src/CCL/Gfp.ML

--- a/src/CCL/Gfp.ML	Sat Sep 17 14:02:31 2005 +0200
+++ b/src/CCL/Gfp.ML	Sat Sep 17 17:35:26 2005 +0200
@@ -1,55 +1,46 @@
-(*  Title:      CCL/gfp
+(*  Title:      CCL/Gfp.ML
     ID:         $Id$
-
-Modified version of
-    Title:      HOL/gfp
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1993  University of Cambridge
-
-For gfp.thy.  The Knaster-Tarski Theorem for greatest fixed points.
 *)
 
-open Gfp;
-
 (*** Proof of Knaster-Tarski Theorem using gfp ***)
 
 (* gfp(f) is the least upper bound of {u. u <= f(u)} *)
 
-val prems = goalw Gfp.thy [gfp_def] "[| A <= f(A) |] ==> A <= gfp(f)";
+val prems = goalw (the_context ()) [gfp_def] "[| A <= f(A) |] ==> A <= gfp(f)";
 by (rtac (CollectI RS Union_upper) 1);
 by (resolve_tac prems 1);
 qed "gfp_upperbound";
 
-val prems = goalw Gfp.thy [gfp_def]
+val prems = goalw (the_context ()) [gfp_def]
     "[| !!u. u <= f(u) ==> u<=A |] ==> gfp(f) <= A";
 by (REPEAT (ares_tac ([Union_least]@prems) 1));
 by (etac CollectD 1);
 qed "gfp_least";
 
-val [mono] = goal Gfp.thy "mono(f) ==> gfp(f) <= f(gfp(f))";
+val [mono] = goal (the_context ()) "mono(f) ==> gfp(f) <= f(gfp(f))";
 by (EVERY1 [rtac gfp_least, rtac subset_trans, atac,
             rtac (mono RS monoD), rtac gfp_upperbound, atac]);
 qed "gfp_lemma2";
 
-val [mono] = goal Gfp.thy "mono(f) ==> f(gfp(f)) <= gfp(f)";
+val [mono] = goal (the_context ()) "mono(f) ==> f(gfp(f)) <= gfp(f)";
 by (EVERY1 [rtac gfp_upperbound, rtac (mono RS monoD), 
             rtac gfp_lemma2, rtac mono]);
 qed "gfp_lemma3";
 
-val [mono] = goal Gfp.thy "mono(f) ==> gfp(f) = f(gfp(f))";
+val [mono] = goal (the_context ()) "mono(f) ==> gfp(f) = f(gfp(f))";
 by (REPEAT (resolve_tac [equalityI,gfp_lemma2,gfp_lemma3,mono] 1));
 qed "gfp_Tarski";
 
 (*** Coinduction rules for greatest fixed points ***)
 
 (*weak version*)
-val prems = goal Gfp.thy
+val prems = goal (the_context ())
     "[| a: A;  A <= f(A) |] ==> a : gfp(f)";
 by (rtac (gfp_upperbound RS subsetD) 1);
 by (REPEAT (ares_tac prems 1));
 qed "coinduct";
 
-val [prem,mono] = goal Gfp.thy
+val [prem,mono] = goal (the_context ())
     "[| A <= f(A) Un gfp(f);  mono(f) |] ==>  \
 \    A Un gfp(f) <= f(A Un gfp(f))";
 by (rtac subset_trans 1);
@@ -60,7 +51,7 @@
 qed "coinduct2_lemma";
 
 (*strong version, thanks to Martin Coen*)
-val ainA::prems = goal Gfp.thy
+val ainA::prems = goal (the_context ())
     "[| a: A;  A <= f(A) Un gfp(f);  mono(f) |] ==> a : gfp(f)";
 by (rtac coinduct 1);
 by (rtac (prems MRS coinduct2_lemma) 2);
@@ -71,11 +62,11 @@
          - instead of the condition  A <= f(A)
                            consider  A <= (f(A) Un f(f(A)) ...) Un gfp(A) ***)
 
-val [prem] = goal Gfp.thy "mono(f) ==> mono(%x. f(x) Un A Un B)";
+val [prem] = goal (the_context ()) "mono(f) ==> mono(%x. f(x) Un A Un B)";
 by (REPEAT (ares_tac [subset_refl, monoI, Un_mono, prem RS monoD] 1));
 qed "coinduct3_mono_lemma";
 
-val [prem,mono] = goal Gfp.thy
+val [prem,mono] = goal (the_context ())
     "[| A <= f(lfp(%x. f(x) Un A Un gfp(f)));  mono(f) |] ==> \
 \    lfp(%x. f(x) Un A Un gfp(f)) <= f(lfp(%x. f(x) Un A Un gfp(f)))";
 by (rtac subset_trans 1);
@@ -89,7 +80,7 @@
 by (rtac Un_upper2 1);
 qed "coinduct3_lemma";
 
-val ainA::prems = goal Gfp.thy
+val ainA::prems = goal (the_context ())
     "[| a:A;  A <= f(lfp(%x. f(x) Un A Un gfp(f))); mono(f) |] ==> a : gfp(f)";
 by (rtac coinduct 1);
 by (rtac (prems MRS coinduct3_lemma) 2);
@@ -100,31 +91,31 @@
 
 (** Definition forms of gfp_Tarski, to control unfolding **)
 
-val [rew,mono] = goal Gfp.thy "[| h==gfp(f);  mono(f) |] ==> h = f(h)";
+val [rew,mono] = goal (the_context ()) "[| h==gfp(f);  mono(f) |] ==> h = f(h)";
 by (rewtac rew);
 by (rtac (mono RS gfp_Tarski) 1);
 qed "def_gfp_Tarski";
 
-val rew::prems = goal Gfp.thy
+val rew::prems = goal (the_context ())
     "[| h==gfp(f);  a:A;  A <= f(A) |] ==> a: h";
 by (rewtac rew);
 by (REPEAT (ares_tac (prems @ [coinduct]) 1));
 qed "def_coinduct";
 
-val rew::prems = goal Gfp.thy
+val rew::prems = goal (the_context ())
     "[| h==gfp(f);  a:A;  A <= f(A) Un h; mono(f) |] ==> a: h";
 by (rewtac rew);
 by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct2]) 1));
 qed "def_coinduct2";
 
-val rew::prems = goal Gfp.thy
+val rew::prems = goal (the_context ())
     "[| h==gfp(f);  a:A;  A <= f(lfp(%x. f(x) Un A Un h)); mono(f) |] ==> a: h";
 by (rewtac rew);
 by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct3]) 1));
 qed "def_coinduct3";
 
 (*Monotonicity of gfp!*)
-val prems = goal Gfp.thy
+val prems = goal (the_context ())
     "[| mono(f);  !!Z. f(Z)<=g(Z) |] ==> gfp(f) <= gfp(g)";
 by (rtac gfp_upperbound 1);
 by (rtac subset_trans 1);