src/HOL/Tools/simpdata.ML
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(*  Title:      HOL/simpdata.ML
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    Author:     Tobias Nipkow
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    Copyright   1991  University of Cambridge
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Instantiation of the generic simplifier for HOL.
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*)
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(** tools setup **)
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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(@{const_name "op ="},_)) $ s $ t) = SOME (c, s, t)
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    | dest_eq _ = NONE;
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  fun dest_conj ((c as Const(@{const_name "op &"},_)) $ s $ t) = SOME (c, s, t)
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    | dest_conj _ = NONE;
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  fun dest_imp ((c as Const(@{const_name "op -->"},_)) $ s $ t) = SOME (c, s, t)
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    | dest_imp _ = NONE;
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  val conj = HOLogic.conj
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  val imp  = HOLogic.imp
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  (*rules*)
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  val iff_reflection = @{thm eq_reflection}
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  val iffI = @{thm iffI}
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  val iff_trans = @{thm 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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structure Simpdata =
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struct
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fun mk_meta_eq r = r RS @{thm eq_reflection};
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fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
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fun mk_eq th = case concl_of th
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  (*expects Trueprop if not == *)
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  of Const (@{const_name "=="},_) $ _ $ _ => th
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   | _ $ (Const (@{const_name "op ="}, _) $ _ $ _) => mk_meta_eq th
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   | _ $ (Const (@{const_name "Not"}, _) $ _) => th RS @{thm Eq_FalseI}
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   | _ => th RS @{thm Eq_TrueI}
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fun mk_eq_True r =
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  SOME (r RS @{thm meta_eq_to_obj_eq} RS @{thm Eq_TrueI}) handle Thm.THM _ => NONE;
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(* Produce theorems of the form
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  (P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y)
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*)
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fun lift_meta_eq_to_obj_eq i st =
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  let
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    fun count_imp (Const (@{const_name HOL.simp_implies}, _) $ P $ Q) = 1 + count_imp Q
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      | count_imp _ = 0;
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    val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i - 1)))
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  in if j = 0 then @{thm meta_eq_to_obj_eq}
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    else
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      let
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        val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j);
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        fun mk_simp_implies Q = fold_rev (fn R => fn S =>
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          Const (@{const_name HOL.simp_implies}, propT --> propT --> propT) $ R $ S) Ps Q
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        val aT = TFree ("'a", HOLogic.typeS);
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        val x = Free ("x", aT);
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        val y = Free ("y", aT)
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      in Goal.prove_global (Thm.theory_of_thm st) []
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        [mk_simp_implies (Logic.mk_equals (x, y))]
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        (mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))
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        (fn {prems, ...} => EVERY
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         [rewrite_goals_tac @{thms simp_implies_def},
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          REPEAT (ares_tac (@{thm meta_eq_to_obj_eq} ::
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            map (rewrite_rule @{thms simp_implies_def}) prems) 1)])
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      end
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  end;
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(*Congruence rules for = (instead of ==)*)
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fun mk_meta_cong rl = zero_var_indexes
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  (let val rl' = Seq.hd (TRYALL (fn i => fn st =>
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     rtac (lift_meta_eq_to_obj_eq i st) i st) rl)
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   in mk_meta_eq rl' handle THM _ =>
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     if can Logic.dest_equals (concl_of rl') then rl'
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     else error "Conclusion of congruence rules must be =-equality"
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   end);
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fun mk_atomize pairs =
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  let
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    fun atoms thm =
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      let
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        fun res th = map (fn rl => th RS rl);   (*exception THM*)
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        fun res_fixed rls =
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          if Thm.maxidx_of (Thm.adjust_maxidx_thm ~1 thm) = ~1 then res thm rls
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          else Variable.trade (K (fn [thm'] => res thm' rls)) (Variable.thm_context thm) [thm];
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      in
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        case concl_of thm
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          of Const (@{const_name Trueprop}, _) $ p => (case head_of p
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            of Const (a, _) => (case AList.lookup (op =) pairs a
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              of SOME rls => (maps atoms (res_fixed rls) handle THM _ => [thm])
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              | NONE => [thm])
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            | _ => [thm])
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          | _ => [thm]
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      end;
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  in atoms end;
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fun mksimps pairs =
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  map_filter (try mk_eq) o mk_atomize pairs o gen_all;
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fun unsafe_solver_tac prems =
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  (fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'
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  FIRST' [resolve_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems), atac,
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    etac @{thm FalseE}];
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val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
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(*No premature instantiation of variables during simplification*)
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fun safe_solver_tac prems =
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  (fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'
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  FIRST' [match_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: prems),
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         eq_assume_tac, ematch_tac @{thms FalseE}];
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val safe_solver = mk_solver "HOL safe" safe_solver_tac;
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structure Splitter = Splitter
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(
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  val thy = @{theory}
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  val mk_eq = mk_eq
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  val meta_eq_to_iff = @{thm meta_eq_to_obj_eq}
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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_nn}
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  val contrapos2 = @{thm contrapos_pp}
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  val notnotD = @{thm notnotD}
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);
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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 op addsplits = Splitter.addsplits;
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val op delsplits = Splitter.delsplits;
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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  = Classical 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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val _ = ML_Antiquote.value "clasimpset"
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  (Scan.succeed "Clasimp.clasimpset_of (ML_Context.the_local_context ())");
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val mksimps_pairs =
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 [(@{const_name "op -->"}, [@{thm mp}]),
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  (@{const_name "op &"}, [@{thm conjunct1}, @{thm conjunct2}]),
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  (@{const_name All}, [@{thm spec}]),
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  (@{const_name True}, []),
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  (@{const_name False}, []),
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  (@{const_name If}, [@{thm if_bool_eq_conj} RS @{thm iffD1}])];
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val HOL_basic_ss =
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  Simplifier.global_context @{theory} empty_ss
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    setsubgoaler asm_simp_tac
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    setSSolver safe_solver
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    setSolver unsafe_solver
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    setmksimps (mksimps mksimps_pairs)
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    setmkeqTrue mk_eq_True
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    setmkcong mk_meta_cong;
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fun hol_simplify rews = Simplifier.full_simplify (HOL_basic_ss addsimps rews);
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fun unfold_tac ths =
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  let val ss0 = Simplifier.clear_ss HOL_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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val defALL_regroup =
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  Simplifier.simproc @{theory}
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    "defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all;
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val defEX_regroup =
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  Simplifier.simproc @{theory}
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    "defined EX" ["EX x. P x"] Quantifier1.rearrange_ex;
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val simpset_simprocs = HOL_basic_ss addsimprocs [defALL_regroup, defEX_regroup]
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end;
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structure Splitter = Simpdata.Splitter;
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structure Clasimp = Simpdata.Clasimp;