author berghofe Fri, 01 Jul 2005 13:54:12 +0200 changeset 16633 208ebc9311f2 parent 16632 ad2895beef79 child 16634 f19d58cfb47a
Implemented trick (due to Tobias Nipkow) for fine-tuning simplification of premises of congruence rules.
 src/HOL/HOL.thy file | annotate | diff | comparison | revisions src/HOL/simpdata.ML file | annotate | diff | comparison | revisions
--- a/src/HOL/HOL.thy	Fri Jul 01 13:51:11 2005 +0200
+++ b/src/HOL/HOL.thy	Fri Jul 01 13:54:12 2005 +0200
@@ -1122,6 +1122,53 @@
lemma Let_unfold: "f x \<equiv> g \<Longrightarrow>  Let x f \<equiv> g"
by (unfold Let_def)

+text {*
+The following copy of the implication operator is useful for
+fine-tuning congruence rules.
+*}
+
+consts
+  simp_implies :: "[prop, prop] => prop"  ("(_/ =simp=> _)" [2, 1] 1)
+defs simp_implies_def: "simp_implies \<equiv> op ==>"
+
+lemma simp_impliesI:
+  assumes PQ: "(PROP P \<Longrightarrow> PROP Q)"
+  shows "PROP P =simp=> PROP Q"
+  apply (unfold simp_implies_def)
+  apply (rule PQ)
+  apply assumption
+  done
+
+lemma simp_impliesE:
+  assumes PQ:"PROP P =simp=> PROP Q"
+  and P: "PROP P"
+  and QR: "PROP Q \<Longrightarrow> PROP R"
+  shows "PROP R"
+  apply (rule QR)
+  apply (rule PQ [unfolded simp_implies_def])
+  apply (rule P)
+  done
+
+lemma simp_implies_cong:
+  assumes PP' :"PROP P == PROP P'"
+  and P'QQ': "PROP P' ==> (PROP Q == PROP Q')"
+  shows "(PROP P =simp=> PROP Q) == (PROP P' =simp=> PROP Q')"
+proof (unfold simp_implies_def, rule equal_intr_rule)
+  assume PQ: "PROP P \<Longrightarrow> PROP Q"
+  and P': "PROP P'"
+  from PP' [symmetric] and P' have "PROP P"
+    by (rule equal_elim_rule1)
+  hence "PROP Q" by (rule PQ)
+  with P'QQ' [OF P'] show "PROP Q'" by (rule equal_elim_rule1)
+next
+  assume P'Q': "PROP P' \<Longrightarrow> PROP Q'"
+  and P: "PROP P"
+  from PP' and P have P': "PROP P'" by (rule equal_elim_rule1)
+  hence "PROP Q'" by (rule P'Q')
+  with P'QQ' [OF P', symmetric] show "PROP Q"
+    by (rule equal_elim_rule1)
+qed
+
subsubsection {* Actual Installation of the Simplifier *}

use "simpdata.ML"
--- a/src/HOL/simpdata.ML	Fri Jul 01 13:51:11 2005 +0200
+++ b/src/HOL/simpdata.ML	Fri Jul 01 13:54:12 2005 +0200
@@ -69,6 +69,10 @@
val not_imp = thm "not_imp";
val not_not = thm "not_not";
val rev_conj_cong = thm "rev_conj_cong";
+val simp_impliesE = thm "simp_impliesI";
+val simp_impliesI = thm "simp_impliesI";
+val simp_implies_cong = thm "simp_implies_cong";
+val simp_implies_def = thm "simp_implies_def";
val simp_thms = thms "simp_thms";
val split_if = thm "split_if";
val split_if_asm = thm "split_if_asm";
@@ -198,11 +202,40 @@
fun mk_eq_True r =
SOME (r RS meta_eq_to_obj_eq RS 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
+    val {sign, ...} = rep_thm st;
+    fun count_imp (Const ("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 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 = foldr (fn (R, S) =>
+          Const ("HOL.simp_implies", propT --> propT --> propT) \$ R \$ S) Q Ps
+        val aT = TFree ("'a", HOLogic.typeS);
+        val x = Free ("x", aT);
+        val y = Free ("y", aT)
+      in prove_goalw_cterm [simp_implies_def]
+        (cterm_of sign (Logic.mk_implies
+          (mk_simp_implies (Logic.mk_equals (x, y)),
+           mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))))
+        (fn hyps => [REPEAT (ares_tac (meta_eq_to_obj_eq :: hyps) 1)])
+      end
+  end;
+
(*Congruence rules for = (instead of ==)*)
-fun mk_meta_cong rl =
-  zero_var_indexes(mk_meta_eq(replicate (nprems_of rl) meta_eq_to_obj_eq MRS rl))
-  handle THM _ =>
-  error("Premises and conclusion of congruence rules must be =-equalities");
+fun mk_meta_cong 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 Logic.is_equals (concl_of rl') then rl'
+     else error "Conclusion of congruence rules must be =-equality"
+   end);

(* Elimination of True from asumptions: *)

@@ -263,11 +296,13 @@
(List.mapPartial (try mk_eq) o mk_atomize pairs o gen_all);

fun unsafe_solver_tac prems =
+  (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
FIRST'[resolve_tac(reflexive_thm::TrueI::refl::prems), atac, etac 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 [simp_impliesI] i)) THEN'
FIRST'[match_tac(reflexive_thm::TrueI::refl::prems),
eq_assume_tac, ematch_tac [FalseE]];
val safe_solver = mk_solver "HOL safe" safe_solver_tac;
@@ -298,7 +333,7 @@
thm "the_eq_trivial", the_sym_eq_trivial]
@ ex_simps @ all_simps @ simp_thms)