(* Title: HOL/Tools/simpdata.ML
Author: Tobias Nipkow
Copyright 1991 University of Cambridge
Instantiation of the generic simplifier for HOL.
*)
(** tools setup **)
structure Quantifier1 = Quantifier1
(
(*abstract syntax*)
fun dest_eq (Const(@{const_name HOL.eq},_) $ s $ t) = SOME (s, t)
| dest_eq _ = NONE;
fun dest_conj (Const(@{const_name HOL.conj},_) $ s $ t) = SOME (s, t)
| dest_conj _ = NONE;
fun dest_imp (Const(@{const_name HOL.implies},_) $ s $ t) = SOME (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}
);
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 HOL.eq}, _) $ _ $ _) => 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 (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 ss =
(fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'
FIRST' [resolve_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: Simplifier.prems_of ss),
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 ss =
(fn i => REPEAT_DETERM (match_tac @{thms simp_impliesI} i)) THEN'
FIRST' [match_tac (reflexive_thm :: @{thm TrueI} :: @{thm refl} :: Simplifier.prems_of ss),
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 = Clasimp
(
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 mksimps_pairs =
[(@{const_name HOL.implies}, [@{thm mp}]),
(@{const_name HOL.conj}, [@{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;
end;
structure Splitter = Simpdata.Splitter;
structure Clasimp = Simpdata.Clasimp;