author | haftmann |
Mon, 27 Nov 2006 13:42:47 +0100 | |
changeset 21551 | d276e7d25017 |
parent 21313 | 26fc3a45547c |
child 21674 | 8a6bf9d7c751 |
permissions | -rw-r--r-- |
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(* Title: HOL/simpdata.ML |
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ID: $Id$ |
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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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local |
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val eq_reflection = thm "eq_reflection" |
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in fun mk_meta_eq r = r RS eq_reflection end; |
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fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r; |
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local |
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val Eq_FalseI = thm "Eq_FalseI" |
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val Eq_TrueI = thm "Eq_TrueI" |
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in 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 Eq_FalseI |
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| _ => th RS Eq_TrueI |
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end; |
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local |
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val meta_eq_to_obj_eq = thm "meta_eq_to_obj_eq" |
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val Eq_TrueI = thm "Eq_TrueI" |
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in fun mk_eq_True r = |
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SOME (r RS meta_eq_to_obj_eq RS Eq_TrueI) handle Thm.THM _ => NONE; |
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end; |
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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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local |
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val meta_eq_to_obj_eq = thm "meta_eq_to_obj_eq" |
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val simp_implies_def = thm "simp_implies_def" |
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in 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 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 = 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 [simp_implies_def], |
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REPEAT (ares_tac (meta_eq_to_obj_eq :: map (rewrite_rule [simp_implies_def]) prems) 1)]) |
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end |
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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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local |
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val simp_impliesI = thm "simp_impliesI" |
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val TrueI = thm "TrueI" |
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val FalseE = thm "FalseE" |
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val refl = thm "refl" |
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in fun unsafe_solver_tac prems = |
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(fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN' |
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FIRST'[resolve_tac(reflexive_thm :: TrueI :: refl :: prems), atac, etac FalseE]; |
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end; |
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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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local |
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val simp_impliesI = thm "simp_impliesI" |
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val TrueI = thm "TrueI" |
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val FalseE = thm "FalseE" |
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val refl = thm "refl" |
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in fun safe_solver_tac prems = |
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(fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN' |
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FIRST'[match_tac(reflexive_thm :: TrueI :: refl :: prems), |
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eq_assume_tac, ematch_tac [FalseE]]; |
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end; |
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val safe_solver = mk_solver "HOL safe" safe_solver_tac; |
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structure SplitterData = |
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struct |
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structure Simplifier = Simplifier |
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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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end; |
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structure Splitter = SplitterFun(SplitterData); |
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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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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 simpset_basic = |
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Simplifier.theory_context (the_context ()) 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 simplify rews = Simplifier.full_simplify (simpset_basic addsimps rews); |
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fun unfold_tac ths = |
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let val ss0 = Simplifier.clear_ss simpset_basic addsimps ths |
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in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end; |
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(** simprocs **) |
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(* simproc for proving "(y = x) == False" from premise "~(x = y)" *) |
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val use_neq_simproc = ref true; |
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local |
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val thy = the_context (); |
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val neq_to_EQ_False = thm "not_sym" RS thm "Eq_FalseI"; |
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fun neq_prover sg ss (eq $ lhs $ rhs) = |
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let |
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fun test thm = (case #prop (rep_thm thm) of |
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_ $ (Not $ (eq' $ l' $ r')) => |
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Not = HOLogic.Not andalso eq' = eq andalso |
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r' aconv lhs andalso l' aconv rhs |
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| _ => false) |
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in if !use_neq_simproc then case find_first test (prems_of_ss ss) |
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of NONE => NONE |
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| SOME thm => SOME (thm RS neq_to_EQ_False) |
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else NONE |
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end |
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in |
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val neq_simproc = Simplifier.simproc thy "neq_simproc" ["x = y"] neq_prover; |
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end; |
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(* simproc for Let *) |
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val use_let_simproc = ref true; |
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local |
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val thy = the_context (); |
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val Let_folded = thm "Let_folded"; |
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val Let_unfold = thm "Let_unfold"; |
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val Let_def = thm "Let_def"; |
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val (f_Let_unfold, x_Let_unfold) = |
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let val [(_$(f$x)$_)] = prems_of Let_unfold |
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in (cterm_of thy f, cterm_of thy x) end |
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val (f_Let_folded, x_Let_folded) = |
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let val [(_$(f$x)$_)] = prems_of Let_folded |
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in (cterm_of thy f, cterm_of thy x) end; |
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val g_Let_folded = |
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let val [(_$_$(g$_))] = prems_of Let_folded in cterm_of thy g end; |
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in |
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val let_simproc = |
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Simplifier.simproc thy "let_simp" ["Let x f"] |
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(fn sg => fn ss => fn t => |
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let val ctxt = Simplifier.the_context ss; |
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val ([t'], ctxt') = Variable.import_terms false [t] ctxt; |
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in Option.map (hd o Variable.export ctxt' ctxt o single) |
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(case t' of (Const ("Let",_)$x$f) => (* x and f are already in normal form *) |
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if not (!use_let_simproc) then NONE |
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else if is_Free x orelse is_Bound x orelse is_Const x |
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then SOME Let_def |
21163 | 252 |
else |
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let |
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val n = case f of (Abs (x,_,_)) => x | _ => "x"; |
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val cx = cterm_of sg x; |
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val {T=xT,...} = rep_cterm cx; |
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val cf = cterm_of sg f; |
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val fx_g = Simplifier.rewrite ss (Thm.capply cf cx); |
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val (_$_$g) = prop_of fx_g; |
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val g' = abstract_over (x,g); |
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in (if (g aconv g') |
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then |
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let |
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val rl = cterm_instantiate [(f_Let_unfold,cf),(x_Let_unfold,cx)] Let_unfold; |
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in SOME (rl OF [fx_g]) end |
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else if Term.betapply (f,x) aconv g then NONE (*avoid identity conversion*) |
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else let |
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val abs_g'= Abs (n,xT,g'); |
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val g'x = abs_g'$x; |
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val g_g'x = symmetric (beta_conversion false (cterm_of sg g'x)); |
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val rl = cterm_instantiate |
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[(f_Let_folded,cterm_of sg f),(x_Let_folded,cx), |
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(g_Let_folded,cterm_of sg abs_g')] |
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Let_folded; |
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in SOME (rl OF [transitive fx_g g_g'x]) |
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276 |
end) |
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277 |
end |
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| _ => NONE) |
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279 |
end) |
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end; |
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(* generic refutation procedure *) |
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285 |
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286 |
(* parameters: |
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287 |
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288 |
test: term -> bool |
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289 |
tests if a term is at all relevant to the refutation proof; |
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290 |
if not, then it can be discarded. Can improve performance, |
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esp. if disjunctions can be discarded (no case distinction needed!). |
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293 |
prep_tac: int -> tactic |
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294 |
A preparation tactic to be applied to the goal once all relevant premises |
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295 |
have been moved to the conclusion. |
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296 |
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297 |
ref_tac: int -> tactic |
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298 |
the actual refutation tactic. Should be able to deal with goals |
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299 |
[| A1; ...; An |] ==> False |
|
300 |
where the Ai are atomic, i.e. no top-level &, | or EX |
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301 |
*) |
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302 |
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303 |
local |
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21551 | 304 |
val conjE = thm "conjE" |
305 |
val exE = thm "exE" |
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306 |
val disjE = thm "disjE" |
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307 |
val notE = thm "notE" |
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308 |
val rev_mp = thm "rev_mp" |
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309 |
val ccontr = thm "ccontr" |
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21163 | 310 |
val nnf_simpset = |
311 |
empty_ss setmkeqTrue mk_eq_True |
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312 |
setmksimps (mksimps mksimps_pairs) |
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313 |
addsimps [thm "imp_conv_disj", thm "iff_conv_conj_imp", thm "de_Morgan_disj", thm "de_Morgan_conj", |
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314 |
thm "not_all", thm "not_ex", thm "not_not"]; |
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315 |
fun prem_nnf_tac i st = |
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316 |
full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st; |
|
317 |
in |
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318 |
fun refute_tac test prep_tac ref_tac = |
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319 |
let val refute_prems_tac = |
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320 |
REPEAT_DETERM |
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321 |
(eresolve_tac [conjE, exE] 1 ORELSE |
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322 |
filter_prems_tac test 1 ORELSE |
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323 |
etac disjE 1) THEN |
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324 |
((etac notE 1 THEN eq_assume_tac 1) ORELSE |
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325 |
ref_tac 1); |
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326 |
in EVERY'[TRY o filter_prems_tac test, |
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327 |
REPEAT_DETERM o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac, |
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328 |
SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)] |
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329 |
end; |
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end; |
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332 |
val defALL_regroup = |
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333 |
Simplifier.simproc (the_context ()) |
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334 |
"defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all; |
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336 |
val defEX_regroup = |
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337 |
Simplifier.simproc (the_context ()) |
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338 |
"defined EX" ["EX x. P x"] Quantifier1.rearrange_ex; |
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341 |
val simpset_simprocs = simpset_basic |
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342 |
addsimprocs [defALL_regroup, defEX_regroup, neq_simproc, let_simproc] |
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mk_atomize: careful matching against rules admits overloading;
wenzelm
parents:
21163
diff
changeset
|
344 |
end; |
21551 | 345 |
|
346 |
structure Splitter = Simpdata.Splitter; |
|
347 |
structure Clasimp = Simpdata.Clasimp; |