;
- val extend = I;
- fun merge _ = Graph.merge eq_pred_data;
-);
-
-(* queries *)
-
-fun lookup_pred_data thy name =
- Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name)
-
-fun the_pred_data thy name = case lookup_pred_data thy name
- of NONE => error ("No such predicate " ^ quote name)
- | SOME data => data;
-
-val is_registered = is_some oo lookup_pred_data
-
-val all_preds_of = Graph.keys o PredData.get
-
-val intros_of = #intros oo the_pred_data
-
-fun the_elim_of thy name = case #elim (the_pred_data thy name)
- of NONE => error ("No elimination rule for predicate " ^ quote name)
- | SOME thm => thm
-
-val has_elim = is_some o #elim oo the_pred_data;
-
-val nparams_of = #nparams oo the_pred_data
-
-val modes_of = (map fst) o #functions oo the_pred_data
-
-fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy)
-
-val is_compiled = not o null o #functions oo the_pred_data
-
-fun lookup_predfun_data thy name mode =
- Option.map rep_predfun_data (AList.lookup (op =)
- (#functions (the_pred_data thy name)) mode)
-
-fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode
- of NONE => error ("No function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
- | SOME data => data;
-
-val predfun_name_of = #name ooo the_predfun_data
-
-val predfun_definition_of = #definition ooo the_predfun_data
-
-val predfun_intro_of = #intro ooo the_predfun_data
-
-val predfun_elim_of = #elim ooo the_predfun_data
-
-fun lookup_generator_data thy name mode =
- Option.map rep_function_data (AList.lookup (op =)
- (#generators (the_pred_data thy name)) mode)
-
-fun the_generator_data thy name mode = case lookup_generator_data thy name mode
- of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
- | SOME data => data
-
-val generator_name_of = #name ooo the_generator_data
-
-val generator_modes_of = (map fst) o #generators oo the_pred_data
-
-fun all_generator_modes_of thy =
- map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy)
-
-fun lookup_sizelim_function_data thy name mode =
- Option.map rep_function_data (AList.lookup (op =)
- (#sizelim_functions (the_pred_data thy name)) mode)
-
-fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode
- of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode
- ^ " of predicate " ^ name)
- | SOME data => data
-
-val sizelim_function_name_of = #name ooo the_sizelim_function_data
-
-(*val generator_modes_of = (map fst) o #generators oo the_pred_data*)
-
-(* diagnostic display functions *)
-
-fun print_modes modes = Output.tracing ("Inferred modes:\n" ^
- cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
- string_of_mode ms)) modes));
-
-fun print_pred_mode_table string_of_entry thy pred_mode_table =
- let
- fun print_mode pred (mode, entry) = "mode : " ^ (string_of_mode mode)
- ^ (string_of_entry pred mode entry)
- fun print_pred (pred, modes) =
- "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
- val _ = Output.tracing (cat_lines (map print_pred pred_mode_table))
- in () end;
-
-fun string_of_moded_prem thy (Prem (ts, p), tmode) =
- (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
- "(" ^ (string_of_tmode tmode) ^ ")"
- | string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) =
- (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
- "(generator_mode: " ^ (string_of_mode predmode) ^ ")"
- | string_of_moded_prem thy (Generator (v, T), _) =
- "Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T)
- | string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) =
- (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
- "(negative mode: " ^ (space_implode ", " (map string_of_int is)) ^ ")"
- | string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) =
- (Syntax.string_of_term_global thy t) ^
- "(sidecond mode: " ^ (space_implode ", " (map string_of_int is)) ^ ")"
- | string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented"
-
-fun print_moded_clauses thy =
- let
- fun string_of_clause pred mode clauses =
- cat_lines (map (fn (ts, prems) => (space_implode " --> "
- (map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " "
- ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses)
- in print_pred_mode_table string_of_clause thy end;
-
-fun print_compiled_terms thy =
- print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy
-
-fun print_stored_rules thy =
- let
- val preds = (Graph.keys o PredData.get) thy
- fun print pred () = let
- val _ = writeln ("predicate: " ^ pred)
- val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred))
- val _ = writeln ("introrules: ")
- val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm))
- (rev (intros_of thy pred)) ()
- in
- if (has_elim thy pred) then
- writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred))
- else
- writeln ("no elimrule defined")
- end
- in
- fold print preds ()
- end;
-
-fun print_all_modes thy =
- let
- val _ = writeln ("Inferred modes:")
- fun print (pred, modes) u =
- let
- val _ = writeln ("predicate: " ^ pred)
- val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
- in u end
- in
- fold print (all_modes_of thy) ()
- end
-
-(** preprocessing rules **)
-
-fun imp_prems_conv cv ct =
- case Thm.term_of ct of
- Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
- | _ => Conv.all_conv ct
-
-fun Trueprop_conv cv ct =
- case Thm.term_of ct of
- Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct
- | _ => error "Trueprop_conv"
-
-fun preprocess_intro thy rule =
- Conv.fconv_rule
- (imp_prems_conv
- (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
- (Thm.transfer thy rule)
-
-fun preprocess_elim thy nparams elimrule =
- let
- fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) =
- HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)
- | replace_eqs t = t
- val prems = Thm.prems_of elimrule
- val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams
- fun preprocess_case t =
- let
- val params = Logic.strip_params t
- val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t)
- val assums_hyp' = assums1 @ (map replace_eqs assums2)
- in
- list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t))
- end
- val cases' = map preprocess_case (tl prems)
- val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule)
- in
- Thm.equal_elim
- (Thm.symmetric (Conv.implies_concl_conv (MetaSimplifier.rewrite true [@{thm eq_is_eq}])
- (cterm_of thy elimrule')))
- elimrule
- end;
-
-(* special case: predicate with no introduction rule *)
-fun noclause thy predname elim = let
- val T = (Logic.unvarifyT o Sign.the_const_type thy) predname
- val Ts = binder_types T
- val names = Name.variant_list []
- (map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts)))
- val vs = map2 (curry Free) names Ts
- val clausehd = HOLogic.mk_Trueprop (list_comb (Const (predname, T), vs))
- val intro_t = Logic.mk_implies (@{prop False}, clausehd)
- val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))
- val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P)
- val intro = Goal.prove (ProofContext.init thy) names [] intro_t
- (fn {...} => etac @{thm FalseE} 1)
- val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
- (fn {...} => etac elim 1)
-in
- ([intro], elim)
-end
-
-fun fetch_pred_data thy name =
- case try (Inductive.the_inductive (ProofContext.init thy)) name of
- SOME (info as (_, result)) =>
- let
- fun is_intro_of intro =
- let
- val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro))
- in (fst (dest_Const const) = name) end;
- val intros = ind_set_codegen_preproc thy ((map (preprocess_intro thy))
- (filter is_intro_of (#intrs result)))
- val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info)))
- val nparams = length (Inductive.params_of (#raw_induct result))
- val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
- val (intros, elim) = if null intros then noclause thy name elim else (intros, elim)
- in
- mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
- end
- | NONE => error ("No such predicate: " ^ quote name)
-
-(* updaters *)
-
-fun apfst3 f (x, y, z) = (f x, y, z)
-fun apsnd3 f (x, y, z) = (x, f y, z)
-fun aptrd3 f (x, y, z) = (x, y, f z)
-
-fun add_predfun name mode data =
- let
- val add = (apsnd o apfst3 o cons) (mode, mk_predfun_data data)
- in PredData.map (Graph.map_node name (map_pred_data add)) end
-
-fun is_inductive_predicate thy name =
- is_some (try (Inductive.the_inductive (ProofContext.init thy)) name)
-
-fun depending_preds_of thy (key, value) =
- let
- val intros = (#intros o rep_pred_data) value
- in
- fold Term.add_const_names (map Thm.prop_of intros) []
- |> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c))
- end;
-
-
-(* code dependency graph *)
-(*
-fun dependencies_of thy name =
- let
- val (intros, elim, nparams) = fetch_pred_data thy name
- val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
- val keys = depending_preds_of thy intros
- in
- (data, keys)
- end;
-*)
-(* guessing number of parameters *)
-fun find_indexes pred xs =
- let
- fun find is n [] = is
- | find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs;
- in rev (find [] 0 xs) end;
-
-fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
- | is_predT _ = false
-
-fun guess_nparams T =
- let
- val argTs = binder_types T
- val nparams = fold (curry Int.max)
- (map (fn x => x + 1) (find_indexes is_predT argTs)) 0
- in nparams end;
-
-fun add_intro thm thy = let
- val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm)))
- fun cons_intro gr =
- case try (Graph.get_node gr) name of
- SOME pred_data => Graph.map_node name (map_pred_data
- (apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr
- | NONE =>
- let
- val nparams = the_default (guess_nparams T) (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name)
- in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), ([], [], []))) gr end;
- in PredData.map cons_intro thy end
-
-fun set_elim thm = let
- val (name, _) = dest_Const (fst
- (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
- fun set (intros, _, nparams) = (intros, SOME thm, nparams)
- in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
-
-fun set_nparams name nparams = let
- fun set (intros, elim, _ ) = (intros, elim, nparams)
- in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
-
-fun register_predicate (pre_intros, pre_elim, nparams) thy = let
- val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros))))
- (* preprocessing *)
- val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros)
- val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
- in
- PredData.map
- (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy
- end
-
-fun set_generator_name pred mode name =
- let
- val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE))
- in
- PredData.map (Graph.map_node pred (map_pred_data set))
- end
-
-fun set_sizelim_function_name pred mode name =
- let
- val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE))
- in
- PredData.map (Graph.map_node pred (map_pred_data set))
- end
-
-(** data structures for generic compilation for different monads **)
-
-(* maybe rename functions more generic:
- mk_predT -> mk_monadT; dest_predT -> dest_monadT
- mk_single -> mk_return (?)
-*)
-datatype compilation_funs = CompilationFuns of {
- mk_predT : typ -> typ,
- dest_predT : typ -> typ,
- mk_bot : typ -> term,
- mk_single : term -> term,
- mk_bind : term * term -> term,
- mk_sup : term * term -> term,
- mk_if : term -> term,
- mk_not : term -> term,
-(* funT_of : mode -> typ -> typ, *)
-(* mk_fun_of : theory -> (string * typ) -> mode -> term, *)
- mk_map : typ -> typ -> term -> term -> term,
- lift_pred : term -> term
-};
-
-fun mk_predT (CompilationFuns funs) = #mk_predT funs
-fun dest_predT (CompilationFuns funs) = #dest_predT funs
-fun mk_bot (CompilationFuns funs) = #mk_bot funs
-fun mk_single (CompilationFuns funs) = #mk_single funs
-fun mk_bind (CompilationFuns funs) = #mk_bind funs
-fun mk_sup (CompilationFuns funs) = #mk_sup funs
-fun mk_if (CompilationFuns funs) = #mk_if funs
-fun mk_not (CompilationFuns funs) = #mk_not funs
-(*fun funT_of (CompilationFuns funs) = #funT_of funs*)
-(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*)
-fun mk_map (CompilationFuns funs) = #mk_map funs
-fun lift_pred (CompilationFuns funs) = #lift_pred funs
-
-fun funT_of compfuns (iss, is) T =
- let
- val Ts = binder_types T
- val (paramTs, (inargTs, outargTs)) = split_mode (iss, is) Ts
- val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs
- in
- (paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs))
- end;
-
-fun sizelim_funT_of compfuns (iss, is) T =
- let
- val Ts = binder_types T
- val (paramTs, (inargTs, outargTs)) = split_mode (iss, is) Ts
- val paramTs' = map2 (fn SOME is => sizelim_funT_of compfuns ([], is) | NONE => I) iss paramTs
- in
- (paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs))
- end;
-
-fun mk_fun_of compfuns thy (name, T) mode =
- Const (predfun_name_of thy name mode, funT_of compfuns mode T)
-
-fun mk_sizelim_fun_of compfuns thy (name, T) mode =
- Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T)
-
-fun mk_generator_of compfuns thy (name, T) mode =
- Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T)
-
-
-structure PredicateCompFuns =
-struct
-
-fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T])
-
-fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T
- | dest_predT T = raise TYPE ("dest_predT", [T], []);
-
-fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T);
-
-fun mk_single t =
- let val T = fastype_of t
- in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end;
-
-fun mk_bind (x, f) =
- let val T as Type ("fun", [_, U]) = fastype_of f
- in
- Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f
- end;
-
-val mk_sup = HOLogic.mk_binop @{const_name sup};
-
-fun mk_if cond = Const (@{const_name Predicate.if_pred},
- HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
-
-fun mk_not t = let val T = mk_predT HOLogic.unitT
- in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
-
-fun mk_Enum f =
- let val T as Type ("fun", [T', _]) = fastype_of f
- in
- Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f
- end;
-
-fun mk_Eval (f, x) =
- let
- val T = fastype_of x
- in
- Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x
- end;
-
-fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map},
- (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp;
-
-val lift_pred = I
-
-val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
- mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
- mk_map = mk_map, lift_pred = lift_pred};
-
-end;
-
-(* termify_code:
-val termT = Type ("Code_Eval.term", []);
-fun termifyT T = HOLogic.mk_prodT (T, HOLogic.unitT --> termT)
-*)
-(*
-fun lift_random random =
- let
- val T = dest_randomT (fastype_of random)
- in
- mk_scomp (random,
- mk_fun_comp (HOLogic.pair_const (PredicateCompFuns.mk_predT T) @{typ Random.seed},
- mk_fun_comp (Const (@{const_name Predicate.single}, T --> (PredicateCompFuns.mk_predT T)),
- Const (@{const_name "fst"}, HOLogic.mk_prodT (T, @{typ "unit => term"}) --> T))))
- end;
-*)
-
-structure RPredCompFuns =
-struct
-
-fun mk_rpredT T =
- @{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"})
-
-fun dest_rpredT (Type ("fun", [_,
- Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T
- | dest_rpredT T = raise TYPE ("dest_rpredT", [T], []);
-
-fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T)
-
-fun mk_single t =
- let
- val T = fastype_of t
- in
- Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t
- end;
-
-fun mk_bind (x, f) =
- let
- val T as (Type ("fun", [_, U])) = fastype_of f
- in
- Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f
- end
-
-val mk_sup = HOLogic.mk_binop @{const_name RPred.supp}
-
-fun mk_if cond = Const (@{const_name RPred.if_rpred},
- HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond;
-
-fun mk_not t = error "Negation is not defined for RPred"
-
-fun mk_map t = error "FIXME" (*FIXME*)
-
-fun lift_pred t =
- let
- val T = PredicateCompFuns.dest_predT (fastype_of t)
- val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T
- in
- Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t
- end;
-
-val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot,
- mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
- mk_map = mk_map, lift_pred = lift_pred};
-
-end;
-(* for external use with interactive mode *)
-val rpred_compfuns = RPredCompFuns.compfuns;
-
-fun lift_random random =
- let
- val T = dest_randomT (fastype_of random)
- in
- Const (@{const_name lift_random}, (@{typ Random.seed} -->
- HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
- RPredCompFuns.mk_rpredT T) $ random
- end;
-
-(* Mode analysis *)
-
-(*** check if a term contains only constructor functions ***)
-fun is_constrt thy =
- let
- val cnstrs = flat (maps
- (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
- (Symtab.dest (Datatype.get_all thy)));
- fun check t = (case strip_comb t of
- (Free _, []) => true
- | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
- (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
- | _ => false)
- | _ => false)
- in check end;
-
-(*** check if a type is an equality type (i.e. doesn't contain fun)
- FIXME this is only an approximation ***)
-fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
- | is_eqT _ = true;
-
-fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
-val terms_vs = distinct (op =) o maps term_vs;
-
-(** collect all Frees in a term (with duplicates!) **)
-fun term_vTs tm =
- fold_aterms (fn Free xT => cons xT | _ => I) tm [];
-
-(*FIXME this function should not be named merge... make it local instead*)
-fun merge xs [] = xs
- | merge [] ys = ys
- | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
- else y::merge (x::xs) ys;
-
-fun subsets i j = if i <= j then
- let val is = subsets (i+1) j
- in merge (map (fn ks => i::ks) is) is end
- else [[]];
-
-(* FIXME: should be in library - map_prod *)
-fun cprod ([], ys) = []
- | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
-
-fun cprods xss = foldr (map op :: o cprod) [[]] xss;
-
-
-
-(*TODO: cleanup function and put together with modes_of_term *)
-(*
-fun modes_of_param default modes t = let
- val (vs, t') = strip_abs t
- val b = length vs
- fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
- let
- val (args1, args2) =
- if length args < length iss then
- error ("Too few arguments for inductive predicate " ^ name)
- else chop (length iss) args;
- val k = length args2;
- val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1)
- (1 upto b)
- val partial_mode = (1 upto k) \\ perm
- in
- if not (partial_mode subset is) then [] else
- let
- val is' =
- (fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm [])
- |> fold (fn i => if i > k then cons (i - k + b) else I) is
-
- val res = map (fn x => Mode (m, is', x)) (cprods (map
- (fn (NONE, _) => [NONE]
- | (SOME js, arg) => map SOME (filter
- (fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
- (iss ~~ args1)))
- in res end
- end)) (AList.lookup op = modes name)
- in case strip_comb t' of
- (Const (name, _), args) => the_default default (mk_modes name args)
- | (Var ((name, _), _), args) => the (mk_modes name args)
- | (Free (name, _), args) => the (mk_modes name args)
- | _ => default end
-
-and
-*)
-fun modes_of_term modes t =
- let
- val ks = 1 upto length (binder_types (fastype_of t));
- val default = [Mode (([], ks), ks, [])];
- fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
- let
- val (args1, args2) =
- if length args < length iss then
- error ("Too few arguments for inductive predicate " ^ name)
- else chop (length iss) args;
- val k = length args2;
- val prfx = 1 upto k
- in
- if not (is_prefix op = prfx is) then [] else
- let val is' = map (fn i => i - k) (List.drop (is, k))
- in map (fn x => Mode (m, is', x)) (cprods (map
- (fn (NONE, _) => [NONE]
- | (SOME js, arg) => map SOME (filter
- (fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
- (iss ~~ args1)))
- end
- end)) (AList.lookup op = modes name)
-
- in
- case strip_comb (Envir.eta_contract t) of
- (Const (name, _), args) => the_default default (mk_modes name args)
- | (Var ((name, _), _), args) => the (mk_modes name args)
- | (Free (name, _), args) => the (mk_modes name args)
- | (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *)
- | _ => default
- end
-
-fun select_mode_prem thy modes vs ps =
- find_first (is_some o snd) (ps ~~ map
- (fn Prem (us, t) => find_first (fn Mode (_, is, _) =>
- let
- val (in_ts, out_ts) = split_smode is us;
- val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
- val vTs = maps term_vTs out_ts';
- val dupTs = map snd (duplicates (op =) vTs) @
- List.mapPartial (AList.lookup (op =) vTs) vs;
- in
- terms_vs (in_ts @ in_ts') subset vs andalso
- forall (is_eqT o fastype_of) in_ts' andalso
- term_vs t subset vs andalso
- forall is_eqT dupTs
- end)
- (modes_of_term modes t handle Option =>
- error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
- | Negprem (us, t) => find_first (fn Mode (_, is, _) =>
- length us = length is andalso
- terms_vs us subset vs andalso
- term_vs t subset vs)
- (modes_of_term modes t handle Option =>
- error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
- | Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), [], []))
- else NONE
- ) ps);
-
-fun fold_prem f (Prem (args, _)) = fold f args
- | fold_prem f (Negprem (args, _)) = fold f args
- | fold_prem f (Sidecond t) = f t
-
-fun all_subsets [] = [[]]
- | all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end
-
-fun generator vTs v =
- let
- val T = the (AList.lookup (op =) vTs v)
- in
- (Generator (v, T), Mode (([], []), [], []))
- end;
-
-fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t)
- | gen_prem _ = error "gen_prem : invalid input for gen_prem"
-
-fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) =
- if member (op =) param_vs v then
- GeneratorPrem (us, t)
- else p
- | param_gen_prem param_vs p = p
-
-fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) =
- let
- val modes' = modes @ List.mapPartial
- (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
- (param_vs ~~ iss);
- val gen_modes' = gen_modes @ List.mapPartial
- (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
- (param_vs ~~ iss);
- val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts []))
- val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps [])
- fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs)
- | check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of
- NONE =>
- (if with_generator then
- (case select_mode_prem thy gen_modes' vs ps of
- SOME (p, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps)
- (case p of Prem (us, _) => vs union terms_vs us | _ => vs)
- (filter_out (equal p) ps)
- | NONE =>
- let
- val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length))
- in
- case (find_first (fn generator_vs => is_some
- (select_mode_prem thy modes' (vs union generator_vs) ps)) all_generator_vs) of
- SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps)
- (vs union generator_vs) ps
- | NONE => NONE
- end)
- else
- NONE)
- | SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps)
- (case p of Prem (us, _) => vs union terms_vs us | _ => vs)
- (filter_out (equal p) ps))
- val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts));
- val in_vs = terms_vs in_ts;
- val concl_vs = terms_vs ts
- in
- if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
- forall (is_eqT o fastype_of) in_ts' then
- case check_mode_prems [] (param_vs union in_vs) ps of
- NONE => NONE
- | SOME (acc_ps, vs) =>
- if with_generator then
- SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs)))
- else
- if concl_vs subset vs then SOME (ts, rev acc_ps) else NONE
- else NONE
- end;
-
-fun check_modes_pred with_generator thy param_vs preds modes gen_modes (p, ms) =
- let val SOME rs = AList.lookup (op =) preds p
- in (p, List.filter (fn m => case find_index
- (is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of
- ~1 => true
- | i => (Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^
- p ^ " violates mode " ^ string_of_mode m); false)) ms)
- end;
-
-fun get_modes_pred with_generator thy param_vs preds modes gen_modes (p, ms) =
- let
- val SOME rs = AList.lookup (op =) preds p
- in
- (p, map (fn m =>
- (m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms)
- end;
-
-fun fixp f (x : (string * mode list) list) =
- let val y = f x
- in if x = y then x else fixp f y end;
-
-fun modes_of_arities arities =
- (map (fn (s, (ks, k)) => (s, cprod (cprods (map
- (fn NONE => [NONE]
- | SOME k' => map SOME (subsets 1 k')) ks),
- subsets 1 k))) arities)
-
-fun infer_modes with_generator thy extra_modes arities param_vs preds =
- let
- val modes =
- fixp (fn modes =>
- map (check_modes_pred with_generator thy param_vs preds (modes @ extra_modes) []) modes)
- (modes_of_arities arities)
- in
- map (get_modes_pred with_generator thy param_vs preds (modes @ extra_modes) []) modes
- end;
-
-fun remove_from rem [] = []
- | remove_from rem ((k, vs) :: xs) =
- (case AList.lookup (op =) rem k of
- NONE => (k, vs)
- | SOME vs' => (k, vs \\ vs'))
- :: remove_from rem xs
-
-fun infer_modes_with_generator thy extra_modes arities param_vs preds =
- let
- val prednames = map fst preds
- val extra_modes = all_modes_of thy
- val gen_modes = all_generator_modes_of thy
- |> filter_out (fn (name, _) => member (op =) prednames name)
- val starting_modes = remove_from extra_modes (modes_of_arities arities)
- val modes =
- fixp (fn modes =>
- map (check_modes_pred true thy param_vs preds extra_modes (gen_modes @ modes)) modes)
- starting_modes
- in
- map (get_modes_pred true thy param_vs preds extra_modes (gen_modes @ modes)) modes
- end;
-
-(* term construction *)
-
-fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of
- NONE => (Free (s, T), (names, (s, [])::vs))
- | SOME xs =>
- let
- val s' = Name.variant names s;
- val v = Free (s', T)
- in
- (v, (s'::names, AList.update (op =) (s, v::xs) vs))
- end);
-
-fun distinct_v (Free (s, T)) nvs = mk_v nvs s T
- | distinct_v (t $ u) nvs =
- let
- val (t', nvs') = distinct_v t nvs;
- val (u', nvs'') = distinct_v u nvs';
- in (t' $ u', nvs'') end
- | distinct_v x nvs = (x, nvs);
-
-fun compile_match thy compfuns eqs eqs' out_ts success_t =
- let
- val eqs'' = maps mk_eq eqs @ eqs'
- val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) [];
- val name = Name.variant names "x";
- val name' = Name.variant (name :: names) "y";
- val T = mk_tupleT (map fastype_of out_ts);
- val U = fastype_of success_t;
- val U' = dest_predT compfuns U;
- val v = Free (name, T);
- val v' = Free (name', T);
- in
- lambda v (fst (Datatype.make_case
- (ProofContext.init thy) false [] v
- [(mk_tuple out_ts,
- if null eqs'' then success_t
- else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $
- foldr1 HOLogic.mk_conj eqs'' $ success_t $
- mk_bot compfuns U'),
- (v', mk_bot compfuns U')]))
- end;
-
-(*FIXME function can be removed*)
-fun mk_funcomp f t =
- let
- val names = Term.add_free_names t [];
- val Ts = binder_types (fastype_of t);
- val vs = map Free
- (Name.variant_list names (replicate (length Ts) "x") ~~ Ts)
- in
- fold_rev lambda vs (f (list_comb (t, vs)))
- end;
-(*
-fun compile_param_ext thy compfuns modes (NONE, t) = t
- | compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
- let
- val (vs, u) = strip_abs t
- val (ivs, ovs) = split_mode is vs
- val (f, args) = strip_comb u
- val (params, args') = chop (length ms) args
- val (inargs, outargs) = split_mode is' args'
- val b = length vs
- val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b)
- val outp_perm =
- snd (split_mode is perm)
- |> map (fn i => i - length (filter (fn x => x < i) is'))
- val names = [] -- TODO
- val out_names = Name.variant_list names (replicate (length outargs) "x")
- val f' = case f of
- Const (name, T) =>
- if AList.defined op = modes name then
- mk_predfun_of thy compfuns (name, T) (iss, is')
- else error "compile param: Not an inductive predicate with correct mode"
- | Free (name, T) => Free (name, param_funT_of compfuns T (SOME is'))
- val outTs = dest_tupleT (dest_predT compfuns (body_type (fastype_of f')))
- val out_vs = map Free (out_names ~~ outTs)
- val params' = map (compile_param thy modes) (ms ~~ params)
- val f_app = list_comb (f', params' @ inargs)
- val single_t = (mk_single compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm)))
- val match_t = compile_match thy compfuns [] [] out_vs single_t
- in list_abs (ivs,
- mk_bind compfuns (f_app, match_t))
- end
- | compile_param_ext _ _ _ _ = error "compile params"
-*)
-
-fun compile_param size thy compfuns (NONE, t) = t
- | compile_param size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) =
- let
- val (f, args) = strip_comb (Envir.eta_contract t)
- val (params, args') = chop (length ms) args
- val params' = map (compile_param size thy compfuns) (ms ~~ params)
- val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
- val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
- val f' =
- case f of
- Const (name, T) =>
- mk_fun_of compfuns thy (name, T) (iss, is')
- | Free (name, T) => Free (name, funT_of compfuns (iss, is') T)
- | _ => error ("PredicateCompiler: illegal parameter term")
- in list_comb (f', params' @ args') end
-
-fun compile_expr size thy ((Mode (mode, is, ms)), t) =
- case strip_comb t of
- (Const (name, T), params) =>
- let
- val params' = map (compile_param size thy PredicateCompFuns.compfuns) (ms ~~ params)
- val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
- in
- list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params')
- end
- | (Free (name, T), args) =>
- let
- val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
- in
- list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args)
- end;
-
-fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) =
- case strip_comb t of
- (Const (name, T), params) =>
- let
- val params' = map (compile_param size thy compfuns) (ms ~~ params)
- in
- list_comb (mk_generator_of compfuns thy (name, T) mode, params')
- end
- | (Free (name, T), args) =>
- list_comb (Free (name, sizelim_funT_of RPredCompFuns.compfuns ([], is) T), args)
-
-(** specific rpred functions -- move them to the correct place in this file *)
-
-(* uncommented termify code; causes more trouble than expected at first *)
-(*
-fun mk_valtermify_term (t as Const (c, T)) = HOLogic.mk_prod (t, Abs ("u", HOLogic.unitT, HOLogic.reflect_term t))
- | mk_valtermify_term (Free (x, T)) = Free (x, termifyT T)
- | mk_valtermify_term (t1 $ t2) =
- let
- val T = fastype_of t1
- val (T1, T2) = dest_funT T
- val t1' = mk_valtermify_term t1
- val t2' = mk_valtermify_term t2
- in
- Const ("Code_Eval.valapp", termifyT T --> termifyT T1 --> termifyT T2) $ t1' $ t2'
- end
- | mk_valtermify_term _ = error "Not a valid term for mk_valtermify_term"
-*)
-
-fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) =
- let
- fun check_constrt t (names, eqs) =
- if is_constrt thy t then (t, (names, eqs)) else
- let
- val s = Name.variant names "x";
- val v = Free (s, fastype_of t)
- in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;
-
- val (in_ts, out_ts) = split_smode is ts;
- val (in_ts', (all_vs', eqs)) =
- fold_map check_constrt in_ts (all_vs, []);
-
- fun compile_prems out_ts' vs names [] =
- let
- val (out_ts'', (names', eqs')) =
- fold_map check_constrt out_ts' (names, []);
- val (out_ts''', (names'', constr_vs)) = fold_map distinct_v
- out_ts'' (names', map (rpair []) vs);
- in
- (* termify code:
- compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
- (mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts)))
- *)
- compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
- (final_term out_ts)
- end
- | compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) =
- let
- val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
- val (out_ts', (names', eqs)) =
- fold_map check_constrt out_ts (names, [])
- val (out_ts'', (names'', constr_vs')) = fold_map distinct_v
- out_ts' ((names', map (rpair []) vs))
- val (compiled_clause, rest) = case p of
- Prem (us, t) =>
- let
- val (in_ts, out_ts''') = split_smode is us;
- val args = case size of
- NONE => in_ts
- | SOME size_t => in_ts @ [size_t]
- val u = lift_pred compfuns
- (list_comb (compile_expr size thy (mode, t), args))
- val rest = compile_prems out_ts''' vs' names'' ps
- in
- (u, rest)
- end
- | Negprem (us, t) =>
- let
- val (in_ts, out_ts''') = split_smode is us
- val u = lift_pred compfuns
- (mk_not PredicateCompFuns.compfuns (list_comb (compile_expr NONE thy (mode, t), in_ts)))
- val rest = compile_prems out_ts''' vs' names'' ps
- in
- (u, rest)
- end
- | Sidecond t =>
- let
- val rest = compile_prems [] vs' names'' ps;
- in
- (mk_if compfuns t, rest)
- end
- | GeneratorPrem (us, t) =>
- let
- val (in_ts, out_ts''') = split_smode is us;
- val args = case size of
- NONE => in_ts
- | SOME size_t => in_ts @ [size_t]
- val u = list_comb (compile_gen_expr size thy compfuns (mode, t), args)
- val rest = compile_prems out_ts''' vs' names'' ps
- in
- (u, rest)
- end
- | Generator (v, T) =>
- let
- val u = lift_random (HOLogic.mk_random T @{term "1::code_numeral"})
- val rest = compile_prems [Free (v, T)] vs' names'' ps;
- in
- (u, rest)
- end
- in
- compile_match thy compfuns constr_vs' eqs out_ts''
- (mk_bind compfuns (compiled_clause, rest))
- end
- val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps;
- in
- mk_bind compfuns (mk_single compfuns inp, prem_t)
- end
-
-fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls =
- let
- val (Ts1, (Us1, Us2)) = split_mode mode (binder_types T)
- val funT_of = if use_size then sizelim_funT_of else funT_of
- val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) (fst mode) Ts1
- val xnames = Name.variant_list (all_vs @ param_vs)
- (map (fn i => "x" ^ string_of_int i) (snd mode));
- val size_name = Name.variant (all_vs @ param_vs @ xnames) "size"
- (* termify code: val xs = map2 (fn s => fn T => Free (s, termifyT T)) xnames Us1; *)
- val xs = map2 (fn s => fn T => Free (s, T)) xnames Us1;
- val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1'
- val size = Free (size_name, @{typ "code_numeral"})
- val decr_size =
- if use_size then
- SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"})
- $ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"}))
- else
- NONE
- val cl_ts =
- map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts))
- thy all_vs param_vs mode (mk_tuple xs)) moded_cls;
- val t = foldr1 (mk_sup compfuns) cl_ts
- val T' = mk_predT compfuns (mk_tupleT Us2)
- val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
- $ HOLogic.mk_eq (size, @{term "0 :: code_numeral"})
- $ mk_bot compfuns (dest_predT compfuns T') $ t
- val fun_const = mk_fun_of compfuns thy (s, T) mode
- val eq = if use_size then
- (list_comb (fun_const, params @ xs @ [size]), size_t)
- else
- (list_comb (fun_const, params @ xs), t)
- in
- HOLogic.mk_Trueprop (HOLogic.mk_eq eq)
- end;
-
-(* special setup for simpset *)
-val HOL_basic_ss' = HOL_basic_ss setSolver
- (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
-
-(* Definition of executable functions and their intro and elim rules *)
-
-fun print_arities arities = tracing ("Arities:\n" ^
- cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^
- space_implode " -> " (map
- (fn NONE => "X" | SOME k' => string_of_int k')
- (ks @ [SOME k]))) arities));
-
-fun mk_Eval_of ((x, T), NONE) names = (x, names)
- | mk_Eval_of ((x, T), SOME mode) names = let
- val Ts = binder_types T
- val argnames = Name.variant_list names
- (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
- val args = map Free (argnames ~~ Ts)
- val (inargs, outargs) = split_smode mode args
- val r = PredicateCompFuns.mk_Eval (list_comb (x, inargs), mk_tuple outargs)
- val t = fold_rev lambda args r
-in
- (t, argnames @ names)
-end;
-
-fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy =
-let
- val Ts = binder_types (fastype_of pred)
- val funtrm = Const (mode_id, funT)
- val argnames = Name.variant_list []
- (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
- val (Ts1, Ts2) = chop (length iss) Ts;
- val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1
- val args = map Free (argnames ~~ (Ts1' @ Ts2))
- val (params, ioargs) = chop (length iss) args
- val (inargs, outargs) = split_smode is ioargs
- val param_names = Name.variant_list argnames
- (map (fn i => "p" ^ string_of_int i) (1 upto (length iss)))
- val param_vs = map Free (param_names ~~ Ts1)
- val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ iss) []
- val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ ioargs))
- val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ ioargs))
- val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params')
- val funargs = params @ inargs
- val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
- if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs))
- val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
- mk_tuple outargs))
- val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)
- val simprules = [defthm, @{thm eval_pred},
- @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}]
- val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1
- val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ ["y"]) [] introtrm (fn {...} => unfolddef_tac)
- val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
- val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P)
- val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac)
-in
- (introthm, elimthm)
-end;
-
-fun create_constname_of_mode thy prefix name mode =
- let
- fun string_of_mode mode = if null mode then "0"
- else space_implode "_" (map string_of_int mode)
- val HOmode = space_implode "_and_"
- (fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) [])
- in
- (Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^
- (if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode))
- end;
-
-fun create_definitions preds (name, modes) thy =
- let
- val compfuns = PredicateCompFuns.compfuns
- val T = AList.lookup (op =) preds name |> the
- fun create_definition (mode as (iss, is)) thy = let
- val mode_cname = create_constname_of_mode thy "" name mode
- val mode_cbasename = Long_Name.base_name mode_cname
- val Ts = binder_types T
- val (Ts1, Ts2) = chop (length iss) Ts
- val (Us1, Us2) = split_smode is Ts2
- val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1
- val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2))
- val names = Name.variant_list []
- (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
- val xs = map Free (names ~~ (Ts1' @ Ts2));
- val (xparams, xargs) = chop (length iss) xs;
- val (xins, xouts) = split_smode is xargs
- val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ iss) names
- fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t
- | mk_split_lambda [x] t = lambda x t
- | mk_split_lambda xs t =
- let
- fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
- | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
- in
- mk_split_lambda' xs t
- end;
- val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts
- (list_comb (Const (name, T), xparams' @ xargs)))
- val lhs = list_comb (Const (mode_cname, funT), xparams @ xins)
- val def = Logic.mk_equals (lhs, predterm)
- val ([definition], thy') = thy |>
- Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |>
- PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])]
- val (intro, elim) =
- create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy'
- in thy' |> add_predfun name mode (mode_cname, definition, intro, elim)
- |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd
- |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim) |> snd
- |> Theory.checkpoint
- end;
- in
- fold create_definition modes thy
- end;
-
-fun sizelim_create_definitions preds (name, modes) thy =
- let
- val T = AList.lookup (op =) preds name |> the
- fun create_definition mode thy =
- let
- val mode_cname = create_constname_of_mode thy "sizelim_" name mode
- val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T
- in
- thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
- |> set_sizelim_function_name name mode mode_cname
- end;
- in
- fold create_definition modes thy
- end;
-
-fun rpred_create_definitions preds (name, modes) thy =
- let
- val T = AList.lookup (op =) preds name |> the
- fun create_definition mode thy =
- let
- val mode_cname = create_constname_of_mode thy "gen_" name mode
- val funT = sizelim_funT_of RPredCompFuns.compfuns mode T
- in
- thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
- |> set_generator_name name mode mode_cname
- end;
- in
- fold create_definition modes thy
- end;
-
-(* Proving equivalence of term *)
-
-fun is_Type (Type _) = true
- | is_Type _ = false
-
-(* returns true if t is an application of an datatype constructor *)
-(* which then consequently would be splitted *)
-(* else false *)
-fun is_constructor thy t =
- if (is_Type (fastype_of t)) then
- (case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of
- NONE => false
- | SOME info => (let
- val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
- val (c, _) = strip_comb t
- in (case c of
- Const (name, _) => name mem_string constr_consts
- | _ => false) end))
- else false
-
-(* MAJOR FIXME: prove_params should be simple
- - different form of introrule for parameters ? *)
-fun prove_param thy (NONE, t) = TRY (rtac @{thm refl} 1)
- | prove_param thy (m as SOME (Mode (mode, is, ms)), t) =
- let
- val (f, args) = strip_comb (Envir.eta_contract t)
- val (params, _) = chop (length ms) args
- val f_tac = case f of
- Const (name, T) => simp_tac (HOL_basic_ss addsimps
- (@{thm eval_pred}::(predfun_definition_of thy name mode)::
- @{thm "Product_Type.split_conv"}::[])) 1
- | Free _ => TRY (rtac @{thm refl} 1)
- | Abs _ => error "prove_param: No valid parameter term"
- in
- REPEAT_DETERM (etac @{thm thin_rl} 1)
- THEN REPEAT_DETERM (rtac @{thm ext} 1)
- THEN print_tac "prove_param"
- THEN f_tac
- THEN print_tac "after simplification in prove_args"
- THEN (EVERY (map (prove_param thy) (ms ~~ params)))
- THEN (REPEAT_DETERM (atac 1))
- end
-
-fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) =
- case strip_comb t of
- (Const (name, T), args) =>
- let
- val introrule = predfun_intro_of thy name mode
- val (args1, args2) = chop (length ms) args
- in
- rtac @{thm bindI} 1
- THEN print_tac "before intro rule:"
- (* for the right assumption in first position *)
- THEN rotate_tac premposition 1
- THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule)
- THEN rtac introrule 1
- THEN print_tac "after intro rule"
- (* work with parameter arguments *)
- THEN (atac 1)
- THEN (print_tac "parameter goal")
- THEN (EVERY (map (prove_param thy) (ms ~~ args1)))
- THEN (REPEAT_DETERM (atac 1))
- end
- | _ => rtac @{thm bindI} 1 THEN atac 1
-
-fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st;
-
-fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st
-
-fun prove_match thy (out_ts : term list) = let
- fun get_case_rewrite t =
- if (is_constructor thy t) then let
- val case_rewrites = (#case_rewrites (Datatype.the_info thy
- ((fst o dest_Type o fastype_of) t)))
- in case_rewrites @ (flat (map get_case_rewrite (snd (strip_comb t)))) end
- else []
- val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: (flat (map get_case_rewrite out_ts))
-(* replace TRY by determining if it necessary - are there equations when calling compile match? *)
-in
- (* make this simpset better! *)
- asm_simp_tac (HOL_basic_ss' addsimps simprules) 1
- THEN print_tac "after prove_match:"
- THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1
- THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))
- THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))))
- THEN print_tac "after if simplification"
-end;
-
-(* corresponds to compile_fun -- maybe call that also compile_sidecond? *)
-
-fun prove_sidecond thy modes t =
- let
- fun preds_of t nameTs = case strip_comb t of
- (f as Const (name, T), args) =>
- if AList.defined (op =) modes name then (name, T) :: nameTs
- else fold preds_of args nameTs
- | _ => nameTs
- val preds = preds_of t []
- val defs = map
- (fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T)))))
- preds
- in
- (* remove not_False_eq_True when simpset in prove_match is better *)
- simp_tac (HOL_basic_ss addsimps @{thm not_False_eq_True} :: @{thm eval_pred} :: defs) 1
- (* need better control here! *)
- end
-
-fun prove_clause thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) =
- let
- val (in_ts, clause_out_ts) = split_smode is ts;
- fun prove_prems out_ts [] =
- (prove_match thy out_ts)
- THEN asm_simp_tac HOL_basic_ss' 1
- THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
- | prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
- let
- val premposition = (find_index (equal p) clauses) + nargs
- val rest_tac = (case p of Prem (us, t) =>
- let
- val (_, out_ts''') = split_smode is us
- val rec_tac = prove_prems out_ts''' ps
- in
- print_tac "before clause:"
- THEN asm_simp_tac HOL_basic_ss 1
- THEN print_tac "before prove_expr:"
- THEN prove_expr thy (mode, t, us) premposition
- THEN print_tac "after prove_expr:"
- THEN rec_tac
- end
- | Negprem (us, t) =>
- let
- val (_, out_ts''') = split_smode is us
- val rec_tac = prove_prems out_ts''' ps
- val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
- val (_, params) = strip_comb t
- in
- rtac @{thm bindI} 1
- THEN (if (is_some name) then
- simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1
- THEN rtac @{thm not_predI} 1
- THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
- THEN (REPEAT_DETERM (atac 1))
- (* FIXME: work with parameter arguments *)
- THEN (EVERY (map (prove_param thy) (param_modes ~~ params)))
- else
- rtac @{thm not_predI'} 1)
- THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
- THEN rec_tac
- end
- | Sidecond t =>
- rtac @{thm bindI} 1
- THEN rtac @{thm if_predI} 1
- THEN print_tac "before sidecond:"
- THEN prove_sidecond thy modes t
- THEN print_tac "after sidecond:"
- THEN prove_prems [] ps)
- in (prove_match thy out_ts)
- THEN rest_tac
- end;
- val prems_tac = prove_prems in_ts moded_ps
- in
- rtac @{thm bindI} 1
- THEN rtac @{thm singleI} 1
- THEN prems_tac
- end;
-
-fun select_sup 1 1 = []
- | select_sup _ 1 = [rtac @{thm supI1}]
- | select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1));
-
-fun prove_one_direction thy clauses preds modes pred mode moded_clauses =
- let
- val T = the (AList.lookup (op =) preds pred)
- val nargs = length (binder_types T) - nparams_of thy pred
- val pred_case_rule = the_elim_of thy pred
- in
- REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
- THEN etac (predfun_elim_of thy pred mode) 1
- THEN etac pred_case_rule 1
- THEN (EVERY (map
- (fn i => EVERY' (select_sup (length moded_clauses) i) i)
- (1 upto (length moded_clauses))))
- THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses))
- THEN print_tac "proved one direction"
- end;
-
-(** Proof in the other direction **)
-
-fun prove_match2 thy out_ts = let
- fun split_term_tac (Free _) = all_tac
- | split_term_tac t =
- if (is_constructor thy t) then let
- val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t)
- val num_of_constrs = length (#case_rewrites info)
- (* special treatment of pairs -- because of fishing *)
- val split_rules = case (fst o dest_Type o fastype_of) t of
- "*" => [@{thm prod.split_asm}]
- | _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm")
- val (_, ts) = strip_comb t
- in
- (Splitter.split_asm_tac split_rules 1)
-(* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1)
- THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *)
- THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2))
- THEN (EVERY (map split_term_tac ts))
- end
- else all_tac
- in
- split_term_tac (mk_tuple out_ts)
- THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2))))
- end
-
-(* VERY LARGE SIMILIRATIY to function prove_param
--- join both functions
-*)
-(* TODO: remove function *)
-
-fun prove_param2 thy (NONE, t) = all_tac
- | prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let
- val (f, args) = strip_comb (Envir.eta_contract t)
- val (params, _) = chop (length ms) args
- val f_tac = case f of
- Const (name, T) => full_simp_tac (HOL_basic_ss addsimps
- (@{thm eval_pred}::(predfun_definition_of thy name mode)
- :: @{thm "Product_Type.split_conv"}::[])) 1
- | Free _ => all_tac
- | _ => error "prove_param2: illegal parameter term"
- in
- print_tac "before simplification in prove_args:"
- THEN f_tac
- THEN print_tac "after simplification in prove_args"
- THEN (EVERY (map (prove_param2 thy) (ms ~~ params)))
- end
-
-
-fun prove_expr2 thy (Mode (mode, is, ms), t) =
- (case strip_comb t of
- (Const (name, T), args) =>
- etac @{thm bindE} 1
- THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
- THEN print_tac "prove_expr2-before"
- THEN (debug_tac (Syntax.string_of_term_global thy
- (prop_of (predfun_elim_of thy name mode))))
- THEN (etac (predfun_elim_of thy name mode) 1)
- THEN print_tac "prove_expr2"
- THEN (EVERY (map (prove_param2 thy) (ms ~~ args)))
- THEN print_tac "finished prove_expr2"
- | _ => etac @{thm bindE} 1)
-
-(* FIXME: what is this for? *)
-(* replace defined by has_mode thy pred *)
-(* TODO: rewrite function *)
-fun prove_sidecond2 thy modes t = let
- fun preds_of t nameTs = case strip_comb t of
- (f as Const (name, T), args) =>
- if AList.defined (op =) modes name then (name, T) :: nameTs
- else fold preds_of args nameTs
- | _ => nameTs
- val preds = preds_of t []
- val defs = map
- (fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T)))))
- preds
- in
- (* only simplify the one assumption *)
- full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1
- (* need better control here! *)
- THEN print_tac "after sidecond2 simplification"
- end
-
-fun prove_clause2 thy modes pred (iss, is) (ts, ps) i =
- let
- val pred_intro_rule = nth (intros_of thy pred) (i - 1)
- val (in_ts, clause_out_ts) = split_smode is ts;
- fun prove_prems2 out_ts [] =
- print_tac "before prove_match2 - last call:"
- THEN prove_match2 thy out_ts
- THEN print_tac "after prove_match2 - last call:"
- THEN (etac @{thm singleE} 1)
- THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
- THEN (asm_full_simp_tac HOL_basic_ss' 1)
- THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
- THEN (asm_full_simp_tac HOL_basic_ss' 1)
- THEN SOLVED (print_tac "state before applying intro rule:"
- THEN (rtac pred_intro_rule 1)
- (* How to handle equality correctly? *)
- THEN (print_tac "state before assumption matching")
- THEN (REPEAT (atac 1 ORELSE
- (CHANGED (asm_full_simp_tac HOL_basic_ss' 1)
- THEN print_tac "state after simp_tac:"))))
- | prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
- let
- val rest_tac = (case p of
- Prem (us, t) =>
- let
- val (_, out_ts''') = split_smode is us
- val rec_tac = prove_prems2 out_ts''' ps
- in
- (prove_expr2 thy (mode, t)) THEN rec_tac
- end
- | Negprem (us, t) =>
- let
- val (_, out_ts''') = split_smode is us
- val rec_tac = prove_prems2 out_ts''' ps
- val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
- val (_, params) = strip_comb t
- in
- print_tac "before neg prem 2"
- THEN etac @{thm bindE} 1
- THEN (if is_some name then
- full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1
- THEN etac @{thm not_predE} 1
- THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
- THEN (EVERY (map (prove_param2 thy) (param_modes ~~ params)))
- else
- etac @{thm not_predE'} 1)
- THEN rec_tac
- end
- | Sidecond t =>
- etac @{thm bindE} 1
- THEN etac @{thm if_predE} 1
- THEN prove_sidecond2 thy modes t
- THEN prove_prems2 [] ps)
- in print_tac "before prove_match2:"
- THEN prove_match2 thy out_ts
- THEN print_tac "after prove_match2:"
- THEN rest_tac
- end;
- val prems_tac = prove_prems2 in_ts ps
- in
- print_tac "starting prove_clause2"
- THEN etac @{thm bindE} 1
- THEN (etac @{thm singleE'} 1)
- THEN (TRY (etac @{thm Pair_inject} 1))
- THEN print_tac "after singleE':"
- THEN prems_tac
- end;
-
-fun prove_other_direction thy modes pred mode moded_clauses =
- let
- fun prove_clause clause i =
- (if i < length moded_clauses then etac @{thm supE} 1 else all_tac)
- THEN (prove_clause2 thy modes pred mode clause i)
- in
- (DETERM (TRY (rtac @{thm unit.induct} 1)))
- THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all})))
- THEN (rtac (predfun_intro_of thy pred mode) 1)
- THEN (REPEAT_DETERM (rtac @{thm refl} 2))
- THEN (EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses))))
- end;
-
-(** proof procedure **)
-
-fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) =
- let
- val ctxt = ProofContext.init thy
- val clauses = the (AList.lookup (op =) clauses pred)
- in
- Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term
- (if !do_proofs then
- (fn _ =>
- rtac @{thm pred_iffI} 1
- THEN prove_one_direction thy clauses preds modes pred mode moded_clauses
- THEN print_tac "proved one direction"
- THEN prove_other_direction thy modes pred mode moded_clauses
- THEN print_tac "proved other direction")
- else (fn _ => mycheat_tac thy 1))
- end;
-
-(* composition of mode inference, definition, compilation and proof *)
-
-(** auxillary combinators for table of preds and modes **)
-
-fun map_preds_modes f preds_modes_table =
- map (fn (pred, modes) =>
- (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table
-
-fun join_preds_modes table1 table2 =
- map_preds_modes (fn pred => fn mode => fn value =>
- (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1
-
-fun maps_modes preds_modes_table =
- map (fn (pred, modes) =>
- (pred, map (fn (mode, value) => value) modes)) preds_modes_table
-
-fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses =
- map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred
- (the (AList.lookup (op =) preds pred))) moded_clauses
-
-fun prove thy clauses preds modes moded_clauses compiled_terms =
- map_preds_modes (prove_pred thy clauses preds modes)
- (join_preds_modes moded_clauses compiled_terms)
-
-fun prove_by_skip thy _ _ _ _ compiled_terms =
- map_preds_modes (fn pred => fn mode => fn t => Drule.standard (SkipProof.make_thm thy t))
- compiled_terms
-
-fun prepare_intrs thy prednames =
- let
- val intrs = maps (intros_of thy) prednames
- |> map (Logic.unvarify o prop_of)
- val nparams = nparams_of thy (hd prednames)
- val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name)
- val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs)
- val _ $ u = Logic.strip_imp_concl (hd intrs);
- val params = List.take (snd (strip_comb u), nparams);
- val param_vs = maps term_vs params
- val all_vs = terms_vs intrs
- fun dest_prem t =
- (case strip_comb t of
- (v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t
- | (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of
- Prem (ts, t) => Negprem (ts, t)
- | Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t)))
- | Sidecond t => Sidecond (c $ t))
- | (c as Const (s, _), ts) =>
- if is_registered thy s then
- let val (ts1, ts2) = chop (nparams_of thy s) ts
- in Prem (ts2, list_comb (c, ts1)) end
- else Sidecond t
- | _ => Sidecond t)
- fun add_clause intr (clauses, arities) =
- let
- val _ $ t = Logic.strip_imp_concl intr;
- val (Const (name, T), ts) = strip_comb t;
- val (ts1, ts2) = chop nparams ts;
- val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr);
- val (Ts, Us) = chop nparams (binder_types T)
- in
- (AList.update op = (name, these (AList.lookup op = clauses name) @
- [(ts2, prems)]) clauses,
- AList.update op = (name, (map (fn U => (case strip_type U of
- (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs)
- | _ => NONE)) Ts,
- length Us)) arities)
- end;
- val (clauses, arities) = fold add_clause intrs ([], []);
- in (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) end;
-
-(** main function of predicate compiler **)
-
-fun add_equations_of steps prednames thy =
- let
- val _ = Output.tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...")
- val (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) =
- prepare_intrs thy prednames
- val _ = Output.tracing "Infering modes..."
- val moded_clauses = #infer_modes steps thy extra_modes arities param_vs clauses
- val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
- val _ = print_modes modes
- val _ = print_moded_clauses thy moded_clauses
- val _ = Output.tracing "Defining executable functions..."
- val thy' = fold (#create_definitions steps preds) modes thy
- |> Theory.checkpoint
- val _ = Output.tracing "Compiling equations..."
- val compiled_terms =
- (#compile_preds steps) thy' all_vs param_vs preds moded_clauses
- val _ = print_compiled_terms thy' compiled_terms
- val _ = Output.tracing "Proving equations..."
- val result_thms = #prove steps thy' clauses preds (extra_modes @ modes)
- moded_clauses compiled_terms
- val qname = #qname steps
- (* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *)
- val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute
- (fn thm => Context.mapping (Code.add_eqn thm) I))))
- val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
- [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),
- [attrib thy ])] thy))
- (maps_modes result_thms) thy'
- |> Theory.checkpoint
- in
- thy''
- end
-
-fun extend' value_of edges_of key (G, visited) =
- let
- val (G', v) = case try (Graph.get_node G) key of
- SOME v => (G, v)
- | NONE => (Graph.new_node (key, value_of key) G, value_of key)
- val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited)
- (G', key :: visited)
- in
- (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited')
- end;
-
-fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, []))
-
-fun gen_add_equations steps names thy =
- let
- val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy
- |> Theory.checkpoint;
- fun strong_conn_of gr keys =
- Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr)
- val scc = strong_conn_of (PredData.get thy') names
- val thy'' = fold_rev
- (fn preds => fn thy =>
- if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy)
- scc thy' |> Theory.checkpoint
- in thy'' end
-
-(* different instantiantions of the predicate compiler *)
-
-val add_equations = gen_add_equations
- {infer_modes = infer_modes false,
- create_definitions = create_definitions,
- compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false,
- prove = prove,
- are_not_defined = (fn thy => forall (null o modes_of thy)),
- qname = "equation"}
-
-val add_sizelim_equations = gen_add_equations
- {infer_modes = infer_modes false,
- create_definitions = sizelim_create_definitions,
- compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true,
- prove = prove_by_skip,
- are_not_defined = (fn thy => fn preds => true), (* TODO *)
- qname = "sizelim_equation"
- }
-
-val add_quickcheck_equations = gen_add_equations
- {infer_modes = infer_modes_with_generator,
- create_definitions = rpred_create_definitions,
- compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true,
- prove = prove_by_skip,
- are_not_defined = (fn thy => fn preds => true), (* TODO *)
- qname = "rpred_equation"}
-
-(** user interface **)
-
-(* generation of case rules from user-given introduction rules *)
-
-fun mk_casesrule ctxt nparams introrules =
- let
- val intros = map (Logic.unvarify o prop_of) introrules
- val (pred, (params, args)) = strip_intro_concl nparams (hd intros)
- val ([propname], ctxt1) = Variable.variant_fixes ["thesis"] ctxt
- val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
- val (argnames, ctxt2) = Variable.variant_fixes
- (map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt1
- val argvs = map2 (curry Free) argnames (map fastype_of args)
- fun mk_case intro =
- let
- val (_, (_, args)) = strip_intro_concl nparams intro
- val prems = Logic.strip_imp_prems intro
- val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args)
- val frees = (fold o fold_aterms)
- (fn t as Free _ =>
- if member (op aconv) params t then I else insert (op aconv) t
- | _ => I) (args @ prems) []
- in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
- val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs))
- val cases = map mk_case intros
- in Logic.list_implies (assm :: cases, prop) end;
-
-(* code_pred_intro attribute *)
-
-fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
-
-val code_pred_intros_attrib = attrib add_intro;
-
-local
-
-(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *)
-(* TODO: must create state to prove multiple cases *)
-fun generic_code_pred prep_const raw_const lthy =
- let
- val thy = ProofContext.theory_of lthy
- val const = prep_const thy raw_const
- val lthy' = LocalTheory.theory (PredData.map
- (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy
- |> LocalTheory.checkpoint
- val thy' = ProofContext.theory_of lthy'
- val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy')
- fun mk_cases const =
- let
- val nparams = nparams_of thy' const
- val intros = intros_of thy' const
- in mk_casesrule lthy' nparams intros end
- val cases_rules = map mk_cases preds
- val cases =
- map (fn case_rule => RuleCases.Case {fixes = [],
- assumes = [("", Logic.strip_imp_prems case_rule)],
- binds = [], cases = []}) cases_rules
- val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases
- val lthy'' = lthy'
- |> fold Variable.auto_fixes cases_rules
- |> ProofContext.add_cases true case_env
- fun after_qed thms goal_ctxt =
- let
- val global_thms = ProofContext.export goal_ctxt
- (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms)
- in
- goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #> add_equations [const])
- end
- in
- Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''
- end;
-
-structure P = OuterParse
-
-in
-
-val code_pred = generic_code_pred (K I);
-val code_pred_cmd = generic_code_pred Code.read_const
-
-val setup = PredData.put (Graph.empty) #>
- Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro))
- "adding alternative introduction rules for code generation of inductive predicates"
-(* Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib)
- "adding alternative elimination rules for code generation of inductive predicates";
- *)
- (*FIXME name discrepancy in attribs and ML code*)
- (*FIXME intros should be better named intro*)
- (*FIXME why distinguished attribute for cases?*)
-
-val _ = OuterSyntax.local_theory_to_proof "code_pred"
- "prove equations for predicate specified by intro/elim rules"
- OuterKeyword.thy_goal (P.term_group >> code_pred_cmd)
-
-end
-
-(*FIXME
-- Naming of auxiliary rules necessary?
-- add default code equations P x y z = P_i_i_i x y z
-*)
-
-(* transformation for code generation *)
-
-val eval_ref = ref (NONE : (unit -> term Predicate.pred) option);
-
-(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
-fun analyze_compr thy t_compr =
- let
- val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t
- | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr);
- val (body, Ts, fp) = HOLogic.strip_psplits split;
- val (pred as Const (name, T), all_args) = strip_comb body;
- val (params, args) = chop (nparams_of thy name) all_args;
- val user_mode = map_filter I (map_index
- (fn (i, t) => case t of Bound j => if j < length Ts then NONE
- else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*)
- val modes = filter (fn Mode (_, is, _) => is = user_mode)
- (modes_of_term (all_modes_of thy) (list_comb (pred, params)));
- val m = case modes
- of [] => error ("No mode possible for comprehension "
- ^ Syntax.string_of_term_global thy t_compr)
- | [m] => m
- | m :: _ :: _ => (warning ("Multiple modes possible for comprehension "
- ^ Syntax.string_of_term_global thy t_compr); m);
- val (inargs, outargs) = split_smode user_mode args;
- val t_pred = list_comb (compile_expr NONE thy (m, list_comb (pred, params)), inargs);
- val t_eval = if null outargs then t_pred else let
- val outargs_bounds = map (fn Bound i => i) outargs;
- val outargsTs = map (nth Ts) outargs_bounds;
- val T_pred = HOLogic.mk_tupleT outargsTs;
- val T_compr = HOLogic.mk_ptupleT fp Ts;
- val arrange_bounds = map_index I outargs_bounds
- |> sort (prod_ord (K EQUAL) int_ord)
- |> map fst;
- val arrange = funpow (length outargs_bounds - 1) HOLogic.mk_split
- (Term.list_abs (map (pair "") outargsTs,
- HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds)))
- in mk_map PredicateCompFuns.compfuns T_pred T_compr arrange t_pred end
- in t_eval end;
-
-fun eval thy t_compr =
- let
- val t = analyze_compr thy t_compr;
- val T = dest_predT PredicateCompFuns.compfuns (fastype_of t);
- val t' = mk_map PredicateCompFuns.compfuns T HOLogic.termT (HOLogic.term_of_const T) t;
- in (T, Code_ML.eval NONE ("Predicate_Compile.eval_ref", eval_ref) Predicate.map thy t' []) end;
-
-fun values ctxt k t_compr =
- let
- val thy = ProofContext.theory_of ctxt;
- val (T, t) = eval thy t_compr;
- val setT = HOLogic.mk_setT T;
- val (ts, _) = Predicate.yieldn k t;
- val elemsT = HOLogic.mk_set T ts;
- in if k = ~1 orelse length ts < k then elemsT
- else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ t_compr
- end;
-
-fun values_cmd modes k raw_t state =
- let
- val ctxt = Toplevel.context_of state;
- val t = Syntax.read_term ctxt raw_t;
- val t' = values ctxt k t;
- val ty' = Term.type_of t';
- val ctxt' = Variable.auto_fixes t' ctxt;
- val p = PrintMode.with_modes modes (fn () =>
- Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,
- Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();
- in Pretty.writeln p end;
-
-local structure P = OuterParse in
-
-val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) [];
-
-val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag
- (opt_modes -- Scan.optional P.nat ~1 -- P.term
- >> (fn ((modes, k), t) => Toplevel.no_timing o Toplevel.keep
- (values_cmd modes k t)));
-
-end;
-
-end;
-
--- a/src/Pure/Concurrent/future.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/Pure/Concurrent/future.ML Thu Sep 24 17:26:05 2009 +0200
@@ -257,7 +257,7 @@
"SCHEDULE: disposed " ^ string_of_int (length dead) ^ " dead worker threads")));
val m = if ! do_shutdown then 0 else Multithreading.max_threads_value ();
- val mm = if m = 9999 then 1 else (m * 3) div 2;
+ val mm = if m = 9999 then 1 else m * 2;
val l = length (! workers);
val _ = excessive := l - mm;
val _ =
--- a/src/Pure/Isar/code.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/Pure/Isar/code.ML Thu Sep 24 17:26:05 2009 +0200
@@ -505,9 +505,10 @@
(*those following are permissive wrt. to overloaded constants!*)
+val head_eqn = dest_Const o fst o strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of;
fun const_typ_eqn thy thm =
let
- val (c, ty) = (dest_Const o fst o strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of) thm;
+ val (c, ty) = head_eqn thm;
val c' = AxClass.unoverload_const thy (c, ty);
in (c', ty) end;
@@ -523,8 +524,8 @@
fun same_typscheme thy thms =
let
- fun tvars_of t = rev (Term.add_tvars t []);
- val vss = map (tvars_of o Thm.prop_of) thms;
+ fun tvars_of T = rev (Term.add_tvarsT T []);
+ val vss = map (tvars_of o snd o head_eqn) thms;
fun inter_sorts vs =
fold (curry (Sorts.inter_sort (Sign.classes_of thy)) o snd) vs [];
val sorts = map_transpose inter_sorts vss;
@@ -547,7 +548,7 @@
fun case_certificate thm =
let
val ((head, raw_case_expr), cases) = (apfst Logic.dest_equals
- o apsnd Logic.dest_conjunctions o Logic.dest_implies o Thm.prop_of) thm;
+ o apsnd Logic.dest_conjunctions o Logic.dest_implies o Thm.plain_prop_of) thm;
val _ = case head of Free _ => true
| Var _ => true
| _ => raise TERM ("case_cert", []);
@@ -759,7 +760,7 @@
end; (*struct*)
-(** type-safe interfaces for data depedent on executable code **)
+(** type-safe interfaces for data dependent on executable code **)
functor Code_Data_Fun(Data: CODE_DATA_ARGS): CODE_DATA =
struct
@@ -779,4 +780,49 @@
end;
+(** datastructure to log definitions for preprocessing of the predicate compiler **)
+(* obviously a clone of Named_Thms *)
+
+signature PREDICATE_COMPILE_PREPROC_CONST_DEFS =
+sig
+ val get: Proof.context -> thm list
+ val add_thm: thm -> Context.generic -> Context.generic
+ val del_thm: thm -> Context.generic -> Context.generic
+
+ val add_attribute : attribute
+ val del_attribute : attribute
+
+ val add_attrib : Attrib.src
+
+ val setup: theory -> theory
+end;
+
+structure Predicate_Compile_Preproc_Const_Defs : PREDICATE_COMPILE_PREPROC_CONST_DEFS =
+struct
+
+structure Data = GenericDataFun
+(
+ type T = thm list;
+ val empty = [];
+ val extend = I;
+ fun merge _ = Thm.merge_thms;
+);
+
+val get = Data.get o Context.Proof;
+
+val add_thm = Data.map o Thm.add_thm;
+val del_thm = Data.map o Thm.del_thm;
+
+val add_attribute = Thm.declaration_attribute add_thm;
+val del_attribute = Thm.declaration_attribute del_thm;
+
+val add_attrib = Attrib.internal (K add_attribute)
+
+val setup =
+ Attrib.setup (Binding.name "pred_compile_preproc") (Attrib.add_del add_attribute del_attribute)
+ ("declaration of definition for preprocessing of the predicate compiler") #>
+ PureThy.add_thms_dynamic (Binding.name "pred_compile_preproc", Data.get);
+
+end;
+
structure Code : CODE = struct open Code; end;
--- a/src/Pure/Isar/constdefs.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/Pure/Isar/constdefs.ML Thu Sep 24 17:26:05 2009 +0200
@@ -52,7 +52,7 @@
thy
|> Sign.add_consts_i [(b, T, mx)]
|> PureThy.add_defs false [((name, def), atts)]
- |-> (fn [thm] => Code.add_default_eqn thm);
+ |-> (fn [thm] => Code.add_default_eqn thm #> Context.theory_map (Predicate_Compile_Preproc_Const_Defs.add_thm thm));
in ((c, T), thy') end;
fun gen_constdefs prep_vars prep_prop prep_att (raw_structs, specs) thy =
--- a/src/Pure/Isar/specification.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/Pure/Isar/specification.ML Thu Sep 24 17:26:05 2009 +0200
@@ -209,7 +209,8 @@
(var, ((Binding.suffix_name "_raw" name, []), rhs));
val ((def_name, [th']), lthy3) = lthy2
|> LocalTheory.note Thm.definitionK
- ((name, Code.add_default_eqn_attrib :: atts), [prove lthy2 th]);
+ ((name, Predicate_Compile_Preproc_Const_Defs.add_attrib :: Code.add_default_eqn_attrib :: atts),
+ [prove lthy2 th]);
val lhs' = Morphism.term (LocalTheory.target_morphism lthy3) lhs;
val _ =
--- a/src/Pure/envir.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/Pure/envir.ML Thu Sep 24 17:26:05 2009 +0200
@@ -282,12 +282,9 @@
let
val funerr = "fastype: expected function type";
fun fast Ts (f $ u) =
- (case fast Ts f of
+ (case Type.devar tyenv (fast Ts f) of
Type ("fun", [_, T]) => T
- | TVar v =>
- (case Type.lookup tyenv v of
- SOME (Type ("fun", [_, T])) => T
- | _ => raise TERM (funerr, [f $ u]))
+ | TVar v => raise TERM (funerr, [f $ u])
| _ => raise TERM (funerr, [f $ u]))
| fast Ts (Const (_, T)) = T
| fast Ts (Free (_, T)) = T
--- a/src/Pure/type.ML Thu Sep 24 17:25:42 2009 +0200
+++ b/src/Pure/type.ML Thu Sep 24 17:26:05 2009 +0200
@@ -55,6 +55,7 @@
exception TYPE_MATCH
type tyenv = (sort * typ) Vartab.table
val lookup: tyenv -> indexname * sort -> typ option
+ val devar: tyenv -> typ -> typ
val typ_match: tsig -> typ * typ -> tyenv -> tyenv
val typ_instance: tsig -> typ * typ -> bool
val raw_match: typ * typ -> tyenv -> tyenv