src/FOL/simpdata.ML
 author blanchet Tue, 15 Nov 2011 22:13:39 +0100 changeset 45509 624872fc47bf parent 43597 b4a093e755db child 45620 f2a587696afb permissions -rw-r--r--
use consts, not frees, for lambda-lifting
```
(*  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(@{const_name eq},_)\$_\$_)   => th RS @{thm eq_reflection}
| _ \$ (Const(@{const_name iff},_)\$_\$_) => th RS @{thm iff_reflection}
| _                           =>
error("conclusion must be a =-equality or <->");;

fun mk_eq th = case concl_of th of
Const("==",_)\$_\$_           => th
| _ \$ (Const(@{const_name eq},_)\$_\$_)   => mk_meta_eq th
| _ \$ (Const(@{const_name iff},_)\$_\$_) => mk_meta_eq th
| _ \$ (Const(@{const_name Not},_)\$_)      => th RS @{thm iff_reflection_F}
| _                           => th RS @{thm iff_reflection_T};

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

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

val mksimps_pairs =
[(@{const_name imp}, [@{thm mp}]), (@{const_name conj}, [@{thm conjunct1}, @{thm conjunct2}]),
(@{const_name All}, [@{thm spec}]), (@{const_name True}, []), (@{const_name False}, [])];

fun mk_atomize pairs =
let fun atoms th =
(case concl_of th of
Const(@{const_name Trueprop},_) \$ p =>
(case head_of p of
Const(a,_) =>
(case AList.lookup (op =) pairs a of
SOME(rls) => maps atoms ([th] RL rls)
| NONE => [th])
| _ => [th])
| _ => [th])
in atoms end;

fun mksimps pairs (_: simpset) = map mk_eq o mk_atomize pairs o gen_all;

(** make simplification procedures for quantifier elimination **)
structure Quantifier1 = Quantifier1
(
(*abstract syntax*)
fun dest_eq (Const (@{const_name eq}, _) \$ s \$ t) = SOME (s, t)
| dest_eq _ = NONE
fun dest_conj (Const (@{const_name conj}, _) \$ s \$ t) = SOME (s, t)
| dest_conj _ = NONE
fun dest_imp (Const (@{const_name imp}, _) \$ s \$ t) = SOME (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}
);

(*** 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 ss =
FIRST' [resolve_tac (triv_rls @ Simplifier.prems_of ss), atac, etac @{thm FalseE}];

(*No premature instantiation of variables during simplification*)
fun safe_solver ss =
FIRST' [match_tac (triv_rls @ Simplifier.prems_of ss), eq_assume_tac, ematch_tac @{thms FalseE}];

(*No simprules, but basic infastructure for simplification*)
val FOL_basic_ss =
Simplifier.global_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;

(*** integration of simplifier with classical reasoner ***)

structure Clasimp = Clasimp
(
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;

```