5 CPS1 :: "lt \<Rightarrow> (lt \<Rightarrow> lt) \<Rightarrow> lt" ("_*_" [100,100] 100) |
5 CPS1 :: "lt \<Rightarrow> (lt \<Rightarrow> lt) \<Rightarrow> lt" ("_*_" [100,100] 100) |
6 and |
6 and |
7 CPS2 :: "lt \<Rightarrow> lt \<Rightarrow> lt" ("_^_" [100,100] 100) |
7 CPS2 :: "lt \<Rightarrow> lt \<Rightarrow> lt" ("_^_" [100,100] 100) |
8 where |
8 where |
9 "eqvt k \<Longrightarrow> (x~)*k = k (x~)" |
9 "eqvt k \<Longrightarrow> (x~)*k = k (x~)" |
10 | "eqvt k \<Longrightarrow> (M$N)*k = M*(%m. (N*(%n.((m $ n) $ (Abs c (k (c~)))))))" |
10 | "eqvt k \<Longrightarrow> (M$N)*k = M*(%m. (N*(%n.((m $ n) $ (Lam c (k (c~)))))))" |
11 | "eqvt k \<Longrightarrow> atom c \<sharp> (x, M) \<Longrightarrow> (Abs x M)*k = k (Abs x (Abs c (M^(c~))))" |
11 | "eqvt k \<Longrightarrow> atom c \<sharp> (x, M) \<Longrightarrow> (Lam x M)*k = k (Lam x (Lam c (M^(c~))))" |
12 | "\<not>eqvt k \<Longrightarrow> (CPS1 t k) = t" |
12 | "\<not>eqvt k \<Longrightarrow> (CPS1 t k) = t" |
13 | "(x~)^l = l $ (x~)" |
13 | "(x~)^l = l $ (x~)" |
14 | "(M$N)^l = M*(%m. (N*(%n.((m $ n) $ l))))" |
14 | "(M$N)^l = M*(%m. (N*(%n.((m $ n) $ l))))" |
15 | "atom c \<sharp> (x, M) \<Longrightarrow> (Abs x M)^l = l $ (Abs x (Abs c (M^(c~))))" |
15 | "atom c \<sharp> (x, M) \<Longrightarrow> (Lam x M)^l = l $ (Lam x (Lam c (M^(c~))))" |
16 apply (simp only: eqvt_def CPS1_CPS2_graph_def) |
16 apply (simp only: eqvt_def CPS1_CPS2_graph_def) |
17 apply (rule, perm_simp, rule) |
17 apply (rule, perm_simp, rule) |
18 apply auto |
18 apply auto |
19 apply (case_tac x) |
19 apply (case_tac x) |
20 apply (case_tac a) |
20 apply (case_tac a) |
29 apply blast |
29 apply blast |
30 apply (rule_tac x="(name, lt)" and ?'a="name" in obtain_fresh) |
30 apply (rule_tac x="(name, lt)" and ?'a="name" in obtain_fresh) |
31 apply (simp add: fresh_at_base Abs1_eq_iff) |
31 apply (simp add: fresh_at_base Abs1_eq_iff) |
32 apply blast |
32 apply blast |
33 --"-" |
33 --"-" |
34 apply (subgoal_tac "Abs c (ka (c~)) = Abs ca (ka (ca~))") |
34 apply (subgoal_tac "Lam c (ka (c~)) = Lam ca (ka (ca~))") |
35 apply (simp only:) |
35 apply (simp only:) |
36 apply (simp add: Abs1_eq_iff) |
36 apply (simp add: Abs1_eq_iff) |
37 apply (case_tac "c=ca") |
37 apply (case_tac "c=ca") |
38 apply simp_all[2] |
38 apply simp_all[2] |
39 apply rule |
39 apply rule |
46 --"-" |
46 --"-" |
47 apply (rule arg_cong) |
47 apply (rule arg_cong) |
48 back |
48 back |
49 apply (thin_tac "eqvt ka") |
49 apply (thin_tac "eqvt ka") |
50 apply (rule_tac x="(c, ca, x, xa, M, Ma)" and ?'a="name" in obtain_fresh) |
50 apply (rule_tac x="(c, ca, x, xa, M, Ma)" and ?'a="name" in obtain_fresh) |
51 apply (subgoal_tac "Abs c (CPS1_CPS2_sumC (Inr (M, c~))) = Abs a (CPS1_CPS2_sumC (Inr (M, a~)))") |
51 apply (subgoal_tac "Lam c (CPS1_CPS2_sumC (Inr (M, c~))) = Lam a (CPS1_CPS2_sumC (Inr (M, a~)))") |
52 prefer 2 |
52 prefer 2 |
53 apply (simp add: Abs1_eq_iff') |
53 apply (simp add: Abs1_eq_iff') |
54 apply (case_tac "c = a") |
54 apply (case_tac "c = a") |
55 apply simp_all[2] |
55 apply simp_all[2] |
56 apply rule |
56 apply rule |
57 apply (simp add: eqvt_at_def) |
57 apply (simp add: eqvt_at_def) |
58 apply (simp add: swap_fresh_fresh fresh_Pair_elim) |
58 apply (simp add: swap_fresh_fresh fresh_Pair_elim) |
59 apply (erule fresh_eqvt_at) |
59 apply (erule fresh_eqvt_at) |
60 apply (simp add: supp_Inr finite_supp) |
60 apply (simp add: supp_Inr finite_supp) |
61 apply (simp add: fresh_Inr fresh_Pair lt.fresh fresh_at_base) |
61 apply (simp add: fresh_Inr fresh_Pair lt.fresh fresh_at_base) |
62 apply (subgoal_tac "Abs ca (CPS1_CPS2_sumC (Inr (Ma, ca~))) = Abs a (CPS1_CPS2_sumC (Inr (Ma, a~)))") |
62 apply (subgoal_tac "Lam ca (CPS1_CPS2_sumC (Inr (Ma, ca~))) = Lam a (CPS1_CPS2_sumC (Inr (Ma, a~)))") |
63 prefer 2 |
63 prefer 2 |
64 apply (simp add: Abs1_eq_iff') |
64 apply (simp add: Abs1_eq_iff') |
65 apply (case_tac "ca = a") |
65 apply (case_tac "ca = a") |
66 apply simp_all[2] |
66 apply simp_all[2] |
67 apply rule |
67 apply rule |