src/HOLCF/ex/Coind.ML

 (* ------------------------------------------------------------------------- *)
 (* expand fixed point properties                                             *)
 (* ------------------------------------------------------------------------- *)
 
 
-val nats_def2 = fix_prover Coind.thy nats_def 
-	"nats = scons[dzero][smap[dsucc][nats]]";
+val nats_def2 = fix_prover2 Coind.thy nats_def 
+	"nats = scons`dzero`(smap`dsucc`nats)";
 
-val from_def2 = fix_prover Coind.thy from_def 
-	"from = (LAM n.scons[n][from[dsucc[n]]])";
+val from_def2 = fix_prover2 Coind.thy from_def 
+	"from = (LAM n.scons`n`(from`(dsucc`n)))";
 
 
 
 (* ------------------------------------------------------------------------- *)
 (* recursive  properties                                                     *)
 (* ------------------------------------------------------------------------- *)
 
 
-val from = prove_goal Coind.thy "from[n] = scons[n][from[dsucc[n]]]"
+val from = prove_goal Coind.thy "from`n = scons`n`(from`(dsucc`n))"
  (fn prems =>
 	[
 	(rtac trans 1),
 	(rtac (from_def2 RS ssubst) 1),
 	(simp_tac HOLCF_ss  1),
 	(rtac refl 1)
 	]);
 
 
-val from1 = prove_goal Coind.thy "from[UU] = UU"
+val from1 = prove_goal Coind.thy "from`UU = UU"
  (fn prems =>
 	[
 	(rtac trans 1),
 	(rtac (from RS ssubst) 1),
 	(resolve_tac  stream_constrdef 1),

 	[iterator1, iterator2, iterator3, smap1, smap2,from1];
 
 
 (* ------------------------------------------------------------------------- *)
 (* the example                                                               *)
-(* prove:        nats = from[dzero]                                          *)
+(* prove:        nats = from`dzero                                           *)
 (* ------------------------------------------------------------------------- *)
 
 
-val coind_lemma1 = prove_goal Coind.thy "iterator[n][smap[dsucc]][nats] =\
-\		 scons[n][iterator[dsucc[n]][smap[dsucc]][nats]]"
+val coind_lemma1 = prove_goal Coind.thy "iterator`n`(smap`dsucc)`nats =\
+\		 scons`n`(iterator`(dsucc`n)`(smap`dsucc)`nats)"
  (fn prems =>
 	[
 	(res_inst_tac [("s","n")] dnat_ind 1),
 	(simp_tac (HOLCF_ss addsimps (coind_rews @ stream_rews)) 1),
 	(simp_tac (HOLCF_ss addsimps (coind_rews @ stream_rews)) 1),

 	(rtac cfun_arg_cong 1),
 	(asm_simp_tac (HOLCF_ss addsimps ([iterator3 RS sym] @ dnat_rews)) 1)
 	]);
 
 
-val nats_eq_from = prove_goal Coind.thy "nats = from[dzero]"
+val nats_eq_from = prove_goal Coind.thy "nats = from`dzero"
  (fn prems =>
 	[
 	(res_inst_tac [("R",
-"% p q.? n. p = iterator[n][smap[dsucc]][nats] & q = from[n]")] stream_coind 1),
+"% p q.? n. p = iterator`n`(smap`dsucc)`nats & q = from`n")] stream_coind 1),
 	(res_inst_tac [("x","dzero")] exI 2),
 	(asm_simp_tac (HOLCF_ss addsimps coind_rews) 2),
 	(rewrite_goals_tac [stream_bisim_def]),
 	(strip_tac 1),
 	(etac exE 1),

 	(asm_simp_tac (HOLCF_ss addsimps coind_rews) 1),
 	(rtac disjI2 1),
 	(etac conjE 1),
 	(hyp_subst_tac 1),
 	(res_inst_tac [("x","n")] exI 1),
-	(res_inst_tac [("x","iterator[dsucc[n]][smap[dsucc]][nats]")] exI 1),
-	(res_inst_tac [("x","from[dsucc[n]]")] exI 1),
+	(res_inst_tac [("x","iterator`(dsucc`n)`(smap`dsucc)`nats")] exI 1),
+	(res_inst_tac [("x","from`(dsucc`n)")] exI 1),
 	(etac conjI 1),
 	(rtac conjI 1),
 	(rtac coind_lemma1 1),
 	(rtac conjI 1),
 	(rtac from 1),
-	(res_inst_tac [("x","dsucc[n]")] exI 1),
+	(res_inst_tac [("x","dsucc`n")] exI 1),
 	(fast_tac HOL_cs 1)
 	]);
 
 (* another proof using stream_coind_lemma2 *)
 
-val nats_eq_from = prove_goal Coind.thy "nats = from[dzero]"
+val nats_eq_from = prove_goal Coind.thy "nats = from`dzero"
  (fn prems =>
 	[
 	(res_inst_tac [("R","% p q.? n. p = \
-\	iterator[n][smap[dsucc]][nats] & q = from[n]")] stream_coind 1),
+\	iterator`n`(smap`dsucc)`nats & q = from`n")] stream_coind 1),
 	(rtac stream_coind_lemma2 1),
 	(strip_tac 1),
 	(etac exE 1),
 	(res_inst_tac [("Q","n=UU")] classical2 1),
 	(asm_simp_tac (HOLCF_ss addsimps coind_rews) 1),

 	(hyp_subst_tac 1),
 	(rtac conjI 1),
 	(rtac (coind_lemma1 RS ssubst) 1),
 	(rtac (from RS ssubst) 1),
 	(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1),
-	(res_inst_tac [("x","dsucc[n]")] exI 1),
+	(res_inst_tac [("x","dsucc`n")] exI 1),
 	(rtac conjI 1),
 	(rtac trans 1),
 	(rtac (coind_lemma1 RS ssubst) 1),
 	(asm_simp_tac (HOLCF_ss addsimps stream_rews) 1),
 	(rtac refl 1),