src/FOL/simpdata.ML
author wenzelm
Sat, 15 Mar 2008 22:07:28 +0100
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child 26496 49ae9456eba9
permissions -rw-r--r--
eliminated out-of-scope proofs (cf. theory IFOL and FOL); proper antiquotations;
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(*  Title:      FOL/simpdata.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1994  University of Cambridge
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Simplification data for FOL.
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*)
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(*Make meta-equalities.  The operator below is Trueprop*)
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fun mk_meta_eq th = case concl_of th of
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    _ $ (Const("op =",_)$_$_)   => th RS @{thm eq_reflection}
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  | _ $ (Const("op <->",_)$_$_) => th RS @{thm iff_reflection}
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  | _                           =>
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  error("conclusion must be a =-equality or <->");;
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fun mk_eq th = case concl_of th of
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    Const("==",_)$_$_           => th
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  | _ $ (Const("op =",_)$_$_)   => mk_meta_eq th
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  | _ $ (Const("op <->",_)$_$_) => mk_meta_eq th
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  | _ $ (Const("Not",_)$_)      => th RS @{thm iff_reflection_F}
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  | _                           => th RS @{thm iff_reflection_T};
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(*Replace premises x=y, X<->Y by X==Y*)
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val mk_meta_prems =
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    rule_by_tactic
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      (REPEAT_FIRST (resolve_tac [@{thm meta_eq_to_obj_eq}, @{thm def_imp_iff}]));
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(*Congruence rules for = or <-> (instead of ==)*)
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fun mk_meta_cong rl =
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  standard(mk_meta_eq (mk_meta_prems rl))
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  handle THM _ =>
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  error("Premises and conclusion of congruence rules must use =-equality or <->");
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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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(* ###FIXME: move to simplifier.ML
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val mk_atomize:      (string * thm list) list -> thm -> thm list
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*)
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(* ###FIXME: move to simplifier.ML *)
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fun mk_atomize pairs =
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  let fun atoms th =
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        (case concl_of th of
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           Const("Trueprop",_) $ p =>
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             (case head_of p of
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                Const(a,_) =>
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                  (case AList.lookup (op =) pairs a of
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                     SOME(rls) => List.concat (map atoms ([th] RL rls))
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                   | NONE => [th])
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              | _ => [th])
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         | _ => [th])
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  in atoms end;
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fun mksimps pairs = (map mk_eq o mk_atomize pairs o gen_all);
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(** make simplification procedures for quantifier elimination **)
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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 = FOLogic.conj
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  val imp  = FOLogic.imp
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  (*rules*)
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  val iff_reflection = @{thm iff_reflection}
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  val iffI = @{thm iffI}
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  val iff_trans = @{thm iff_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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val defEX_regroup =
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  Simplifier.simproc (the_context ())
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    "defined EX" ["EX x. P(x)"] Quantifier1.rearrange_ex;
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val defALL_regroup =
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  Simplifier.simproc (the_context ())
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    "defined ALL" ["ALL x. P(x)"] Quantifier1.rearrange_all;
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(*** Case splitting ***)
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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_iff}
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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}
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  val contrapos2     = @{thm contrapos2}
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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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val split_tac        = Splitter.split_tac;
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val split_inside_tac = Splitter.split_inside_tac;
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val split_asm_tac    = Splitter.split_asm_tac;
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val op addsplits     = Splitter.addsplits;
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val op delsplits     = Splitter.delsplits;
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val Addsplits        = Splitter.Addsplits;
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val Delsplits        = Splitter.Delsplits;
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(*** Standard simpsets ***)
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val triv_rls = [@{thm TrueI}, @{thm refl}, reflexive_thm, @{thm iff_refl}, @{thm notFalseI}];
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fun unsafe_solver prems = FIRST'[resolve_tac (triv_rls @ prems),
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                                 atac, etac @{thm FalseE}];
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(*No premature instantiation of variables during simplification*)
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fun   safe_solver prems = FIRST'[match_tac (triv_rls @ prems),
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                                 eq_assume_tac, ematch_tac [@{thm FalseE}]];
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(*No simprules, but basic infastructure for simplification*)
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val FOL_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 (mk_solver "FOL safe" safe_solver)
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  setSolver (mk_solver "FOL unsafe" unsafe_solver)
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  setmksimps (mksimps mksimps_pairs)
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  setmkcong mk_meta_cong;
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fun unfold_tac ths =
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  let val ss0 = Simplifier.clear_ss FOL_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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fb9261990ffe simprocs: Simplifier.inherit_bounds;
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(*intuitionistic simprules only*)
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val IFOL_ss =
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  FOL_basic_ss
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  addsimps (@{thms meta_simps} @ @{thms IFOL_simps} @ @{thms int_ex_simps} @ @{thms int_all_simps})
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  addsimprocs [defALL_regroup, defEX_regroup]    
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  addcongs [@{thm imp_cong}];
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(*classical simprules too*)
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val FOL_ss = IFOL_ss addsimps (@{thms cla_simps} @ @{thms cla_ex_simps} @ @{thms cla_all_simps});
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val simpsetup = (fn thy => (change_simpset_of thy (fn _ => FOL_ss); thy));
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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  = Cla 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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ML_Context.value_antiq "clasimpset"
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  (Scan.succeed ("clasimpset", "Clasimp.local_clasimpset_of (ML_Context.the_local_context ())"));
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val FOL_css = (FOL_cs, FOL_ss);