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Nominal/Ex/CPS/CPS3_DanvyFilinski.thy
changeset 2998 f0fab367453a
parent 2984 1b39ba5db2c1
child 3089 9bcf02a6eea9 
--- a/Nominal/Ex/CPS/CPS3_DanvyFilinski.thy	Fri Aug 19 11:07:17 2011 +0900
+++ b/Nominal/Ex/CPS/CPS3_DanvyFilinski.thy	Fri Aug 19 12:49:38 2011 +0900
@@ -7,12 +7,12 @@
   CPS2 :: "lt \<Rightarrow> lt \<Rightarrow> lt" ("_^_" [100,100] 100)
 where
   "eqvt k \<Longrightarrow> (x~)*k = k (x~)"
-| "eqvt k \<Longrightarrow> (M$N)*k = M*(%m. (N*(%n.((m $ n) $ (Abs c (k (c~)))))))"
-| "eqvt k \<Longrightarrow> atom c \<sharp> (x, M) \<Longrightarrow> (Abs x M)*k = k (Abs x (Abs c (M^(c~))))"
+| "eqvt k \<Longrightarrow> (M$N)*k = M*(%m. (N*(%n.((m $ n) $ (Lam c (k (c~)))))))"
+| "eqvt k \<Longrightarrow> atom c \<sharp> (x, M) \<Longrightarrow> (Lam x M)*k = k (Lam x (Lam c (M^(c~))))"
 | "\<not>eqvt k \<Longrightarrow> (CPS1 t k) = t"
 | "(x~)^l = l $ (x~)"
 | "(M$N)^l = M*(%m. (N*(%n.((m $ n) $ l))))"
-| "atom c \<sharp> (x, M) \<Longrightarrow> (Abs x M)^l = l $ (Abs x (Abs c (M^(c~))))"
+| "atom c \<sharp> (x, M) \<Longrightarrow> (Lam x M)^l = l $ (Lam x (Lam c (M^(c~))))"
   apply (simp only: eqvt_def CPS1_CPS2_graph_def)
   apply (rule, perm_simp, rule)
   apply auto
@@ -31,7 +31,7 @@
   apply (simp add: fresh_at_base Abs1_eq_iff)
   apply blast
 --"-"
-  apply (subgoal_tac "Abs c (ka (c~)) = Abs ca (ka (ca~))")
+  apply (subgoal_tac "Lam c (ka (c~)) = Lam ca (ka (ca~))")
   apply (simp only:)
   apply (simp add: Abs1_eq_iff)
   apply (case_tac "c=ca")
@@ -49,7 +49,7 @@
   apply simp
   apply (thin_tac "eqvt ka")
   apply (rule_tac x="(c, ca, x, xa, M, Ma)" and ?'a="name" in obtain_fresh)
-  apply (subgoal_tac "Abs c (CPS1_CPS2_sumC (Inr (M, c~))) = Abs a (CPS1_CPS2_sumC (Inr (M, a~)))")
+  apply (subgoal_tac "Lam c (CPS1_CPS2_sumC (Inr (M, c~))) = Lam a (CPS1_CPS2_sumC (Inr (M, a~)))")
   prefer 2
   apply (simp add: Abs1_eq_iff')
   apply (case_tac "c = a")
@@ -60,7 +60,7 @@
   apply (erule fresh_eqvt_at)
   apply (simp add: supp_Inr finite_supp)
   apply (simp add: fresh_Inr fresh_Pair lt.fresh fresh_at_base)
-  apply (subgoal_tac "Abs ca (CPS1_CPS2_sumC (Inr (Ma, ca~))) = Abs a (CPS1_CPS2_sumC (Inr (Ma, a~)))")
+  apply (subgoal_tac "Lam ca (CPS1_CPS2_sumC (Inr (Ma, ca~))) = Lam a (CPS1_CPS2_sumC (Inr (Ma, a~)))")
   prefer 2
   apply (simp add: Abs1_eq_iff')
   apply (case_tac "ca = a")
@@ -85,8 +85,8 @@
   apply (drule sym)
   apply (drule sym)
   apply (simp only:)
-  apply (thin_tac "Abs a (CPS1_CPS2_sumC (Inr (M, a~))) = Abs c (CPS1_CPS2_sumC (Inr (M, c~)))")
-  apply (thin_tac "Abs a (CPS1_CPS2_sumC (Inr (Ma, a~))) = Abs ca (CPS1_CPS2_sumC (Inr (Ma, ca~)))")
+  apply (thin_tac "Lam a (CPS1_CPS2_sumC (Inr (M, a~))) = Lam c (CPS1_CPS2_sumC (Inr (M, c~)))")
+  apply (thin_tac "Lam a (CPS1_CPS2_sumC (Inr (Ma, a~))) = Lam ca (CPS1_CPS2_sumC (Inr (Ma, ca~)))")
   apply (thin_tac "atom a \<sharp> (c, ca, x, xa, M, Ma)")
   apply (simp add: fresh_Pair_elim)
   apply (subst iffD1[OF meta_eq_to_obj_eq[OF eqvt_at_def]])
@@ -133,7 +133,7 @@
   apply (metis atom_eq_iff permute_swap_cancel2 swap_atom_simps(3))
 --"-"
   apply (rule_tac x="(c, ca, x, xa, M, Ma)" and ?'a="name" in obtain_fresh)
-  apply (subgoal_tac "Abs c (CPS1_CPS2_sumC (Inr (M, c~))) = Abs a (CPS1_CPS2_sumC (Inr (M, a~)))")
+  apply (subgoal_tac "Lam c (CPS1_CPS2_sumC (Inr (M, c~))) = Lam a (CPS1_CPS2_sumC (Inr (M, a~)))")
   prefer 2
   apply (simp add: Abs1_eq_iff')
   apply (case_tac "c = a")
@@ -144,7 +144,7 @@
   apply (erule fresh_eqvt_at)
   apply (simp add: supp_Inr finite_supp)
   apply (simp add: fresh_Inr fresh_Pair lt.fresh fresh_at_base)
-  apply (subgoal_tac "Abs ca (CPS1_CPS2_sumC (Inr (Ma, ca~))) = Abs a (CPS1_CPS2_sumC (Inr (Ma, a~)))")
+  apply (subgoal_tac "Lam ca (CPS1_CPS2_sumC (Inr (Ma, ca~))) = Lam a (CPS1_CPS2_sumC (Inr (Ma, a~)))")
   prefer 2
   apply (simp add: Abs1_eq_iff')
   apply (case_tac "ca = a")
@@ -169,8 +169,8 @@
   apply (drule sym)
   apply (drule sym)
   apply (simp only:)
-  apply (thin_tac "Abs a (CPS1_CPS2_sumC (Inr (M, a~))) = Abs c (CPS1_CPS2_sumC (Inr (M, c~)))")
-  apply (thin_tac "Abs a (CPS1_CPS2_sumC (Inr (Ma, a~))) = Abs ca (CPS1_CPS2_sumC (Inr (Ma, ca~)))")
+  apply (thin_tac "Lam a (CPS1_CPS2_sumC (Inr (M, a~))) = Lam c (CPS1_CPS2_sumC (Inr (M, c~)))")
+  apply (thin_tac "Lam a (CPS1_CPS2_sumC (Inr (Ma, a~))) = Lam ca (CPS1_CPS2_sumC (Inr (Ma, ca~)))")
   apply (thin_tac "atom a \<sharp> (c, ca, x, xa, M, Ma)")
   apply (simp add: fresh_Pair_elim)
   apply (subst iffD1[OF meta_eq_to_obj_eq[OF eqvt_at_def]])
@@ -242,7 +242,7 @@
   apply simp
   done
 
-lemma value_eq3' : "~isValue M \<Longrightarrow> eqvt k \<Longrightarrow> M*k = (M^(Abs n (k (Var n))))"
+lemma value_eq3' : "~isValue M \<Longrightarrow> eqvt k \<Longrightarrow> M*k = (M^(Lam n (k (Var n))))"
   by (cases M rule: lt.exhaust) auto
nominal2