(*  Title:      HOL/simpdata.ML

    Author:     Tobias Nipkow

    Copyright   1991  University of Cambridge

Instantiation of the generic simplifier for HOL.

*)

(** tools setup **)

structure Quantifier1 = Quantifier1Fun

(struct

  (*abstract syntax*)

  fun dest_eq ((c as Const(@{const_name "op ="},_)) $ s $ t) = SOME (c, s, t)

    | dest_eq _ = NONE;

  fun dest_conj ((c as Const(@{const_name "op &"},_)) $ s $ t) = SOME (c, s, t)

    | dest_conj _ = NONE;

  fun dest_imp ((c as Const(@{const_name "op -->"},_)) $ s $ t) = SOME (c, s, t)

    | dest_imp _ = NONE;

  val conj = HOLogic.conj

  val imp  = HOLogic.imp

  (*rules*)

  val iff_reflection = @{thm eq_reflection}

  val iffI = @{thm iffI}

  val iff_trans = @{thm 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);

structure Simpdata =

struct

fun mk_meta_eq r = r RS @{thm eq_reflection};

fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;

fun mk_eq th = case concl_of th

  (*expects Trueprop if not == *)

  of Const (@{const_name "=="},_) $ _ $ _ => th

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

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

   | _ => th RS @{thm Eq_TrueI}

fun mk_eq_True (_: simpset) r =

  SOME (r RS @{thm meta_eq_to_obj_eq} RS @{thm Eq_TrueI}) handle Thm.THM _ => NONE;

(* Produce theorems of the form

  (P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y)

*)

fun lift_meta_eq_to_obj_eq i st =

  let

    fun count_imp (Const (@{const_name HOL.simp_implies}, _) $ P $ Q) = 1 + count_imp Q

      | count_imp _ = 0;

    val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i - 1)))

  in if j = 0 then @{thm meta_eq_to_obj_eq}

    else

      let

        val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j);

        fun mk_simp_implies Q = fold_rev (fn R => fn S =>

          Const (@{const_name HOL.simp_implies}, propT --> propT --> propT) $ R $ S) Ps Q

        val aT = TFree ("'a", HOLogic.typeS);

        val x = Free ("x", aT);

        val y = Free ("y", aT)

      in Goal.prove_global (Thm.theory_of_thm st) []

        [mk_simp_implies (Logic.mk_equals (x, y))]

        (mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))

        (fn {prems, ...} => EVERY

         [rewrite_goals_tac @{thms simp_implies_def},

          REPEAT (ares_tac (@{thm meta_eq_to_obj_eq} ::

            map (rewrite_rule @{thms simp_implies_def}) prems) 1)])

      end

  end;

(*Congruence rules for = (instead of ==)*)

fun mk_meta_cong (_: simpset) rl = zero_var_indexes

  (let val rl' = Seq.hd (TRYALL (fn i => fn st =>

     rtac (lift_meta_eq_to_obj_eq i st) i st) rl)

   in mk_meta_eq rl' handle THM _ =>

     if can Logic.dest_equals (concl_of rl') then rl'

     else error "Conclusion of congruence rules must be =-equality"

   end);

fun mk_atomize pairs =

  let

    fun atoms thm =

      let

        fun res th = map (fn rl => th RS rl);   (*exception THM*)

        fun res_fixed rls =

          if Thm.maxidx_of (Thm.adjust_maxidx_thm ~1 thm) = ~1 then res thm rls

          else Variable.trade (K (fn [thm'] => res thm' rls)) (Variable.global_thm_context thm) [thm];

      in

        case concl_of thm

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

            of Const (a, _) => (case AList.lookup (op =) pairs a

              of SOME rls => (maps atoms (res_fixed rls) handle THM _ => [thm])

              | NONE => [thm])

            | _ => [thm])

          | _ => [thm]

      end;

  in atoms end;

fun mksimps pairs (_: simpset) =

  map_filter (try mk_eq) o mk_atomize pairs o gen_all;

fun unsafe_solver_tac prems =

  (fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'

  FIRST' [resolve_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems), atac,

    etac @{thm FalseE}];

val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;

(*No premature instantiation of variables during simplification*)

fun safe_solver_tac prems =

  (fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'

  FIRST' [match_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems),

         eq_assume_tac, ematch_tac @{thms FalseE}];

val safe_solver = mk_solver "HOL safe" safe_solver_tac;

structure Splitter = Splitter

(

  val thy = @{theory}

  val mk_eq = mk_eq

  val meta_eq_to_iff = @{thm meta_eq_to_obj_eq}

  val iffD = @{thm iffD2}

  val disjE = @{thm disjE}

  val conjE = @{thm conjE}

  val exE = @{thm exE}

  val contrapos = @{thm contrapos_nn}

  val contrapos2 = @{thm contrapos_pp}

  val notnotD = @{thm notnotD}

);

val split_tac = Splitter.split_tac;

val split_inside_tac = Splitter.split_inside_tac;

val op addsplits = Splitter.addsplits;

val op delsplits = Splitter.delsplits;

(* integration of simplifier with classical reasoner *)

structure Clasimp = ClasimpFun

 (structure Simplifier = Simplifier and Splitter = Splitter

  and Classical  = Classical and Blast = Blast

  val iffD1 = @{thm iffD1} val iffD2 = @{thm iffD2} val notE = @{thm notE});

open Clasimp;

val _ = ML_Antiquote.value "clasimpset"

  (Scan.succeed "Clasimp.clasimpset_of (ML_Context.the_local_context ())");

val mksimps_pairs =

 [(@{const_name "op -->"}, [@{thm mp}]),

  (@{const_name "op &"}, [@{thm conjunct1}, @{thm conjunct2}]),

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

  (@{const_name True}, []),

  (@{const_name False}, []),

  (@{const_name If}, [@{thm if_bool_eq_conj} RS @{thm iffD1}])];

val HOL_basic_ss =

  Simplifier.global_context @{theory} empty_ss

    setsubgoaler asm_simp_tac

    setSSolver safe_solver

    setSolver unsafe_solver

    setmksimps (mksimps mksimps_pairs)

    setmkeqTrue mk_eq_True

    setmkcong mk_meta_cong;

fun hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);

fun unfold_tac ths =

  let val ss0 = Simplifier.clear_ss HOL_basic_ss addsimps ths

  in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end;

val defALL_regroup =

  Simplifier.simproc @{theory}

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

val defEX_regroup =

  Simplifier.simproc @{theory}

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

val simpset_simprocs = HOL_basic_ss addsimprocs [defALL_regroup, defEX_regroup]

end;

structure Splitter = Simpdata.Splitter;

structure Clasimp = Simpdata.Clasimp;