src/Sequents/simpdata.ML
 author haftmann Thu, 23 Nov 2017 17:03:27 +0000 changeset 67087 733017b19de9 parent 61268 abe08fb15a12 child 69593 3dda49e08b9d permissions -rw-r--r--
generalized more lemmas
```
(*  Title:      Sequents/simpdata.ML
Author:     Lawrence C Paulson

Instantiation of the generic simplifier for LK.

Borrows from the DC simplifier of Soren Heilmann.
*)

(** Conversion into rewrite rules **)

(*Make atomic rewrite rules*)
fun atomize r =
case Thm.concl_of r of
Const(@{const_name Trueprop},_) \$ Abs(_,_,a) \$ Abs(_,_,c) =>
(case (Cla.forms_of_seq a, Cla.forms_of_seq c) of
([], [p]) =>
(case p of
Const(@{const_name imp},_)\$_\$_ => atomize(r RS @{thm mp_R})
| Const(@{const_name conj},_)\$_\$_   => atomize(r RS @{thm conjunct1}) @
atomize(r RS @{thm conjunct2})
| Const(@{const_name All},_)\$_      => atomize(r RS @{thm spec})
| Const(@{const_name True},_)       => []    (*True is DELETED*)
| Const(@{const_name False},_)      => []    (*should False do something?*)
| _                     => [r])
| _ => [])  (*ignore theorem unless it has precisely one conclusion*)
| _ => [r];

(*Make meta-equalities.*)
fun mk_meta_eq ctxt th = case Thm.concl_of th of
Const(@{const_name Pure.eq},_)\$_\$_ => th
| Const(@{const_name Trueprop},_) \$ Abs(_,_,a) \$ Abs(_,_,c) =>
(case (Cla.forms_of_seq a, Cla.forms_of_seq c) of
([], [p]) =>
(case p of
(Const(@{const_name equal},_)\$_\$_)   => th RS @{thm eq_reflection}
| (Const(@{const_name iff},_)\$_\$_) => th RS @{thm iff_reflection}
| (Const(@{const_name Not},_)\$_)      => th RS @{thm iff_reflection_F}
| _                       => th RS @{thm iff_reflection_T})
| _ => error ("addsimps: unable to use theorem\n" ^ Thm.string_of_thm ctxt th));

(*Replace premises x=y, X<->Y by X==Y*)
fun mk_meta_prems ctxt =
rule_by_tactic ctxt
(REPEAT_FIRST (resolve_tac ctxt [@{thm meta_eq_to_obj_eq}, @{thm def_imp_iff}]));

(*Congruence rules for = or <-> (instead of ==)*)
fun mk_meta_cong ctxt rl =
Drule.zero_var_indexes (mk_meta_eq ctxt (mk_meta_prems ctxt rl))
handle THM _ =>
error("Premises and conclusion of congruence rules must use =-equality or <->");

(*** Standard simpsets ***)

val triv_rls = [@{thm FalseL}, @{thm TrueR}, @{thm basic}, @{thm refl},
@{thm iff_refl}, reflexive_thm];

fun unsafe_solver ctxt =
FIRST' [resolve_tac ctxt (triv_rls @ Simplifier.prems_of ctxt), assume_tac ctxt];

(*No premature instantiation of variables during simplification*)
fun safe_solver ctxt =
FIRST' [fn i => DETERM (match_tac ctxt (triv_rls @ Simplifier.prems_of ctxt) i),
eq_assume_tac];

(*No simprules, but basic infrastructure for simplification*)
val LK_basic_ss =
empty_simpset @{context}
setSSolver (mk_solver "safe" safe_solver)
setSolver (mk_solver "unsafe" unsafe_solver)
|> Simplifier.set_subgoaler asm_simp_tac
|> Simplifier.set_mksimps (fn ctxt => map (mk_meta_eq ctxt) o atomize o Variable.gen_all ctxt)
|> Simplifier.set_mkcong mk_meta_cong
|> simpset_of;

val LK_simps =
[@{thm triv_forall_equality}, (* prunes params *)
@{thm refl} RS @{thm P_iff_T}] @
@{thms conj_simps} @ @{thms disj_simps} @ @{thms not_simps} @
@{thms imp_simps} @ @{thms iff_simps} @ @{thms quant_simps} @
@{thms all_simps} @ @{thms ex_simps} @
[@{thm de_Morgan_conj}, @{thm de_Morgan_disj}, @{thm imp_disj1}, @{thm imp_disj2}] @
@{thms LK_extra_simps};

val LK_ss =