--- a/src/HOL/simpdata.ML Wed Oct 11 10:49:36 2006 +0200
+++ b/src/HOL/simpdata.ML Wed Oct 11 14:51:24 2006 +0200
@@ -6,40 +6,16 @@
Instantiation of the generic simplifier for HOL.
*)
-(* legacy ML bindings - FIXME get rid of this *)
-
-val Eq_FalseI = thm "Eq_FalseI";
-val Eq_TrueI = thm "Eq_TrueI";
-val de_Morgan_conj = thm "de_Morgan_conj";
-val de_Morgan_disj = thm "de_Morgan_disj";
-val iff_conv_conj_imp = thm "iff_conv_conj_imp";
-val imp_cong = thm "imp_cong";
-val imp_conv_disj = thm "imp_conv_disj";
-val imp_disj1 = thm "imp_disj1";
-val imp_disj2 = thm "imp_disj2";
-val imp_disjL = thm "imp_disjL";
-val simp_impliesI = thm "simp_impliesI";
-val simp_implies_cong = thm "simp_implies_cong";
-val simp_implies_def = thm "simp_implies_def";
-
-local
- val uncurry = thm "uncurry"
- val iff_allI = thm "iff_allI"
- val iff_exI = thm "iff_exI"
- val all_comm = thm "all_comm"
- val ex_comm = thm "ex_comm"
-in
-
-(*** make simplification procedures for quantifier elimination ***)
+(** tools setup **)
structure Quantifier1 = Quantifier1Fun
(struct
(*abstract syntax*)
- fun dest_eq((c as Const("op =",_)) $ s $ t) = SOME(c,s,t)
+ fun dest_eq ((c as Const("op =",_)) $ s $ t) = SOME (c, s, t)
| dest_eq _ = NONE;
- fun dest_conj((c as Const("op &",_)) $ s $ t) = SOME(c,s,t)
+ fun dest_conj ((c as Const("op &",_)) $ s $ t) = SOME (c, s, t)
| dest_conj _ = NONE;
- fun dest_imp((c as Const("op -->",_)) $ s $ t) = SOME(c,s,t)
+ fun dest_imp ((c as Const("op -->",_)) $ s $ t) = SOME (c, s, t)
| dest_imp _ = NONE;
val conj = HOLogic.conj
val imp = HOLogic.imp
@@ -51,32 +27,162 @@
val conjE= HOL.conjE
val impI = HOL.impI
val mp = HOL.mp
- val uncurry = uncurry
+ val uncurry = thm "uncurry"
val exI = HOL.exI
val exE = HOL.exE
- val iff_allI = iff_allI
- val iff_exI = iff_exI
- val all_comm = all_comm
- val ex_comm = ex_comm
+ val iff_allI = thm "iff_allI"
+ val iff_exI = thm "iff_exI"
+ val all_comm = thm "all_comm"
+ val ex_comm = thm "ex_comm"
end);
+structure HOL =
+struct
+
+open HOL;
+
+val Eq_FalseI = thm "Eq_FalseI";
+val Eq_TrueI = thm "Eq_TrueI";
+val simp_implies_def = thm "simp_implies_def";
+val simp_impliesI = thm "simp_impliesI";
+
+fun mk_meta_eq r = r RS eq_reflection;
+fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
+
+fun mk_eq thm = case concl_of thm
+ (*expects Trueprop if not == *)
+ of Const ("==",_) $ _ $ _ => thm
+ | _ $ (Const ("op =", _) $ _ $ _) => mk_meta_eq thm
+ | _ $ (Const ("Not", _) $ _) => thm RS Eq_FalseI
+ | _ => thm RS Eq_TrueI;
+
+fun mk_eq_True r =
+ SOME (r RS meta_eq_to_obj_eq RS Eq_TrueI) handle Thm.THM _ => NONE;
+
+(* Produce theorems of the form
+ (P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y)
+*)
+fun lift_meta_eq_to_obj_eq i st =
+ let
+ fun count_imp (Const ("HOL.simp_implies", _) $ P $ Q) = 1 + count_imp Q
+ | count_imp _ = 0;
+ val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i - 1)))
+ in if j = 0 then meta_eq_to_obj_eq
+ else
+ let
+ val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j);
+ fun mk_simp_implies Q = foldr (fn (R, S) =>
+ Const ("HOL.simp_implies", propT --> propT --> propT) $ R $ S) Q Ps
+ val aT = TFree ("'a", HOLogic.typeS);
+ val x = Free ("x", aT);
+ val y = Free ("y", aT)
+ in Goal.prove_global (Thm.theory_of_thm st) []
+ [mk_simp_implies (Logic.mk_equals (x, y))]
+ (mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))
+ (fn prems => EVERY
+ [rewrite_goals_tac [simp_implies_def],
+ REPEAT (ares_tac (meta_eq_to_obj_eq :: map (rewrite_rule [simp_implies_def]) prems) 1)])
+ end
+ end;
+
+(*Congruence rules for = (instead of ==)*)
+fun mk_meta_cong rl = zero_var_indexes
+ (let val rl' = Seq.hd (TRYALL (fn i => fn st =>
+ rtac (lift_meta_eq_to_obj_eq i st) i st) rl)
+ in mk_meta_eq rl' handle THM _ =>
+ if can Logic.dest_equals (concl_of rl') then rl'
+ else error "Conclusion of congruence rules must be =-equality"
+ end);
+
+(*
+val mk_atomize: (string * thm list) list -> thm -> thm list
+looks too specific to move it somewhere else
+*)
+fun mk_atomize pairs =
+ let
+ fun atoms thm = case concl_of thm
+ of Const("Trueprop", _) $ p => (case head_of p
+ of Const(a, _) => (case AList.lookup (op =) pairs a
+ of SOME rls => maps atoms ([thm] RL rls)
+ | NONE => [thm])
+ | _ => [thm])
+ | _ => [thm]
+ in atoms end;
+
+fun mksimps pairs =
+ (map_filter (try mk_eq) o mk_atomize pairs o gen_all);
+
+fun unsafe_solver_tac prems =
+ (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
+ FIRST'[resolve_tac(reflexive_thm :: TrueI :: refl :: prems), atac, etac FalseE];
+val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
+
+(*No premature instantiation of variables during simplification*)
+fun safe_solver_tac prems =
+ (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
+ FIRST'[match_tac(reflexive_thm :: TrueI :: refl :: prems),
+ eq_assume_tac, ematch_tac [FalseE]];
+val safe_solver = mk_solver "HOL safe" safe_solver_tac;
+
end;
-val defEX_regroup =
- Simplifier.simproc (the_context ())
- "defined EX" ["EX x. P x"] Quantifier1.rearrange_ex;
+structure SplitterData =
+struct
+ structure Simplifier = Simplifier
+ val mk_eq = HOL.mk_eq
+ val meta_eq_to_iff = HOL.meta_eq_to_obj_eq
+ val iffD = HOL.iffD2
+ val disjE = HOL.disjE
+ val conjE = HOL.conjE
+ val exE = HOL.exE
+ val contrapos = HOL.contrapos_nn
+ val contrapos2 = HOL.contrapos_pp
+ val notnotD = HOL.notnotD
+end;
+
+structure Splitter = SplitterFun(SplitterData);
+
+(* integration of simplifier with classical reasoner *)
+
+structure Clasimp = ClasimpFun
+ (structure Simplifier = Simplifier and Splitter = Splitter
+ and Classical = Classical and Blast = Blast
+ val iffD1 = HOL.iffD1 val iffD2 = HOL.iffD2 val notE = HOL.notE);
-val defALL_regroup =
- Simplifier.simproc (the_context ())
- "defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all;
+structure HOL =
+struct
+
+open HOL;
+
+val mksimps_pairs =
+ [("op -->", [mp]), ("op &", [thm "conjunct1", thm "conjunct2"]),
+ ("All", [spec]), ("True", []), ("False", []),
+ ("HOL.If", [thm "if_bool_eq_conj" RS iffD1])];
+val simpset_basic =
+ Simplifier.theory_context (the_context ()) empty_ss
+ setsubgoaler asm_simp_tac
+ setSSolver safe_solver
+ setSolver unsafe_solver
+ setmksimps (mksimps mksimps_pairs)
+ setmkeqTrue mk_eq_True
+ setmkcong mk_meta_cong;
+
+fun simplify rews = Simplifier.full_simplify (simpset_basic addsimps rews);
+
+fun unfold_tac ths =
+ let val ss0 = Simplifier.clear_ss simpset_basic addsimps ths
+ in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end;
+
+(** simprocs **)
(* simproc for proving "(y = x) == False" from premise "~(x = y)" *)
val use_neq_simproc = ref true;
local
- val neq_to_EQ_False = thm "not_sym" RS Eq_FalseI;
+ val thy = the_context ();
+ val neq_to_EQ_False = thm "not_sym" RS HOL.Eq_FalseI;
fun neq_prover sg ss (eq $ lhs $ rhs) =
let
fun test thm = (case #prop (rep_thm thm) of
@@ -91,10 +197,9 @@
end
in
-val neq_simproc = Simplifier.simproc (the_context ())
- "neq_simproc" ["x = y"] neq_prover;
+val neq_simproc = Simplifier.simproc thy "neq_simproc" ["x = y"] neq_prover;
-end;
+end; (*local*)
(* Simproc for Let *)
@@ -102,23 +207,24 @@
val use_let_simproc = ref true;
local
+ val thy = the_context ();
val Let_folded = thm "Let_folded";
val Let_unfold = thm "Let_unfold";
- val (f_Let_unfold,x_Let_unfold) =
+ val (f_Let_unfold, x_Let_unfold) =
let val [(_$(f$x)$_)] = prems_of Let_unfold
- in (cterm_of (the_context ()) f,cterm_of (the_context ()) x) end
- val (f_Let_folded,x_Let_folded) =
+ in (cterm_of thy f, cterm_of thy x) end
+ val (f_Let_folded, x_Let_folded) =
let val [(_$(f$x)$_)] = prems_of Let_folded
- in (cterm_of (the_context ()) f, cterm_of (the_context ()) x) end;
+ in (cterm_of thy f, cterm_of thy x) end;
val g_Let_folded =
- let val [(_$_$(g$_))] = prems_of Let_folded in cterm_of (the_context ()) g end;
+ let val [(_$_$(g$_))] = prems_of Let_folded in cterm_of thy g end;
in
val let_simproc =
- Simplifier.simproc (the_context ()) "let_simp" ["Let x f"]
+ Simplifier.simproc thy "let_simp" ["Let x f"]
(fn sg => fn ss => fn t =>
let val ctxt = Simplifier.the_context ss;
- val ([t'],ctxt') = Variable.import_terms false [t] ctxt;
+ val ([t'], ctxt') = Variable.import_terms false [t] ctxt;
in Option.map (hd o Variable.export ctxt' ctxt o single)
(case t' of (Const ("Let",_)$x$f) => (* x and f are already in normal form *)
if not (!use_let_simproc) then NONE
@@ -153,192 +259,9 @@
| _ => NONE)
end)
-end
-
-(*** Case splitting ***)
-
-(*Make meta-equalities. The operator below is Trueprop*)
-
-fun mk_meta_eq r = r RS HOL.eq_reflection;
-fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
-
-fun mk_eq th = case concl_of th of
- Const("==",_)$_$_ => th
- | _$(Const("op =",_)$_$_) => mk_meta_eq th
- | _$(Const("Not",_)$_) => th RS Eq_FalseI
- | _ => th RS Eq_TrueI;
-(* Expects Trueprop(.) if not == *)
-
-fun mk_eq_True r =
- SOME (r RS HOL.meta_eq_to_obj_eq RS Eq_TrueI) handle Thm.THM _ => NONE;
-
-(* Produce theorems of the form
- (P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y)
-*)
-fun lift_meta_eq_to_obj_eq i st =
- let
- val {sign, ...} = rep_thm st;
- fun count_imp (Const ("HOL.simp_implies", _) $ P $ Q) = 1 + count_imp Q
- | count_imp _ = 0;
- val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i - 1)))
- in if j = 0 then HOL.meta_eq_to_obj_eq
- else
- let
- val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j);
- fun mk_simp_implies Q = foldr (fn (R, S) =>
- Const ("HOL.simp_implies", propT --> propT --> propT) $ R $ S) Q Ps
- val aT = TFree ("'a", HOLogic.typeS);
- val x = Free ("x", aT);
- val y = Free ("y", aT)
- in Goal.prove_global (Thm.theory_of_thm st) []
- [mk_simp_implies (Logic.mk_equals (x, y))]
- (mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))
- (fn prems => EVERY
- [rewrite_goals_tac [simp_implies_def],
- REPEAT (ares_tac (HOL.meta_eq_to_obj_eq :: map (rewrite_rule [simp_implies_def]) prems) 1)])
- end
- end;
-
-(*Congruence rules for = (instead of ==)*)
-fun mk_meta_cong rl = zero_var_indexes
- (let val rl' = Seq.hd (TRYALL (fn i => fn st =>
- rtac (lift_meta_eq_to_obj_eq i st) i st) rl)
- in mk_meta_eq rl' handle THM _ =>
- if can Logic.dest_equals (concl_of rl') then rl'
- else error "Conclusion of congruence rules must be =-equality"
- end);
-
-structure SplitterData =
-struct
- structure Simplifier = Simplifier
- val mk_eq = mk_eq
- val meta_eq_to_iff = HOL.meta_eq_to_obj_eq
- val iffD = HOL.iffD2
- val disjE = HOL.disjE
- val conjE = HOL.conjE
- val exE = HOL.exE
- val contrapos = HOL.contrapos_nn
- val contrapos2 = HOL.contrapos_pp
- val notnotD = HOL.notnotD
-end;
-
-structure Splitter = SplitterFun(SplitterData);
-
-val split_tac = Splitter.split_tac;
-val split_inside_tac = Splitter.split_inside_tac;
-val split_asm_tac = Splitter.split_asm_tac;
-val op addsplits = Splitter.addsplits;
-val op delsplits = Splitter.delsplits;
-val Addsplits = Splitter.Addsplits;
-val Delsplits = Splitter.Delsplits;
-
-val mksimps_pairs =
- [("op -->", [HOL.mp]), ("op &", [thm "conjunct1", thm "conjunct2"]),
- ("All", [HOL.spec]), ("True", []), ("False", []),
- ("HOL.If", [thm "if_bool_eq_conj" RS HOL.iffD1])];
+end; (*local*)
-(*
-val mk_atomize: (string * thm list) list -> thm -> thm list
-looks too specific to move it somewhere else
-*)
-fun mk_atomize pairs =
- let fun atoms th =
- (case concl_of th of
- Const("Trueprop",_) $ p =>
- (case head_of p of
- Const(a,_) =>
- (case AList.lookup (op =) pairs a of
- SOME(rls) => List.concat (map atoms ([th] RL rls))
- | NONE => [th])
- | _ => [th])
- | _ => [th])
- in atoms end;
-
-fun mksimps pairs =
- (List.mapPartial (try mk_eq) o mk_atomize pairs o gen_all);
-
-fun unsafe_solver_tac prems =
- (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
- FIRST'[resolve_tac(reflexive_thm :: HOL.TrueI :: HOL.refl :: prems), atac, etac HOL.FalseE];
-val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
-
-(*No premature instantiation of variables during simplification*)
-fun safe_solver_tac prems =
- (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
- FIRST'[match_tac(reflexive_thm :: HOL.TrueI :: HOL.refl :: prems),
- eq_assume_tac, ematch_tac [HOL.FalseE]];
-val safe_solver = mk_solver "HOL safe" safe_solver_tac;
-
-val HOL_basic_ss =
- Simplifier.theory_context (the_context ()) empty_ss
- setsubgoaler asm_simp_tac
- setSSolver safe_solver
- setSolver unsafe_solver
- setmksimps (mksimps mksimps_pairs)
- setmkeqTrue mk_eq_True
- setmkcong mk_meta_cong;
-
-fun unfold_tac ths =
- let val ss0 = Simplifier.clear_ss HOL_basic_ss addsimps ths
- in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end;
-
-(*In general it seems wrong to add distributive laws by default: they
- might cause exponential blow-up. But imp_disjL has been in for a while
- and cannot be removed without affecting existing proofs. Moreover,
- rewriting by "(P|Q --> R) = ((P-->R)&(Q-->R))" might be justified on the
- grounds that it allows simplification of R in the two cases.*)
-
-local
- val ex_simps = thms "ex_simps";
- val all_simps = thms "all_simps";
- val simp_thms = thms "simp_thms";
- val cases_simp = thm "cases_simp";
- val conj_assoc = thm "conj_assoc";
- val if_False = thm "if_False";
- val if_True = thm "if_True";
- val disj_assoc = thm "disj_assoc";
- val disj_not1 = thm "disj_not1";
- val if_cancel = thm "if_cancel";
- val if_eq_cancel = thm "if_eq_cancel";
- val True_implies_equals = thm "True_implies_equals";
-in
-
-val HOL_ss =
- HOL_basic_ss addsimps
- ([triv_forall_equality, (* prunes params *)
- True_implies_equals, (* prune asms `True' *)
- if_True, if_False, if_cancel, if_eq_cancel,
- imp_disjL, conj_assoc, disj_assoc,
- de_Morgan_conj, de_Morgan_disj, imp_disj1, imp_disj2, thm "not_imp",
- disj_not1, thm "not_all", thm "not_ex", cases_simp,
- thm "the_eq_trivial", HOL.the_sym_eq_trivial]
- @ ex_simps @ all_simps @ simp_thms)
- addsimprocs [defALL_regroup,defEX_regroup,neq_simproc,let_simproc]
- addcongs [imp_cong, simp_implies_cong]
- addsplits [thm "split_if"];
-
-end;
-
-fun hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);
-
-(* default simpset *)
-val simpsetup =
- (fn thy => (change_simpset_of thy (fn _ => HOL_ss); thy));
-
-
-(*** integration of simplifier with classical reasoner ***)
-
-structure Clasimp = ClasimpFun
- (structure Simplifier = Simplifier and Splitter = Splitter
- and Classical = Classical and Blast = Blast
- val iffD1 = HOL.iffD1 val iffD2 = HOL.iffD2 val notE = HOL.notE);
-open Clasimp;
-
-val HOL_css = (HOL_cs, HOL_ss);
-
-
-
-(*** A general refutation procedure ***)
+(* A general refutation procedure *)
(* Parameters:
@@ -361,7 +284,7 @@
val nnf_simpset =
empty_ss setmkeqTrue mk_eq_True
setmksimps (mksimps mksimps_pairs)
- addsimps [imp_conv_disj,iff_conv_conj_imp,de_Morgan_disj,de_Morgan_conj,
+ addsimps [thm "imp_conv_disj", thm "iff_conv_conj_imp", thm "de_Morgan_disj", thm "de_Morgan_conj",
thm "not_all", thm "not_ex", thm "not_not"];
fun prem_nnf_tac i st =
full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st;
@@ -369,13 +292,27 @@
fun refute_tac test prep_tac ref_tac =
let val refute_prems_tac =
REPEAT_DETERM
- (eresolve_tac [HOL.conjE, HOL.exE] 1 ORELSE
+ (eresolve_tac [conjE, exE] 1 ORELSE
filter_prems_tac test 1 ORELSE
- etac HOL.disjE 1) THEN
- ((etac HOL.notE 1 THEN eq_assume_tac 1) ORELSE
+ etac disjE 1) THEN
+ ((etac notE 1 THEN eq_assume_tac 1) ORELSE
ref_tac 1);
in EVERY'[TRY o filter_prems_tac test,
- REPEAT_DETERM o etac HOL.rev_mp, prep_tac, rtac HOL.ccontr, prem_nnf_tac,
+ REPEAT_DETERM o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
end;
-end;
+end; (*local*)
+
+val defALL_regroup =
+ Simplifier.simproc (the_context ())
+ "defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all;
+
+val defEX_regroup =
+ Simplifier.simproc (the_context ())
+ "defined EX" ["EX x. P x"] Quantifier1.rearrange_ex;
+
+
+val simpset_simprocs = simpset_basic
+ addsimprocs [defALL_regroup, defEX_regroup, neq_simproc, let_simproc]
+
+end; (*struct*)
\ No newline at end of file