(*  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;

val Addsplits        = Splitter.Addsplits;

val 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 @{theory} 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 = (fn thy => (change_simpset_of thy (fn _ => FOL_ss); thy));

(*** 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_Context.value_antiq "clasimpset"

  (Scan.succeed ("clasimpset", "Clasimp.local_clasimpset_of (ML_Context.the_local_context ())"));

val FOL_css = (FOL_cs, FOL_ss);