(*  Title:      FOL/simpdata.ML

    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(@{const_name eq},_)$_$_)   => th RS @{thm eq_reflection}

  | _ $ (Const(@{const_name iff},_)$_$_) => th RS @{thm iff_reflection}

  | _                           =>

  error("conclusion must be a =-equality or <->");;

fun mk_eq th = case concl_of th of

    Const("==",_)$_$_           => th

  | _ $ (Const(@{const_name eq},_)$_$_)   => mk_meta_eq th

  | _ $ (Const(@{const_name iff},_)$_$_) => mk_meta_eq th

  | _ $ (Const(@{const_name Not},_)$_)      => th RS @{thm iff_reflection_F}

  | _                           => th RS @{thm iff_reflection_T};

(*Replace premises x=y, X<->Y by X==Y*)

fun mk_meta_prems ctxt =

    rule_by_tactic ctxt

      (REPEAT_FIRST (resolve_tac [@{thm meta_eq_to_obj_eq}, @{thm def_imp_iff}]));

(*Congruence rules for = or <-> (instead of ==)*)

fun mk_meta_cong ss rl =

  Drule.export_without_context (mk_meta_eq (mk_meta_prems (Simplifier.the_context ss) rl))

    handle THM _ =>

      error("Premises and conclusion of congruence rules must use =-equality or <->");

val mksimps_pairs =

  [(@{const_name imp}, [@{thm mp}]), (@{const_name conj}, [@{thm conjunct1}, @{thm conjunct2}]),

   (@{const_name All}, [@{thm spec}]), (@{const_name True}, []), (@{const_name False}, [])];

fun mk_atomize pairs =

  let fun atoms th =

        (case concl_of th of

           Const(@{const_name Trueprop},_) $ p =>

             (case head_of p of

                Const(a,_) =>

                  (case AList.lookup (op =) pairs a of

                     SOME(rls) => maps atoms ([th] RL rls)

                   | NONE => [th])

              | _ => [th])

         | _ => [th])

  in atoms end;

fun mksimps pairs (_: simpset) = map mk_eq o mk_atomize pairs o gen_all;

(** make simplification procedures for quantifier elimination **)

structure Quantifier1 = Quantifier1

(

  (*abstract syntax*)

  fun dest_eq (Const (@{const_name eq}, _) $ s $ t) = SOME (s, t)

    | dest_eq _ = NONE

  fun dest_conj (Const (@{const_name conj}, _) $ s $ t) = SOME (s, t)

    | dest_conj _ = NONE

  fun dest_imp (Const (@{const_name imp}, _) $ s $ t) = SOME (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}

);

(*** Case splitting ***)

structure Splitter = Splitter

(

  val thy = @{theory}

  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}

);

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 ss = FIRST'[resolve_tac (triv_rls @ prems_of_ss ss),

                                 atac, etac @{thm FalseE}];

(*No premature instantiation of variables during simplification*)

fun safe_solver ss = FIRST'[match_tac (triv_rls @ prems_of_ss ss),

                                 eq_assume_tac, ematch_tac [@{thm FalseE}]];

(*No simprules, but basic infastructure for simplification*)

val FOL_basic_ss =

  Simplifier.global_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;

(*** integration of simplifier with classical reasoner ***)

structure Clasimp = Clasimp

(

  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;