--- a/src/CCL/Fix.ML Sat Sep 17 14:02:31 2005 +0200
+++ b/src/CCL/Fix.ML Sat Sep 17 17:35:26 2005 +0200
@@ -1,16 +1,12 @@
-(* Title: CCL/fix
+(* Title: CCL/Fix.ML
ID: $Id$
Author: Martin Coen, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
-
-For fix.thy.
*)
-open Fix;
-
(*** Fixed Point Induction ***)
-val [base,step,incl] = goalw Fix.thy [INCL_def]
+val [base,step,incl] = goalw (the_context ()) [INCL_def]
"[| P(bot); !!x. P(x) ==> P(f(x)); INCL(P) |] ==> P(fix(f))";
by (rtac (incl RS spec RS mp) 1);
by (rtac (Nat_ind RS ballI) 1 THEN atac 1);
@@ -20,23 +16,23 @@
(*** Inclusive Predicates ***)
-val prems = goalw Fix.thy [INCL_def]
+val prems = goalw (the_context ()) [INCL_def]
"INCL(P) <-> (ALL f. (ALL n:Nat. P(f ^ n ` bot)) --> P(fix(f)))";
by (rtac iff_refl 1);
qed "inclXH";
-val prems = goal Fix.thy
+val prems = goal (the_context ())
"[| !!f. ALL n:Nat. P(f^n`bot) ==> P(fix(f)) |] ==> INCL(%x. P(x))";
by (fast_tac (term_cs addIs (prems @ [XH_to_I inclXH])) 1);
qed "inclI";
-val incl::prems = goal Fix.thy
+val incl::prems = goal (the_context ())
"[| INCL(P); !!n. n:Nat ==> P(f^n`bot) |] ==> P(fix(f))";
-by (fast_tac (term_cs addIs ([ballI RS (incl RS (XH_to_D inclXH) RS spec RS mp)]
+by (fast_tac (term_cs addIs ([ballI RS (incl RS (XH_to_D inclXH) RS spec RS mp)]
@ prems)) 1);
qed "inclD";
-val incl::prems = goal Fix.thy
+val incl::prems = goal (the_context ())
"[| INCL(P); (ALL n:Nat. P(f^n`bot))-->P(fix(f)) ==> R |] ==> R";
by (fast_tac (term_cs addIs ([incl RS inclD] @ prems)) 1);
qed "inclE";
@@ -55,15 +51,15 @@
by (rtac po_cong 1 THEN rtac po_bot 1);
qed "npo_INCL";
-val prems = goal Fix.thy "[| INCL(P); INCL(Q) |] ==> INCL(%x. P(x) & Q(x))";
+val prems = goal (the_context ()) "[| INCL(P); INCL(Q) |] ==> INCL(%x. P(x) & Q(x))";
by (fast_tac (set_cs addSIs ([inclI] @ (prems RL [inclD]))) 1);;
qed "conj_INCL";
-val prems = goal Fix.thy "[| !!a. INCL(P(a)) |] ==> INCL(%x. ALL a. P(a,x))";
+val prems = goal (the_context ()) "[| !!a. INCL(P(a)) |] ==> INCL(%x. ALL a. P(a,x))";
by (fast_tac (set_cs addSIs ([inclI] @ (prems RL [inclD]))) 1);;
qed "all_INCL";
-val prems = goal Fix.thy "[| !!a. a:A ==> INCL(P(a)) |] ==> INCL(%x. ALL a:A. P(a,x))";
+val prems = goal (the_context ()) "[| !!a. a:A ==> INCL(P(a)) |] ==> INCL(%x. ALL a:A. P(a,x))";
by (fast_tac (set_cs addSIs ([inclI] @ (prems RL [inclD]))) 1);;
qed "ball_INCL";
@@ -88,7 +84,7 @@
(* All fixed points are lam-expressions *)
-val [prem] = goal Fix.thy "idgen(d) = d ==> d = lam x.?f(x)";
+val [prem] = goal (the_context ()) "idgen(d) = d ==> d = lam x.?f(x)";
by (rtac (prem RS subst) 1);
by (rewtac idgen_def);
by (rtac refl 1);
@@ -96,13 +92,13 @@
(* Lemmas for rewriting fixed points of idgen *)
-val prems = goalw Fix.thy [idgen_def]
+val prems = goalw (the_context ()) [idgen_def]
"[| a = b; a ` t = u |] ==> b ` t = u";
by (simp_tac (term_ss addsimps (prems RL [sym])) 1);
qed "l_lemma";
val idgen_lemmas =
- let fun mk_thm s = prove_goalw Fix.thy [idgen_def] s
+ let fun mk_thm s = prove_goalw (the_context ()) [idgen_def] s
(fn [prem] => [rtac (prem RS l_lemma) 1,simp_tac term_ss 1])
in map mk_thm
[ "idgen(d) = d ==> d ` bot = bot",
@@ -112,22 +108,22 @@
"idgen(d) = d ==> d ` (lam x. f(x)) = lam x. d ` f(x)"]
end;
-(* Proof of Reachability law - show that fix and lam x.x both give LEAST fixed points
+(* Proof of Reachability law - show that fix and lam x.x both give LEAST fixed points
of idgen and hence are they same *)
-val [p1,p2,p3] = goal CCL.thy
+val [p1,p2,p3] = goal (the_context ())
"[| ALL x. t ` x [= u ` x; EX f. t=lam x. f(x); EX f. u=lam x. f(x) |] ==> t [= u";
by (stac (p2 RS cond_eta) 1);
by (stac (p3 RS cond_eta) 1);
by (rtac (p1 RS (po_lam RS iffD2)) 1);
qed "po_eta";
-val [prem] = goalw Fix.thy [idgen_def] "idgen(d) = d ==> d = lam x.?f(x)";
+val [prem] = goalw (the_context ()) [idgen_def] "idgen(d) = d ==> d = lam x.?f(x)";
by (rtac (prem RS subst) 1);
by (rtac refl 1);
qed "po_eta_lemma";
-val [prem] = goal Fix.thy
+val [prem] = goal (the_context ())
"idgen(d) = d ==> \
\ {p. EX a b. p=<a,b> & (EX t. a=fix(idgen) ` t & b = d ` t)} <= \
\ POgen({p. EX a b. p=<a,b> & (EX t. a=fix(idgen) ` t & b = d ` t)})";
@@ -137,14 +133,14 @@
by (ALLGOALS (fast_tac set_cs));
qed "lemma1";
-val [prem] = goal Fix.thy
+val [prem] = goal (the_context ())
"idgen(d) = d ==> fix(idgen) [= d";
by (rtac (allI RS po_eta) 1);
by (rtac (lemma1 RSN(2,po_coinduct)) 1);
by (ALLGOALS (fast_tac (term_cs addIs [prem,po_eta_lemma,fix_idgenfp])));
qed "fix_least_idgen";
-val [prem] = goal Fix.thy
+val [prem] = goal (the_context ())
"idgen(d) = d ==> \
\ {p. EX a b. p=<a,b> & b = d ` a} <= POgen({p. EX a b. p=<a,b> & b = d ` a})";
by (REPEAT (step_tac term_cs 1));
@@ -153,7 +149,7 @@
by (ALLGOALS (fast_tac set_cs));
qed "lemma2";
-val [prem] = goal Fix.thy
+val [prem] = goal (the_context ())
"idgen(d) = d ==> lam x. x [= d";
by (rtac (allI RS po_eta) 1);
by (rtac (lemma2 RSN(2,po_coinduct)) 1);
@@ -169,12 +165,12 @@
(********)
-val [prem] = goal Fix.thy "f = lam x. x ==> f`t = t";
+val [prem] = goal (the_context ()) "f = lam x. x ==> f`t = t";
by (rtac (prem RS sym RS subst) 1);
by (rtac applyB 1);
qed "id_apply";
-val prems = goal Fix.thy
+val prems = goal (the_context ())
"[| P(bot); P(true); P(false); \
\ !!x y.[| P(x); P(y) |] ==> P(<x,y>); \
\ !!u.(!!x. P(u(x))) ==> P(lam x. u(x)); INCL(P) |] ==> \
@@ -191,4 +187,3 @@
by (ALLGOALS (simp_tac term_ss));
by (ALLGOALS (fast_tac (term_cs addIs ([all_INCL,INCL_subst] @ prems))));
qed "term_ind";
-