(*  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("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 @{theory}

     "defined EX" ["EX x. P(x)"] Quantifier1.rearrange_ex;

 val defALL_regroup =

   Simplifier.simproc @{theory}

     "defined ALL" ["ALL x. P(x)"] Quantifier1.rearrange_all;

 (*** 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 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 = 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.clasimpset_of (ML_Context.the_local_context ())");

 val FOL_css = (FOL_cs, FOL_ss);