(* Title: FOL/simpdata.ML ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1994 University of Cambridge Simplification data for FOL. *) (*Make meta-equalities. The operator below is Trueprop*) fun mk_meta_eq th = case concl_of th of _ $ (Const("op =",_)$_$_) => th RS @{thm eq_reflection} | _ $ (Const("op <->",_)$_$_) => th RS @{thm iff_reflection} | _ => error("conclusion must be a =-equality or <->");; fun mk_eq th = case concl_of th of Const("==",_)$_$_ => th | _ $ (Const("op =",_)$_$_) => mk_meta_eq th | _ $ (Const("op <->",_)$_$_) => mk_meta_eq th | _ $ (Const("Not",_)$_) => th RS @{thm iff_reflection_F} | _ => th RS @{thm iff_reflection_T}; (*Replace premises x=y, X<->Y by X==Y*) val mk_meta_prems = rule_by_tactic (REPEAT_FIRST (resolve_tac [@{thm meta_eq_to_obj_eq}, @{thm def_imp_iff}])); (*Congruence rules for = or <-> (instead of ==)*) fun mk_meta_cong rl = standard(mk_meta_eq (mk_meta_prems rl)) handle THM _ => error("Premises and conclusion of congruence rules must use =-equality or <->"); val mksimps_pairs = [("op -->", [@{thm mp}]), ("op &", [@{thm conjunct1}, @{thm conjunct2}]), ("All", [@{thm spec}]), ("True", []), ("False", [])]; (* ###FIXME: move to simplifier.ML val mk_atomize: (string * thm list) list -> thm -> thm list *) (* ###FIXME: move to simplifier.ML *) 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 = (map mk_eq o mk_atomize pairs o gen_all); (** make simplification procedures for quantifier elimination **) 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 = FOLogic.conj val imp = FOLogic.imp (*rules*) val iff_reflection = @{thm iff_reflection} val iffI = @{thm iffI} val iff_trans = @{thm iff_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); val defEX_regroup = Simplifier.simproc (the_context ()) "defined EX" ["EX x. P(x)"] Quantifier1.rearrange_ex; val defALL_regroup = Simplifier.simproc (the_context ()) "defined ALL" ["ALL x. P(x)"] Quantifier1.rearrange_all; (*** Case splitting ***) structure SplitterData = struct structure Simplifier = Simplifier val mk_eq = mk_eq val meta_eq_to_iff = @{thm meta_eq_to_iff} val iffD = @{thm iffD2} val disjE = @{thm disjE} val conjE = @{thm conjE} val exE = @{thm exE} val contrapos = @{thm contrapos} val contrapos2 = @{thm contrapos2} val notnotD = @{thm 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; (*** Standard simpsets ***) val triv_rls = [@{thm TrueI}, @{thm refl}, reflexive_thm, @{thm iff_refl}, @{thm notFalseI}]; fun unsafe_solver prems = FIRST'[resolve_tac (triv_rls @ prems), atac, etac @{thm FalseE}]; (*No premature instantiation of variables during simplification*) fun safe_solver prems = FIRST'[match_tac (triv_rls @ prems), eq_assume_tac, ematch_tac [@{thm FalseE}]]; (*No simprules, but basic infastructure for simplification*) val FOL_basic_ss = Simplifier.theory_context (the_context ()) empty_ss setsubgoaler asm_simp_tac setSSolver (mk_solver "FOL safe" safe_solver) setSolver (mk_solver "FOL unsafe" unsafe_solver) setmksimps (mksimps mksimps_pairs) setmkcong mk_meta_cong; fun unfold_tac ths = let val ss0 = Simplifier.clear_ss FOL_basic_ss addsimps ths in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end; (*intuitionistic simprules only*) val IFOL_ss = FOL_basic_ss addsimps (@{thms meta_simps} @ @{thms IFOL_simps} @ @{thms int_ex_simps} @ @{thms int_all_simps}) addsimprocs [defALL_regroup, defEX_regroup] addcongs [@{thm imp_cong}]; (*classical simprules too*) val FOL_ss = IFOL_ss addsimps (@{thms cla_simps} @ @{thms cla_ex_simps} @ @{thms cla_all_simps}); val simpsetup = Simplifier.map_simpset (K FOL_ss); (*** integration of simplifier with classical reasoner ***) structure Clasimp = ClasimpFun (structure Simplifier = Simplifier and Splitter = Splitter and Classical = Cla and Blast = Blast val iffD1 = @{thm iffD1} val iffD2 = @{thm iffD2} val notE = @{thm notE}); open Clasimp; ML_Antiquote.value "clasimpset" (Scan.succeed "Clasimp.local_clasimpset_of (ML_Context.the_local_context ())"); val FOL_css = (FOL_cs, FOL_ss);