author  wenzelm 
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parent 32155  e2bf2f73b0c8 
child 33339  d41f77196338 
permissions  rwrr 
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(* Title: HOL/simpdata.ML 
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Author: Tobias Nipkow 

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Copyright 1991 University of Cambridge 

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Instantiation of the generic simplifier for HOL. 

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*) 

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(** tools setup **) 

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structure Quantifier1 = Quantifier1Fun 

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(struct 

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(*abstract syntax*) 

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fun dest_eq ((c as Const("op =",_)) $ s $ t) = SOME (c, s, t) 

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 dest_eq _ = NONE; 

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fun dest_conj ((c as Const("op &",_)) $ s $ t) = SOME (c, s, t) 

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 dest_conj _ = NONE; 

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fun dest_imp ((c as Const("op >",_)) $ s $ t) = SOME (c, s, t) 

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 dest_imp _ = NONE; 

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val conj = HOLogic.conj 

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val imp = HOLogic.imp 

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(*rules*) 

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val iff_reflection = @{thm eq_reflection} 
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val iffI = @{thm iffI} 

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val iff_trans = @{thm trans} 

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val conjI= @{thm conjI} 

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val conjE= @{thm conjE} 

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val impI = @{thm impI} 

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val mp = @{thm mp} 

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val uncurry = @{thm uncurry} 

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val exI = @{thm exI} 

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val exE = @{thm exE} 

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val iff_allI = @{thm iff_allI} 

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val iff_exI = @{thm iff_exI} 

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val all_comm = @{thm all_comm} 

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val ex_comm = @{thm ex_comm} 

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end); 
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structure Simpdata = 
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struct 
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fun mk_meta_eq r = r RS @{thm eq_reflection}; 
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fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r; 
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fun mk_eq th = case concl_of th 
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(*expects Trueprop if not == *) 
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of Const ("==",_) $ _ $ _ => th 
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 _ $ (Const ("op =", _) $ _ $ _) => mk_meta_eq th 

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 _ $ (Const ("Not", _) $ _) => th RS @{thm Eq_FalseI} 
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 _ => th RS @{thm Eq_TrueI} 

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fun mk_eq_True r = 
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SOME (r RS @{thm meta_eq_to_obj_eq} RS @{thm Eq_TrueI}) handle Thm.THM _ => NONE; 

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(* Produce theorems of the form 

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(P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y) 

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*) 

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fun lift_meta_eq_to_obj_eq i st = 
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let 
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fun count_imp (Const ("HOL.simp_implies", _) $ P $ Q) = 1 + count_imp Q 

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 count_imp _ = 0; 

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val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i  1))) 

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in if j = 0 then @{thm meta_eq_to_obj_eq} 
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else 
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let 

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val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j); 

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fun mk_simp_implies Q = List.foldr (fn (R, S) => 
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Const ("HOL.simp_implies", propT > propT > propT) $ R $ S) Q Ps 
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val aT = TFree ("'a", HOLogic.typeS); 

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val x = Free ("x", aT); 

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val y = Free ("y", aT) 

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in Goal.prove_global (Thm.theory_of_thm st) [] 

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[mk_simp_implies (Logic.mk_equals (x, y))] 

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(mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y)))) 

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(fn {prems, ...} => EVERY 
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[rewrite_goals_tac @{thms simp_implies_def}, 
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REPEAT (ares_tac (@{thm meta_eq_to_obj_eq} :: 

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map (rewrite_rule @{thms simp_implies_def}) prems) 1)]) 

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end 
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end; 

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(*Congruence rules for = (instead of ==)*) 

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fun mk_meta_cong rl = zero_var_indexes 

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(let val rl' = Seq.hd (TRYALL (fn i => fn st => 

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rtac (lift_meta_eq_to_obj_eq i st) i st) rl) 

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in mk_meta_eq rl' handle THM _ => 

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if can Logic.dest_equals (concl_of rl') then rl' 

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else error "Conclusion of congruence rules must be =equality" 

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end); 

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fun mk_atomize pairs = 

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let 

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fun atoms thm = 
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let 
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fun res th = map (fn rl => th RS rl); (*exception THM*) 
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fun res_fixed rls = 
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if Thm.maxidx_of (Thm.adjust_maxidx_thm ~1 thm) = ~1 then res thm rls 
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else Variable.trade (K (fn [thm'] => res thm' rls)) (Variable.thm_context thm) [thm]; 
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in 
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case concl_of thm 
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of Const ("Trueprop", _) $ p => (case head_of p 
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of Const (a, _) => (case AList.lookup (op =) pairs a 
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of SOME rls => (maps atoms (res_fixed rls) handle THM _ => [thm]) 
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 NONE => [thm]) 
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 _ => [thm]) 
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 _ => [thm] 
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end; 
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in atoms end; 
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fun mksimps pairs = 

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map_filter (try mk_eq) o mk_atomize pairs o gen_all; 
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fun unsafe_solver_tac prems = 
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(fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN' 

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FIRST' [resolve_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems), atac, 

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etac @{thm FalseE}]; 

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val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac; 
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(*No premature instantiation of variables during simplification*) 
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fun safe_solver_tac prems = 
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(fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN' 

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FIRST' [match_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems), 

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eq_assume_tac, ematch_tac @{thms FalseE}]; 

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val safe_solver = mk_solver "HOL safe" safe_solver_tac; 
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structure Splitter = Splitter 
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( 
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val thy = @{theory} 
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val mk_eq = mk_eq 
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val meta_eq_to_iff = @{thm meta_eq_to_obj_eq} 
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val iffD = @{thm iffD2} 
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val disjE = @{thm disjE} 
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val conjE = @{thm conjE} 
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val exE = @{thm exE} 
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val contrapos = @{thm contrapos_nn} 
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val contrapos2 = @{thm contrapos_pp} 
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val notnotD = @{thm notnotD} 
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); 
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val split_tac = Splitter.split_tac; 
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val split_inside_tac = Splitter.split_inside_tac; 
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val op addsplits = Splitter.addsplits; 
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val op delsplits = Splitter.delsplits; 
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(* integration of simplifier with classical reasoner *) 
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structure Clasimp = ClasimpFun 

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(structure Simplifier = Simplifier and Splitter = Splitter 

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and Classical = Classical and Blast = Blast 

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val iffD1 = @{thm iffD1} val iffD2 = @{thm iffD2} val notE = @{thm notE}); 
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open Clasimp; 
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val _ = ML_Antiquote.value "clasimpset" 
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(Scan.succeed "Clasimp.clasimpset_of (ML_Context.the_local_context ())"); 
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val mksimps_pairs = 
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[("op >", [@{thm mp}]), ("op &", [@{thm conjunct1}, @{thm conjunct2}]), 
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("All", [@{thm spec}]), ("True", []), ("False", []), 

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("HOL.If", [@{thm if_bool_eq_conj} RS @{thm iffD1}])]; 

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val HOL_basic_ss = 
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Simplifier.theory_context @{theory} empty_ss 
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setsubgoaler asm_simp_tac 
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setSSolver safe_solver 

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setSolver unsafe_solver 

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setmksimps (mksimps mksimps_pairs) 

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setmkeqTrue mk_eq_True 

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setmkcong mk_meta_cong; 

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fun hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews); 
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fun unfold_tac ths = 

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let val ss0 = Simplifier.clear_ss HOL_basic_ss addsimps ths 
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in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end; 
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val defALL_regroup = 

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Simplifier.simproc @{theory} 
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"defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all; 
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val defEX_regroup = 

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Simplifier.simproc @{theory} 
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"defined EX" ["EX x. P x"] Quantifier1.rearrange_ex; 
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val simpset_simprocs = HOL_basic_ss addsimprocs [defALL_regroup, defEX_regroup] 
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end; 
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structure Splitter = Simpdata.Splitter; 

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structure Clasimp = Simpdata.Clasimp; 