# HG changeset patch
# User nipkow
# Date 764513025 -3600
# Node ID 3a0485439396c4730ee99b86bfe76770357079e0
# Parent  5ef75ff3baeb943719758274193c27dc47348a27
structural induction for strict lists

diff -r 5ef75ff3baeb -r 3a0485439396 src/HOLCF/Dlist.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Dlist.ML	Thu Mar 24 13:43:45 1994 +0100
@@ -0,0 +1,563 @@
+(*  Title: 	HOLCF/dlist.ML
+    Author: 	Franz Regensburger
+    ID:         $ $
+    Copyright   1994 Technische Universitaet Muenchen
+
+Lemmas for dlist.thy
+*)
+
+open Dlist;
+
+(* ------------------------------------------------------------------------*)
+(* The isomorphisms dlist_rep_iso and dlist_abs_iso are strict             *)
+(* ------------------------------------------------------------------------*)
+
+val dlist_iso_strict= dlist_rep_iso RS (dlist_abs_iso RS 
+	(allI  RSN (2,allI RS iso_strict)));
+
+val dlist_rews = [dlist_iso_strict RS conjunct1,
+		dlist_iso_strict RS conjunct2];
+
+(* ------------------------------------------------------------------------*)
+(* Properties of dlist_copy                                                *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goalw Dlist.thy  [dlist_copy_def] "dlist_copy[f][UU]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1)
+	]);
+
+val dlist_copy = [temp];
+
+
+val temp = prove_goalw Dlist.thy  [dlist_copy_def,dnil_def] 
+    "dlist_copy[f][dnil]=dnil"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1)
+	]);
+
+val dlist_copy = temp :: dlist_copy;
+
+
+val temp = prove_goalw Dlist.thy  [dlist_copy_def,dcons_def] 
+	"xl~=UU ==> dlist_copy[f][dcons[x][xl]]= dcons[x][f[xl]]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac HOLCF_ss  1),
+	(asm_simp_tac (HOLCF_ss addsimps [defined_spair]) 1)
+	]);
+
+val dlist_copy = temp :: dlist_copy;
+
+val dlist_rews =  dlist_copy @ dlist_rews; 
+
+(* ------------------------------------------------------------------------*)
+(* Exhaustion and elimination for dlists                                   *)
+(* ------------------------------------------------------------------------*)
+
+val Exh_dlist = prove_goalw Dlist.thy [dcons_def,dnil_def]
+	"l = UU | l = dnil | (? x xl. x~=UU &xl~=UU & l = dcons[x][xl])"
+ (fn prems =>
+	[
+	(simp_tac HOLCF_ss  1),
+	(rtac (dlist_rep_iso RS subst) 1),
+	(res_inst_tac [("p","dlist_rep[l]")] ssumE 1),
+	(rtac disjI1 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(rtac disjI2 1),
+	(rtac disjI1 1),
+	(res_inst_tac [("p","x")] oneE 1),
+	(contr_tac 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(rtac disjI2 1),
+	(rtac disjI2 1),
+	(res_inst_tac [("p","y")] sprodE 1),
+	(contr_tac 1),
+	(rtac exI 1),
+	(rtac exI 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val dlistE = prove_goal Dlist.thy 
+"[| l=UU ==> Q; l=dnil ==> Q;!!x xl.[|l=dcons[x][xl];x~=UU;xl~=UU|]==>Q|]==>Q"
+ (fn prems =>
+	[
+	(rtac (Exh_dlist RS disjE) 1),
+	(eresolve_tac prems 1),
+	(etac disjE 1),
+	(eresolve_tac prems 1),
+	(etac exE 1),
+	(etac exE 1),
+	(resolve_tac prems 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+(* ------------------------------------------------------------------------*)
+(* Properties of dlist_when                                                *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goalw  Dlist.thy  [dlist_when_def] "dlist_when[f1][f2][UU]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps [dlist_iso_strict]) 1)
+	]);
+
+val dlist_when = [temp];
+
+val temp = prove_goalw  Dlist.thy [dlist_when_def,dnil_def]
+ "dlist_when[f1][f2][dnil]= f1"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps [dlist_abs_iso]) 1)
+	]);
+
+val dlist_when = temp::dlist_when;
+
+val temp = prove_goalw  Dlist.thy [dlist_when_def,dcons_def]
+ "[|x~=UU;xl~=UU|] ==> dlist_when[f1][f2][dcons[x][xl]]= f2[x][xl]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps [dlist_abs_iso,defined_spair]) 1)
+	]);
+
+val dlist_when = temp::dlist_when;
+
+val dlist_rews = dlist_when @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Rewrites for  discriminators and  selectors                             *)
+(* ------------------------------------------------------------------------*)
+
+fun prover defs thm = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_discsel = [
+	prover [is_dnil_def] "is_dnil[UU]=UU",
+	prover [is_dcons_def] "is_dcons[UU]=UU",
+	prover [dhd_def] "dhd[UU]=UU",
+	prover [dtl_def] "dtl[UU]=UU"
+	];
+
+fun prover defs thm = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_discsel = [
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "is_dnil[dnil]=TT",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> is_dnil[dcons[x][xl]]=FF",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "is_dcons[dnil]=FF",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> is_dcons[dcons[x][xl]]=TT",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "dhd[dnil]=UU",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> dhd[dcons[x][xl]]=x",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "dtl[dnil]=UU",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> dtl[dcons[x][xl]]=xl"] @ dlist_discsel;
+
+val dlist_rews = dlist_discsel @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Definedness and strictness                                              *)
+(* ------------------------------------------------------------------------*)
+
+fun prover contr thm = prove_goal Dlist.thy thm
+ (fn prems =>
+	[
+	(res_inst_tac [("P1",contr)] classical3 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(dtac sym 1),
+	(asm_simp_tac HOLCF_ss  1),
+	(simp_tac (HOLCF_ss addsimps (prems @ dlist_rews)) 1)
+	]);
+
+
+val dlist_constrdef = [
+prover "is_dnil[UU] ~= UU" "dnil~=UU",
+prover "is_dcons[UU] ~= UU" "[|x~=UU;xl~=UU|] ==> dcons[x][xl]~=UU"
+ ];
+
+
+fun prover defs thm = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_constrdef = [
+	prover [dcons_def] "dcons[UU][xl]=UU",
+	prover [dcons_def] "dcons[x][UU]=UU"
+	] @ dlist_constrdef;
+
+val dlist_rews = dlist_constrdef @ dlist_rews;
+
+
+(* ------------------------------------------------------------------------*)
+(* Distinctness wrt. << and =                                              *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goal Dlist.thy  "~dnil << dcons[x][xl]"
+ (fn prems =>
+	[
+	(res_inst_tac [("P1","TT << FF")] classical3 1),
+	(resolve_tac dist_less_tr 1),
+	(dres_inst_tac [("fo5","is_dnil")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_dist_less = [temp];
+
+val temp = prove_goal Dlist.thy  "[|x~=UU;xl~=UU|]==>~dcons[x][xl] << dnil"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("P1","TT << FF")] classical3 1),
+	(resolve_tac dist_less_tr 1),
+	(dres_inst_tac [("fo5","is_dcons")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_dist_less = temp::dlist_dist_less;
+
+val temp = prove_goal Dlist.thy  "dnil ~= dcons[x][xl]"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("P1","TT = FF")] classical3 1),
+	(resolve_tac dist_eq_tr 1),
+	(dres_inst_tac [("f","is_dnil")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_dist_eq = [temp,temp RS not_sym];
+
+val dlist_rews = dlist_dist_less @ dlist_dist_eq @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Invertibility                                                           *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goal Dlist.thy "[|x1~=UU; y1~=UU;x2~=UU; y2~=UU;\
+\ dcons[x1][x2] << dcons[y1][y2]|] ==> x1<< y1 & x2 << y2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac conjI 1),
+	(dres_inst_tac [("fo5","dlist_when[UU][LAM x l.x]")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(dres_inst_tac [("fo5","dlist_when[UU][LAM x l.l]")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1)
+	]);
+
+val dlist_invert =[temp];
+
+(* ------------------------------------------------------------------------*)
+(* Injectivity                                                             *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goal Dlist.thy "[|x1~=UU; y1~=UU;x2~=UU; y2~=UU;\
+\ dcons[x1][x2] = dcons[y1][y2]|] ==> x1= y1 & x2 = y2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac conjI 1),
+	(dres_inst_tac [("f","dlist_when[UU][LAM x l.x]")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(dres_inst_tac [("f","dlist_when[UU][LAM x l.l]")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1)
+	]);
+
+val dlist_inject = [temp];
+ 
+
+(* ------------------------------------------------------------------------*)
+(* definedness for  discriminators and  selectors                          *)
+(* ------------------------------------------------------------------------*)
+
+fun prover thm = prove_goal Dlist.thy thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac dlistE 1),
+	(contr_tac 1),
+	(REPEAT (asm_simp_tac (HOLCF_ss addsimps dlist_discsel) 1))
+	]);
+
+val dlist_discsel_def = 
+	[
+	prover "l~=UU ==> is_dnil[l]~=UU", 
+	prover "l~=UU ==> is_dcons[l]~=UU" 
+	];
+
+val dlist_rews = dlist_discsel_def @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* enhance the simplifier                                                  *)
+(* ------------------------------------------------------------------------*)
+
+val dhd2 = prove_goal Dlist.thy "xl~=UU ==> dhd[dcons[x][xl]]=x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dtl2 = prove_goal Dlist.thy "x~=UU ==> dtl[dcons[x][xl]]=xl"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_rews = dhd2 :: dtl2 :: dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Properties dlist_take                                                   *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goalw Dlist.thy [dlist_take_def] "dlist_take(n)[UU]=UU"
+ (fn prems =>
+	[
+	(res_inst_tac [("n","n")] natE 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_take = [temp];
+
+val temp = prove_goalw Dlist.thy [dlist_take_def] "dlist_take(0)[xs]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac iterate_ss 1)
+	]);
+
+val dlist_take = temp::dlist_take;
+
+val temp = prove_goalw Dlist.thy [dlist_take_def]
+	"dlist_take(Suc(n))[dnil]=dnil"
+ (fn prems =>
+	[
+	(asm_simp_tac iterate_ss 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_take = temp::dlist_take;
+
+val temp = prove_goalw Dlist.thy [dlist_take_def]
+  "dlist_take(Suc(n))[dcons[x][xl]]=dcons[x][dlist_take(n)[xl]]"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("n","n")] natE 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_take = temp::dlist_take;
+
+val dlist_rews = dlist_take @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* take lemma for dlists                                                  *)
+(* ------------------------------------------------------------------------*)
+
+fun prover reach defs thm  = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(res_inst_tac [("t","l1")] (reach RS subst) 1),
+	(res_inst_tac [("t","l2")] (reach RS subst) 1),
+	(rtac (fix_def2 RS ssubst) 1),
+	(rtac (contlub_cfun_fun RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac (contlub_cfun_fun RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac lub_equal 1),
+	(rtac (is_chain_iterate RS ch2ch_fappL) 1),
+	(rtac (is_chain_iterate RS ch2ch_fappL) 1),
+	(rtac allI 1),
+	(resolve_tac prems 1)
+	]);
+
+val dlist_take_lemma = prover dlist_reach  [dlist_take_def]
+	"(!!n.dlist_take(n)[l1]=dlist_take(n)[l2]) ==> l1=l2";
+
+
+(* ------------------------------------------------------------------------*)
+(* Co -induction for dlists                                               *)
+(* ------------------------------------------------------------------------*)
+
+val dlist_coind_lemma = prove_goalw Dlist.thy [dlist_bisim_def] 
+"dlist_bisim(R) ==> ! p q.R(p,q) --> dlist_take(n)[p]=dlist_take(n)[q]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(strip_tac 1),
+	((etac allE 1) THEN (etac allE 1) THEN (etac (mp RS disjE) 1)),
+	(atac 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(etac disjE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(etac exE 1),
+	(etac exE 1),
+	(etac exE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(REPEAT (etac conjE 1)),
+	(rtac cfun_arg_cong 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val dlist_coind = prove_goal Dlist.thy "[|dlist_bisim(R);R(p,q)|] ==> p = q"
+ (fn prems =>
+	[
+	(rtac dlist_take_lemma 1),
+	(rtac (dlist_coind_lemma RS spec RS spec RS mp) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+(* ------------------------------------------------------------------------*)
+(* structural induction                                                    *)
+(* ------------------------------------------------------------------------*)
+
+val dlist_finite_ind = prove_goal Dlist.thy
+"[|P(UU);P(dnil);\
+\  !! x l1.[|x~=UU;l1~=UU;P(l1)|] ==> P(dcons[x][l1])\
+\  |] ==> !l.P(dlist_take(n)[l])"
+ (fn prems =>
+	[
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(rtac allI 1),
+	(res_inst_tac [("l","l")] dlistE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","dlist_take(n1)[xl]=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(atac 1),
+	(atac 1),
+	(etac spec 1)
+	]);
+
+val dlist_all_finite_lemma1 = prove_goal Dlist.thy
+"!l.dlist_take(n)[l]=UU |dlist_take(n)[l]=l"
+ (fn prems =>
+	[
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(rtac allI 1),
+	(res_inst_tac [("l","l")] dlistE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(eres_inst_tac [("x","xl")] allE 1),
+	(etac disjE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_all_finite_lemma2 = prove_goal Dlist.thy "? n.dlist_take(n)[l]=l"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","l=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(subgoal_tac "(!n.dlist_take(n)[l]=UU) |(? n.dlist_take(n)[l]=l)" 1),
+	(etac disjE 1),
+	(eres_inst_tac [("P","l=UU")] notE 1),
+	(rtac dlist_take_lemma 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(atac 1),
+	(subgoal_tac "!n.!l.dlist_take(n)[l]=UU |dlist_take(n)[l]=l" 1),
+	(fast_tac HOL_cs 1),
+	(rtac allI 1),
+	(rtac dlist_all_finite_lemma1 1)
+	]);
+
+val dlist_all_finite= prove_goalw Dlist.thy [dlist_finite_def] "dlist_finite(l)"
+ (fn prems =>
+	[
+	(rtac  dlist_all_finite_lemma2 1)
+	]);
+
+val dlist_ind = prove_goal Dlist.thy
+"[|P(UU);P(dnil);\
+\  !! x l1.[|x~=UU;l1~=UU;P(l1)|] ==> P(dcons[x][l1])|] ==> P(l)"
+ (fn prems =>
+	[
+	(rtac (dlist_all_finite_lemma2 RS exE) 1),
+	(etac subst 1),
+	(rtac (dlist_finite_ind RS spec) 1),
+	(REPEAT (resolve_tac prems 1)),
+	(REPEAT (atac 1))
+	]);
+
+
+
+
diff -r 5ef75ff3baeb -r 3a0485439396 src/HOLCF/Dlist.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Dlist.thy	Thu Mar 24 13:43:45 1994 +0100
@@ -0,0 +1,111 @@
+(*  Title: 	HOLCF/dlist.thy
+
+    Author: 	Franz Regensburger
+    ID:         $ $
+    Copyright   1994 Technische Universitaet Muenchen
+
+Theory for lists
+*)
+
+Dlist = Stream2 +
+
+types dlist 1
+
+(* ----------------------------------------------------------------------- *)
+(* arity axiom is validated by semantic reasoning                          *)
+(* partial ordering is implicit in the isomorphism axioms and their cont.  *)
+
+arities dlist::(pcpo)pcpo
+
+consts
+
+(* ----------------------------------------------------------------------- *)
+(* essential constants                                                     *)
+
+dlist_rep	:: "('a dlist) -> (one ++ 'a ** 'a dlist)"
+dlist_abs	:: "(one ++ 'a ** 'a dlist) -> ('a dlist)"
+
+(* ----------------------------------------------------------------------- *)
+(* abstract constants and auxiliary constants                              *)
+
+dlist_copy	:: "('a dlist -> 'a dlist) ->'a dlist -> 'a dlist"
+
+dnil            :: "'a dlist"
+dcons		:: "'a -> 'a dlist -> 'a dlist"
+dlist_when	:: " 'b -> ('a -> 'a dlist -> 'b) -> 'a dlist -> 'b"
+is_dnil    	:: "'a dlist -> tr"
+is_dcons	:: "'a dlist -> tr"
+dhd		:: "'a dlist -> 'a"
+dtl		:: "'a dlist -> 'a dlist"
+dlist_take	:: "nat => 'a dlist -> 'a dlist"
+dlist_finite	:: "'a dlist => bool"
+dlist_bisim	:: "('a dlist => 'a dlist => bool) => bool"
+
+rules
+
+(* ----------------------------------------------------------------------- *)
+(* axiomatization of recursive type 'a dlist                               *)
+(* ----------------------------------------------------------------------- *)
+(* ('a dlist,dlist_abs) is the initial F-algebra where                     *)
+(* F is the locally continuous functor determined by domain equation       *)
+(* X = one ++ 'a ** X                                                      *)
+(* ----------------------------------------------------------------------- *)
+(* dlist_abs is an isomorphism with inverse dlist_rep                      *)
+(* identity is the least endomorphism on 'a dlist                          *)
+
+dlist_abs_iso	"dlist_rep[dlist_abs[x]] = x"
+dlist_rep_iso	"dlist_abs[dlist_rep[x]] = x"
+dlist_copy_def	"dlist_copy == (LAM f. dlist_abs oo \
+\ 		(when[sinl][sinr oo (ssplit[LAM x y. x ## f[y]])])\
+\                                oo dlist_rep)"
+dlist_reach	"(fix[dlist_copy])[x]=x"
+
+(* ----------------------------------------------------------------------- *)
+(* properties of additional constants                                      *)
+(* ----------------------------------------------------------------------- *)
+(* constructors                                                            *)
+
+dnil_def	"dnil  == dlist_abs[sinl[one]]"
+dcons_def	"dcons == (LAM x l. dlist_abs[sinr[x##l]])"
+
+(* ----------------------------------------------------------------------- *)
+(* discriminator functional                                                *)
+
+dlist_when_def 
+"dlist_when == (LAM f1 f2 l.\
+\   when[LAM x.f1][ssplit[LAM x l.f2[x][l]]][dlist_rep[l]])"
+
+(* ----------------------------------------------------------------------- *)
+(* discriminators and selectors                                            *)
+
+is_dnil_def	"is_dnil  == dlist_when[TT][LAM x l.FF]"
+is_dcons_def	"is_dcons == dlist_when[FF][LAM x l.TT]"
+dhd_def		"dhd == dlist_when[UU][LAM x l.x]"
+dtl_def		"dtl == dlist_when[UU][LAM x l.l]"
+
+(* ----------------------------------------------------------------------- *)
+(* the taker for dlists                                                   *)
+
+dlist_take_def "dlist_take == (%n.iterate(n,dlist_copy,UU))"
+
+(* ----------------------------------------------------------------------- *)
+
+dlist_finite_def	"dlist_finite == (%s.? n.dlist_take(n)[s]=s)"
+
+(* ----------------------------------------------------------------------- *)
+(* definition of bisimulation is determined by domain equation             *)
+(* simplification and rewriting for abstract constants yields def below    *)
+
+dlist_bisim_def "dlist_bisim ==\
+\ ( %R.!l1 l2.\
+\ 	R(l1,l2) -->\
+\  ((l1=UU & l2=UU) |\
+\   (l1=dnil & l2=dnil) |\
+\   (? x l11 l21. x~=UU & l11~=UU & l21~=UU & \
+\               l1=dcons[x][l11] & l2 = dcons[x][l21] & R(l11,l21))))"
+
+end
+
+
+
+
diff -r 5ef75ff3baeb -r 3a0485439396 src/HOLCF/Porder0.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/Porder0.thy	Thu Mar 24 13:43:45 1994 +0100
@@ -0,0 +1,42 @@
+(*  Title: 	HOLCF/porder0.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Definition of class porder (partial order)
+
+The prototype theory for this class is void.thy 
+
+*)
+
+Porder0 = Void +
+
+(* Introduction of new class. The witness is type void. *)
+
+classes po < term
+
+(* default type is still term ! *)
+(* void is the prototype in po *)
+
+arities void :: po
+
+consts	"<<"	::	"['a,'a::po] => bool"	(infixl 55)
+
+rules
+
+(* class axioms: justification is theory Void *)
+
+refl_less	"x << x"	
+				(* witness refl_less_void    *)
+
+antisym_less	"[|x<<y ; y<<x |] ==> x = y"	
+				(* witness antisym_less_void *)
+
+trans_less	"[|x<<y ; y<<z |] ==> x<<z"
+				(* witness trans_less_void   *)
+
+(* instance of << for the prototype void *)
+
+inst_void_po	"(op <<)::[void,void]=>bool = less_void"
+
+end 
diff -r 5ef75ff3baeb -r 3a0485439396 src/HOLCF/dlist.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/dlist.ML	Thu Mar 24 13:43:45 1994 +0100
@@ -0,0 +1,563 @@
+(*  Title: 	HOLCF/dlist.ML
+    Author: 	Franz Regensburger
+    ID:         $ $
+    Copyright   1994 Technische Universitaet Muenchen
+
+Lemmas for dlist.thy
+*)
+
+open Dlist;
+
+(* ------------------------------------------------------------------------*)
+(* The isomorphisms dlist_rep_iso and dlist_abs_iso are strict             *)
+(* ------------------------------------------------------------------------*)
+
+val dlist_iso_strict= dlist_rep_iso RS (dlist_abs_iso RS 
+	(allI  RSN (2,allI RS iso_strict)));
+
+val dlist_rews = [dlist_iso_strict RS conjunct1,
+		dlist_iso_strict RS conjunct2];
+
+(* ------------------------------------------------------------------------*)
+(* Properties of dlist_copy                                                *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goalw Dlist.thy  [dlist_copy_def] "dlist_copy[f][UU]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1)
+	]);
+
+val dlist_copy = [temp];
+
+
+val temp = prove_goalw Dlist.thy  [dlist_copy_def,dnil_def] 
+    "dlist_copy[f][dnil]=dnil"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1)
+	]);
+
+val dlist_copy = temp :: dlist_copy;
+
+
+val temp = prove_goalw Dlist.thy  [dlist_copy_def,dcons_def] 
+	"xl~=UU ==> dlist_copy[f][dcons[x][xl]]= dcons[x][f[xl]]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps 
+		(dlist_rews @ [dlist_abs_iso,dlist_rep_iso])) 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac HOLCF_ss  1),
+	(asm_simp_tac (HOLCF_ss addsimps [defined_spair]) 1)
+	]);
+
+val dlist_copy = temp :: dlist_copy;
+
+val dlist_rews =  dlist_copy @ dlist_rews; 
+
+(* ------------------------------------------------------------------------*)
+(* Exhaustion and elimination for dlists                                   *)
+(* ------------------------------------------------------------------------*)
+
+val Exh_dlist = prove_goalw Dlist.thy [dcons_def,dnil_def]
+	"l = UU | l = dnil | (? x xl. x~=UU &xl~=UU & l = dcons[x][xl])"
+ (fn prems =>
+	[
+	(simp_tac HOLCF_ss  1),
+	(rtac (dlist_rep_iso RS subst) 1),
+	(res_inst_tac [("p","dlist_rep[l]")] ssumE 1),
+	(rtac disjI1 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(rtac disjI2 1),
+	(rtac disjI1 1),
+	(res_inst_tac [("p","x")] oneE 1),
+	(contr_tac 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(rtac disjI2 1),
+	(rtac disjI2 1),
+	(res_inst_tac [("p","y")] sprodE 1),
+	(contr_tac 1),
+	(rtac exI 1),
+	(rtac exI 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+
+val dlistE = prove_goal Dlist.thy 
+"[| l=UU ==> Q; l=dnil ==> Q;!!x xl.[|l=dcons[x][xl];x~=UU;xl~=UU|]==>Q|]==>Q"
+ (fn prems =>
+	[
+	(rtac (Exh_dlist RS disjE) 1),
+	(eresolve_tac prems 1),
+	(etac disjE 1),
+	(eresolve_tac prems 1),
+	(etac exE 1),
+	(etac exE 1),
+	(resolve_tac prems 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+(* ------------------------------------------------------------------------*)
+(* Properties of dlist_when                                                *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goalw  Dlist.thy  [dlist_when_def] "dlist_when[f1][f2][UU]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps [dlist_iso_strict]) 1)
+	]);
+
+val dlist_when = [temp];
+
+val temp = prove_goalw  Dlist.thy [dlist_when_def,dnil_def]
+ "dlist_when[f1][f2][dnil]= f1"
+ (fn prems =>
+	[
+	(asm_simp_tac (HOLCF_ss addsimps [dlist_abs_iso]) 1)
+	]);
+
+val dlist_when = temp::dlist_when;
+
+val temp = prove_goalw  Dlist.thy [dlist_when_def,dcons_def]
+ "[|x~=UU;xl~=UU|] ==> dlist_when[f1][f2][dcons[x][xl]]= f2[x][xl]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps [dlist_abs_iso,defined_spair]) 1)
+	]);
+
+val dlist_when = temp::dlist_when;
+
+val dlist_rews = dlist_when @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Rewrites for  discriminators and  selectors                             *)
+(* ------------------------------------------------------------------------*)
+
+fun prover defs thm = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_discsel = [
+	prover [is_dnil_def] "is_dnil[UU]=UU",
+	prover [is_dcons_def] "is_dcons[UU]=UU",
+	prover [dhd_def] "dhd[UU]=UU",
+	prover [dtl_def] "dtl[UU]=UU"
+	];
+
+fun prover defs thm = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_discsel = [
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "is_dnil[dnil]=TT",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> is_dnil[dcons[x][xl]]=FF",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "is_dcons[dnil]=FF",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> is_dcons[dcons[x][xl]]=TT",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "dhd[dnil]=UU",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> dhd[dcons[x][xl]]=x",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "dtl[dnil]=UU",
+prover [is_dnil_def,is_dcons_def,dhd_def,dtl_def]
+  "[|x~=UU;xl~=UU|] ==> dtl[dcons[x][xl]]=xl"] @ dlist_discsel;
+
+val dlist_rews = dlist_discsel @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Definedness and strictness                                              *)
+(* ------------------------------------------------------------------------*)
+
+fun prover contr thm = prove_goal Dlist.thy thm
+ (fn prems =>
+	[
+	(res_inst_tac [("P1",contr)] classical3 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(dtac sym 1),
+	(asm_simp_tac HOLCF_ss  1),
+	(simp_tac (HOLCF_ss addsimps (prems @ dlist_rews)) 1)
+	]);
+
+
+val dlist_constrdef = [
+prover "is_dnil[UU] ~= UU" "dnil~=UU",
+prover "is_dcons[UU] ~= UU" "[|x~=UU;xl~=UU|] ==> dcons[x][xl]~=UU"
+ ];
+
+
+fun prover defs thm = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_constrdef = [
+	prover [dcons_def] "dcons[UU][xl]=UU",
+	prover [dcons_def] "dcons[x][UU]=UU"
+	] @ dlist_constrdef;
+
+val dlist_rews = dlist_constrdef @ dlist_rews;
+
+
+(* ------------------------------------------------------------------------*)
+(* Distinctness wrt. << and =                                              *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goal Dlist.thy  "~dnil << dcons[x][xl]"
+ (fn prems =>
+	[
+	(res_inst_tac [("P1","TT << FF")] classical3 1),
+	(resolve_tac dist_less_tr 1),
+	(dres_inst_tac [("fo5","is_dnil")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_dist_less = [temp];
+
+val temp = prove_goal Dlist.thy  "[|x~=UU;xl~=UU|]==>~dcons[x][xl] << dnil"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("P1","TT << FF")] classical3 1),
+	(resolve_tac dist_less_tr 1),
+	(dres_inst_tac [("fo5","is_dcons")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_dist_less = temp::dlist_dist_less;
+
+val temp = prove_goal Dlist.thy  "dnil ~= dcons[x][xl]"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("P1","TT = FF")] classical3 1),
+	(resolve_tac dist_eq_tr 1),
+	(dres_inst_tac [("f","is_dnil")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_dist_eq = [temp,temp RS not_sym];
+
+val dlist_rews = dlist_dist_less @ dlist_dist_eq @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Invertibility                                                           *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goal Dlist.thy "[|x1~=UU; y1~=UU;x2~=UU; y2~=UU;\
+\ dcons[x1][x2] << dcons[y1][y2]|] ==> x1<< y1 & x2 << y2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac conjI 1),
+	(dres_inst_tac [("fo5","dlist_when[UU][LAM x l.x]")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(dres_inst_tac [("fo5","dlist_when[UU][LAM x l.l]")] monofun_cfun_arg 1),
+	(etac box_less 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1)
+	]);
+
+val dlist_invert =[temp];
+
+(* ------------------------------------------------------------------------*)
+(* Injectivity                                                             *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goal Dlist.thy "[|x1~=UU; y1~=UU;x2~=UU; y2~=UU;\
+\ dcons[x1][x2] = dcons[y1][y2]|] ==> x1= y1 & x2 = y2"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac conjI 1),
+	(dres_inst_tac [("f","dlist_when[UU][LAM x l.x]")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(dres_inst_tac [("f","dlist_when[UU][LAM x l.l]")] cfun_arg_cong 1),
+	(etac box_equals 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_when) 1)
+	]);
+
+val dlist_inject = [temp];
+ 
+
+(* ------------------------------------------------------------------------*)
+(* definedness for  discriminators and  selectors                          *)
+(* ------------------------------------------------------------------------*)
+
+fun prover thm = prove_goal Dlist.thy thm
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(rtac dlistE 1),
+	(contr_tac 1),
+	(REPEAT (asm_simp_tac (HOLCF_ss addsimps dlist_discsel) 1))
+	]);
+
+val dlist_discsel_def = 
+	[
+	prover "l~=UU ==> is_dnil[l]~=UU", 
+	prover "l~=UU ==> is_dcons[l]~=UU" 
+	];
+
+val dlist_rews = dlist_discsel_def @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* enhance the simplifier                                                  *)
+(* ------------------------------------------------------------------------*)
+
+val dhd2 = prove_goal Dlist.thy "xl~=UU ==> dhd[dcons[x][xl]]=x"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dtl2 = prove_goal Dlist.thy "x~=UU ==> dtl[dcons[x][xl]]=xl"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_rews = dhd2 :: dtl2 :: dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* Properties dlist_take                                                   *)
+(* ------------------------------------------------------------------------*)
+
+val temp = prove_goalw Dlist.thy [dlist_take_def] "dlist_take(n)[UU]=UU"
+ (fn prems =>
+	[
+	(res_inst_tac [("n","n")] natE 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac iterate_ss 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_take = [temp];
+
+val temp = prove_goalw Dlist.thy [dlist_take_def] "dlist_take(0)[xs]=UU"
+ (fn prems =>
+	[
+	(asm_simp_tac iterate_ss 1)
+	]);
+
+val dlist_take = temp::dlist_take;
+
+val temp = prove_goalw Dlist.thy [dlist_take_def]
+	"dlist_take(Suc(n))[dnil]=dnil"
+ (fn prems =>
+	[
+	(asm_simp_tac iterate_ss 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_take = temp::dlist_take;
+
+val temp = prove_goalw Dlist.thy [dlist_take_def]
+  "dlist_take(Suc(n))[dcons[x][xl]]=dcons[x][dlist_take(n)[xl]]"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","x=UU")] classical2 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","xl=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("n","n")] natE 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac iterate_ss 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_take = temp::dlist_take;
+
+val dlist_rews = dlist_take @ dlist_rews;
+
+(* ------------------------------------------------------------------------*)
+(* take lemma for dlists                                                  *)
+(* ------------------------------------------------------------------------*)
+
+fun prover reach defs thm  = prove_goalw Dlist.thy defs thm
+ (fn prems =>
+	[
+	(res_inst_tac [("t","l1")] (reach RS subst) 1),
+	(res_inst_tac [("t","l2")] (reach RS subst) 1),
+	(rtac (fix_def2 RS ssubst) 1),
+	(rtac (contlub_cfun_fun RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac (contlub_cfun_fun RS ssubst) 1),
+	(rtac is_chain_iterate 1),
+	(rtac lub_equal 1),
+	(rtac (is_chain_iterate RS ch2ch_fappL) 1),
+	(rtac (is_chain_iterate RS ch2ch_fappL) 1),
+	(rtac allI 1),
+	(resolve_tac prems 1)
+	]);
+
+val dlist_take_lemma = prover dlist_reach  [dlist_take_def]
+	"(!!n.dlist_take(n)[l1]=dlist_take(n)[l2]) ==> l1=l2";
+
+
+(* ------------------------------------------------------------------------*)
+(* Co -induction for dlists                                               *)
+(* ------------------------------------------------------------------------*)
+
+val dlist_coind_lemma = prove_goalw Dlist.thy [dlist_bisim_def] 
+"dlist_bisim(R) ==> ! p q.R(p,q) --> dlist_take(n)[p]=dlist_take(n)[q]"
+ (fn prems =>
+	[
+	(cut_facts_tac prems 1),
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(strip_tac 1),
+	((etac allE 1) THEN (etac allE 1) THEN (etac (mp RS disjE) 1)),
+	(atac 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(etac disjE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(etac exE 1),
+	(etac exE 1),
+	(etac exE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(REPEAT (etac conjE 1)),
+	(rtac cfun_arg_cong 1),
+	(fast_tac HOL_cs 1)
+	]);
+
+val dlist_coind = prove_goal Dlist.thy "[|dlist_bisim(R);R(p,q)|] ==> p = q"
+ (fn prems =>
+	[
+	(rtac dlist_take_lemma 1),
+	(rtac (dlist_coind_lemma RS spec RS spec RS mp) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1)
+	]);
+
+(* ------------------------------------------------------------------------*)
+(* structural induction                                                    *)
+(* ------------------------------------------------------------------------*)
+
+val dlist_finite_ind = prove_goal Dlist.thy
+"[|P(UU);P(dnil);\
+\  !! x l1.[|x~=UU;l1~=UU;P(l1)|] ==> P(dcons[x][l1])\
+\  |] ==> !l.P(dlist_take(n)[l])"
+ (fn prems =>
+	[
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(rtac allI 1),
+	(res_inst_tac [("l","l")] dlistE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(res_inst_tac [("Q","dlist_take(n1)[xl]=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(resolve_tac prems 1),
+	(resolve_tac prems 1),
+	(atac 1),
+	(atac 1),
+	(etac spec 1)
+	]);
+
+val dlist_all_finite_lemma1 = prove_goal Dlist.thy
+"!l.dlist_take(n)[l]=UU |dlist_take(n)[l]=l"
+ (fn prems =>
+	[
+	(nat_ind_tac "n" 1),
+	(simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(rtac allI 1),
+	(res_inst_tac [("l","l")] dlistE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(eres_inst_tac [("x","xl")] allE 1),
+	(etac disjE 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1)
+	]);
+
+val dlist_all_finite_lemma2 = prove_goal Dlist.thy "? n.dlist_take(n)[l]=l"
+ (fn prems =>
+	[
+	(res_inst_tac [("Q","l=UU")] classical2 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(subgoal_tac "(!n.dlist_take(n)[l]=UU) |(? n.dlist_take(n)[l]=l)" 1),
+	(etac disjE 1),
+	(eres_inst_tac [("P","l=UU")] notE 1),
+	(rtac dlist_take_lemma 1),
+	(asm_simp_tac (HOLCF_ss addsimps dlist_rews) 1),
+	(atac 1),
+	(subgoal_tac "!n.!l.dlist_take(n)[l]=UU |dlist_take(n)[l]=l" 1),
+	(fast_tac HOL_cs 1),
+	(rtac allI 1),
+	(rtac dlist_all_finite_lemma1 1)
+	]);
+
+val dlist_all_finite= prove_goalw Dlist.thy [dlist_finite_def] "dlist_finite(l)"
+ (fn prems =>
+	[
+	(rtac  dlist_all_finite_lemma2 1)
+	]);
+
+val dlist_ind = prove_goal Dlist.thy
+"[|P(UU);P(dnil);\
+\  !! x l1.[|x~=UU;l1~=UU;P(l1)|] ==> P(dcons[x][l1])|] ==> P(l)"
+ (fn prems =>
+	[
+	(rtac (dlist_all_finite_lemma2 RS exE) 1),
+	(etac subst 1),
+	(rtac (dlist_finite_ind RS spec) 1),
+	(REPEAT (resolve_tac prems 1)),
+	(REPEAT (atac 1))
+	]);
+
+
+
+
diff -r 5ef75ff3baeb -r 3a0485439396 src/HOLCF/dlist.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/dlist.thy	Thu Mar 24 13:43:45 1994 +0100
@@ -0,0 +1,111 @@
+(*  Title: 	HOLCF/dlist.thy
+
+    Author: 	Franz Regensburger
+    ID:         $ $
+    Copyright   1994 Technische Universitaet Muenchen
+
+Theory for lists
+*)
+
+Dlist = Stream2 +
+
+types dlist 1
+
+(* ----------------------------------------------------------------------- *)
+(* arity axiom is validated by semantic reasoning                          *)
+(* partial ordering is implicit in the isomorphism axioms and their cont.  *)
+
+arities dlist::(pcpo)pcpo
+
+consts
+
+(* ----------------------------------------------------------------------- *)
+(* essential constants                                                     *)
+
+dlist_rep	:: "('a dlist) -> (one ++ 'a ** 'a dlist)"
+dlist_abs	:: "(one ++ 'a ** 'a dlist) -> ('a dlist)"
+
+(* ----------------------------------------------------------------------- *)
+(* abstract constants and auxiliary constants                              *)
+
+dlist_copy	:: "('a dlist -> 'a dlist) ->'a dlist -> 'a dlist"
+
+dnil            :: "'a dlist"
+dcons		:: "'a -> 'a dlist -> 'a dlist"
+dlist_when	:: " 'b -> ('a -> 'a dlist -> 'b) -> 'a dlist -> 'b"
+is_dnil    	:: "'a dlist -> tr"
+is_dcons	:: "'a dlist -> tr"
+dhd		:: "'a dlist -> 'a"
+dtl		:: "'a dlist -> 'a dlist"
+dlist_take	:: "nat => 'a dlist -> 'a dlist"
+dlist_finite	:: "'a dlist => bool"
+dlist_bisim	:: "('a dlist => 'a dlist => bool) => bool"
+
+rules
+
+(* ----------------------------------------------------------------------- *)
+(* axiomatization of recursive type 'a dlist                               *)
+(* ----------------------------------------------------------------------- *)
+(* ('a dlist,dlist_abs) is the initial F-algebra where                     *)
+(* F is the locally continuous functor determined by domain equation       *)
+(* X = one ++ 'a ** X                                                      *)
+(* ----------------------------------------------------------------------- *)
+(* dlist_abs is an isomorphism with inverse dlist_rep                      *)
+(* identity is the least endomorphism on 'a dlist                          *)
+
+dlist_abs_iso	"dlist_rep[dlist_abs[x]] = x"
+dlist_rep_iso	"dlist_abs[dlist_rep[x]] = x"
+dlist_copy_def	"dlist_copy == (LAM f. dlist_abs oo \
+\ 		(when[sinl][sinr oo (ssplit[LAM x y. x ## f[y]])])\
+\                                oo dlist_rep)"
+dlist_reach	"(fix[dlist_copy])[x]=x"
+
+(* ----------------------------------------------------------------------- *)
+(* properties of additional constants                                      *)
+(* ----------------------------------------------------------------------- *)
+(* constructors                                                            *)
+
+dnil_def	"dnil  == dlist_abs[sinl[one]]"
+dcons_def	"dcons == (LAM x l. dlist_abs[sinr[x##l]])"
+
+(* ----------------------------------------------------------------------- *)
+(* discriminator functional                                                *)
+
+dlist_when_def 
+"dlist_when == (LAM f1 f2 l.\
+\   when[LAM x.f1][ssplit[LAM x l.f2[x][l]]][dlist_rep[l]])"
+
+(* ----------------------------------------------------------------------- *)
+(* discriminators and selectors                                            *)
+
+is_dnil_def	"is_dnil  == dlist_when[TT][LAM x l.FF]"
+is_dcons_def	"is_dcons == dlist_when[FF][LAM x l.TT]"
+dhd_def		"dhd == dlist_when[UU][LAM x l.x]"
+dtl_def		"dtl == dlist_when[UU][LAM x l.l]"
+
+(* ----------------------------------------------------------------------- *)
+(* the taker for dlists                                                   *)
+
+dlist_take_def "dlist_take == (%n.iterate(n,dlist_copy,UU))"
+
+(* ----------------------------------------------------------------------- *)
+
+dlist_finite_def	"dlist_finite == (%s.? n.dlist_take(n)[s]=s)"
+
+(* ----------------------------------------------------------------------- *)
+(* definition of bisimulation is determined by domain equation             *)
+(* simplification and rewriting for abstract constants yields def below    *)
+
+dlist_bisim_def "dlist_bisim ==\
+\ ( %R.!l1 l2.\
+\ 	R(l1,l2) -->\
+\  ((l1=UU & l2=UU) |\
+\   (l1=dnil & l2=dnil) |\
+\   (? x l11 l21. x~=UU & l11~=UU & l21~=UU & \
+\               l1=dcons[x][l11] & l2 = dcons[x][l21] & R(l11,l21))))"
+
+end
+
+
+
+
diff -r 5ef75ff3baeb -r 3a0485439396 src/HOLCF/porder0.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOLCF/porder0.thy	Thu Mar 24 13:43:45 1994 +0100
@@ -0,0 +1,42 @@
+(*  Title: 	HOLCF/porder0.thy
+    ID:         $Id$
+    Author: 	Franz Regensburger
+    Copyright   1993 Technische Universitaet Muenchen
+
+Definition of class porder (partial order)
+
+The prototype theory for this class is void.thy 
+
+*)
+
+Porder0 = Void +
+
+(* Introduction of new class. The witness is type void. *)
+
+classes po < term
+
+(* default type is still term ! *)
+(* void is the prototype in po *)
+
+arities void :: po
+
+consts	"<<"	::	"['a,'a::po] => bool"	(infixl 55)
+
+rules
+
+(* class axioms: justification is theory Void *)
+
+refl_less	"x << x"	
+				(* witness refl_less_void    *)
+
+antisym_less	"[|x<<y ; y<<x |] ==> x = y"	
+				(* witness antisym_less_void *)
+
+trans_less	"[|x<<y ; y<<z |] ==> x<<z"
+				(* witness trans_less_void   *)
+
+(* instance of << for the prototype void *)
+
+inst_void_po	"(op <<)::[void,void]=>bool = less_void"
+
+end