--- a/src/LCF/fix.ML Thu Jun 01 21:14:54 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,75 +0,0 @@
-(* Title: LCF/fix
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 1992 University of Cambridge
-*)
-
-val adm_eq = prove_goal (the_context ()) "adm(%x. t(x)=(u(x)::'a::cpo))"
- (fn _ => [rewtac eq_def,
- REPEAT(rstac[adm_conj,adm_less]1)]);
-
-val adm_not_not = prove_goal (the_context ()) "adm(P) ==> adm(%x.~~P(x))"
- (fn prems => [simp_tac (LCF_ss addsimps prems) 1]);
-
-
-val tac = rtac tr_induct 1 THEN ALLGOALS (simp_tac LCF_ss);
-
-val not_eq_TT = prove_goal (the_context ()) "ALL p. ~p=TT <-> (p=FF | p=UU)"
- (fn _ => [tac]) RS spec;
-
-val not_eq_FF = prove_goal (the_context ()) "ALL p. ~p=FF <-> (p=TT | p=UU)"
- (fn _ => [tac]) RS spec;
-
-val not_eq_UU = prove_goal (the_context ()) "ALL p. ~p=UU <-> (p=TT | p=FF)"
- (fn _ => [tac]) RS spec;
-
-val adm_not_eq_tr = prove_goal (the_context ()) "ALL p::tr. adm(%x. ~t(x)=p)"
- (fn _ => [rtac tr_induct 1,
- REPEAT(simp_tac (LCF_ss addsimps [not_eq_TT,not_eq_FF,not_eq_UU]) 1 THEN
- REPEAT(rstac [adm_disj,adm_eq] 1))]) RS spec;
-
-val adm_lemmas = [adm_not_free,adm_eq,adm_less,adm_not_less,adm_not_eq_tr,
- adm_conj,adm_disj,adm_imp,adm_all];
-
-fun induct_tac v i = res_inst_tac[("f",v)] induct i THEN
- REPEAT(rstac adm_lemmas i);
-
-
-val least_FIX = prove_goal (the_context ()) "f(p) = p ==> FIX(f) << p"
- (fn [prem] => [induct_tac "f" 1, rtac minimal 1, strip_tac 1,
- stac (prem RS sym) 1, etac less_ap_term 1]);
-
-val lfp_is_FIX = prove_goal (the_context ())
- "[| f(p) = p; ALL q. f(q)=q --> p << q |] ==> p = FIX(f)"
- (fn [prem1,prem2] => [rtac less_anti_sym 1,
- rtac (prem2 RS spec RS mp) 1, rtac FIX_eq 1,
- rtac least_FIX 1, rtac prem1 1]);
-
-val ffix = read_instantiate [("f","f::?'a=>?'a")] FIX_eq;
-val gfix = read_instantiate [("f","g::?'a=>?'a")] FIX_eq;
-val ss = LCF_ss addsimps [ffix,gfix];
-
-val FIX_pair = prove_goal (the_context ())
- "<FIX(f),FIX(g)> = FIX(%p.<f(FST(p)),g(SND(p))>)"
- (fn _ => [rtac lfp_is_FIX 1, simp_tac ss 1,
- strip_tac 1, simp_tac (LCF_ss addsimps [PROD_less]) 1,
- rtac conjI 1, rtac least_FIX 1, etac subst 1, rtac (FST RS sym) 1,
- rtac least_FIX 1, etac subst 1, rtac (SND RS sym) 1]);
-
-val FIX_pair_conj = rewrite_rule (map mk_meta_eq [PROD_eq,FST,SND]) FIX_pair;
-
-val FIX1 = FIX_pair_conj RS conjunct1;
-val FIX2 = FIX_pair_conj RS conjunct2;
-
-val induct2 = prove_goal (the_context ())
- "[| adm(%p. P(FST(p),SND(p))); P(UU::'a,UU::'b);\
-\ ALL x y. P(x,y) --> P(f(x),g(y)) |] ==> P(FIX(f),FIX(g))"
- (fn prems => [EVERY1
- [res_inst_tac [("f","f"),("g","g")] (standard(FIX1 RS ssubst)),
- res_inst_tac [("f","f"),("g","g")] (standard(FIX2 RS ssubst)),
- res_inst_tac [("f","%x. <f(FST(x)),g(SND(x))>")] induct,
- rstac prems, simp_tac ss, rstac prems,
- simp_tac (LCF_ss addsimps [expand_all_PROD]), rstac prems]]);
-
-fun induct2_tac (f,g) i = res_inst_tac[("f",f),("g",g)] induct2 i THEN
- REPEAT(rstac adm_lemmas i);