--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/simpdata.ML Wed Dec 03 15:58:44 2008 +0100
@@ -0,0 +1,200 @@
+(* Title: HOL/simpdata.ML
+ ID: $Id$
+ Author: Tobias Nipkow
+ Copyright 1991 University of Cambridge
+
+Instantiation of the generic simplifier for HOL.
+*)
+
+(** tools setup **)
+
+structure Quantifier1 = Quantifier1Fun
+(struct
+ (*abstract syntax*)
+ 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)
+ | dest_conj _ = NONE;
+ fun dest_imp ((c as Const("op -->",_)) $ s $ t) = SOME (c, s, t)
+ | dest_imp _ = NONE;
+ val conj = HOLogic.conj
+ val imp = HOLogic.imp
+ (*rules*)
+ val iff_reflection = @{thm eq_reflection}
+ val iffI = @{thm iffI}
+ val iff_trans = @{thm trans}
+ val conjI= @{thm conjI}
+ val conjE= @{thm conjE}
+ val impI = @{thm impI}
+ val mp = @{thm mp}
+ val uncurry = @{thm uncurry}
+ val exI = @{thm exI}
+ val exE = @{thm exE}
+ 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 Simpdata =
+struct
+
+fun mk_meta_eq r = r RS @{thm eq_reflection};
+fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
+
+fun mk_eq th = case concl_of th
+ (*expects Trueprop if not == *)
+ of Const ("==",_) $ _ $ _ => th
+ | _ $ (Const ("op =", _) $ _ $ _) => mk_meta_eq th
+ | _ $ (Const ("Not", _) $ _) => th RS @{thm Eq_FalseI}
+ | _ => th RS @{thm Eq_TrueI}
+
+fun mk_eq_True r =
+ SOME (r RS @{thm meta_eq_to_obj_eq} RS @{thm 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 @{thm 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 @{thms simp_implies_def},
+ REPEAT (ares_tac (@{thm meta_eq_to_obj_eq} ::
+ map (rewrite_rule @{thms 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);
+
+fun mk_atomize pairs =
+ let
+ fun atoms thm =
+ let
+ fun res th = map (fn rl => th RS rl); (*exception THM*)
+ fun res_fixed rls =
+ if Thm.maxidx_of (Thm.adjust_maxidx_thm ~1 thm) = ~1 then res thm rls
+ else Variable.trade (K (fn [thm'] => res thm' rls)) (Variable.thm_context thm) [thm];
+ in
+ 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 (res_fixed rls) handle THM _ => [thm])
+ | NONE => [thm])
+ | _ => [thm])
+ | _ => [thm]
+ end;
+ 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 @{thms simp_impliesI} i)) THEN'
+ FIRST' [resolve_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems), atac,
+ etac @{thm 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 @{thms simp_impliesI} i)) THEN'
+ FIRST' [match_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems),
+ eq_assume_tac, ematch_tac @{thms FalseE}];
+
+val safe_solver = mk_solver "HOL safe" safe_solver_tac;
+
+structure SplitterData =
+struct
+ structure Simplifier = Simplifier
+ val mk_eq = mk_eq
+ val meta_eq_to_iff = @{thm meta_eq_to_obj_eq}
+ val iffD = @{thm iffD2}
+ val disjE = @{thm disjE}
+ val conjE = @{thm conjE}
+ val exE = @{thm exE}
+ val contrapos = @{thm contrapos_nn}
+ val contrapos2 = @{thm contrapos_pp}
+ val notnotD = @{thm notnotD}
+end;
+
+structure Splitter = SplitterFun(SplitterData);
+
+val split_tac = Splitter.split_tac;
+val split_inside_tac = Splitter.split_inside_tac;
+
+val op addsplits = Splitter.addsplits;
+val op delsplits = Splitter.delsplits;
+val Addsplits = Splitter.Addsplits;
+val Delsplits = Splitter.Delsplits;
+
+
+(* integration of simplifier with classical reasoner *)
+
+structure Clasimp = ClasimpFun
+ (structure Simplifier = Simplifier and Splitter = Splitter
+ and Classical = Classical and Blast = Blast
+ val iffD1 = @{thm iffD1} val iffD2 = @{thm iffD2} val notE = @{thm notE});
+open Clasimp;
+
+val _ = ML_Antiquote.value "clasimpset"
+ (Scan.succeed "Clasimp.local_clasimpset_of (ML_Context.the_local_context ())");
+
+val mksimps_pairs =
+ [("op -->", [@{thm mp}]), ("op &", [@{thm conjunct1}, @{thm conjunct2}]),
+ ("All", [@{thm spec}]), ("True", []), ("False", []),
+ ("HOL.If", [@{thm if_bool_eq_conj} RS @{thm iffD1}])];
+
+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 hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);
+
+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;
+
+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 = HOL_basic_ss addsimprocs [defALL_regroup, defEX_regroup]
+
+end;
+
+structure Splitter = Simpdata.Splitter;
+structure Clasimp = Simpdata.Clasimp;