2861
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 1
header {* CPS conversion *}
2895
+ − 2
theory CPS1_Plotkin
2861
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 3
imports Lt
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 4
begin
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 5
2933
+ − 6
lemma Abs_lst_fcb2:
+ − 7
fixes as bs :: "atom list"
+ − 8
and x y :: "'b :: fs"
+ − 9
and c::"'c::fs"
+ − 10
assumes eq: "[as]lst. x = [bs]lst. y"
+ − 11
and fcb1: "(set as) \<sharp>* c \<Longrightarrow> (set as) \<sharp>* f as x c"
+ − 12
and fresh1: "set as \<sharp>* c"
+ − 13
and fresh2: "set bs \<sharp>* c"
+ − 14
and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f as x c) = f (p \<bullet> as) (p \<bullet> x) c"
+ − 15
and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f bs y c) = f (p \<bullet> bs) (p \<bullet> y) c"
+ − 16
shows "f as x c = f bs y c"
+ − 17
proof -
+ − 18
have "supp (as, x, c) supports (f as x c)"
+ − 19
unfolding supports_def fresh_def[symmetric]
+ − 20
by (simp add: fresh_Pair perm1 fresh_star_def supp_swap swap_fresh_fresh)
+ − 21
then have fin1: "finite (supp (f as x c))"
+ − 22
by (auto intro: supports_finite simp add: finite_supp)
+ − 23
have "supp (bs, y, c) supports (f bs y c)"
+ − 24
unfolding supports_def fresh_def[symmetric]
+ − 25
by (simp add: fresh_Pair perm2 fresh_star_def supp_swap swap_fresh_fresh)
+ − 26
then have fin2: "finite (supp (f bs y c))"
+ − 27
by (auto intro: supports_finite simp add: finite_supp)
+ − 28
obtain q::"perm" where
+ − 29
fr1: "(q \<bullet> (set as)) \<sharp>* (x, c, f as x c, f bs y c)" and
+ − 30
fr2: "supp q \<sharp>* Abs_lst as x" and
+ − 31
inc: "supp q \<subseteq> (set as) \<union> q \<bullet> (set as)"
+ − 32
using at_set_avoiding3[where xs="set as" and c="(x, c, f as x c, f bs y c)" and x="[as]lst. x"]
+ − 33
fin1 fin2
+ − 34
by (auto simp add: supp_Pair finite_supp Abs_fresh_star dest: fresh_star_supp_conv)
+ − 35
have "Abs_lst (q \<bullet> as) (q \<bullet> x) = q \<bullet> Abs_lst as x" by simp
+ − 36
also have "\<dots> = Abs_lst as x"
+ − 37
by (simp only: fr2 perm_supp_eq)
+ − 38
finally have "Abs_lst (q \<bullet> as) (q \<bullet> x) = Abs_lst bs y" using eq by simp
+ − 39
then obtain r::perm where
+ − 40
qq1: "q \<bullet> x = r \<bullet> y" and
+ − 41
qq2: "q \<bullet> as = r \<bullet> bs" and
+ − 42
qq3: "supp r \<subseteq> (q \<bullet> (set as)) \<union> set bs"
+ − 43
apply(drule_tac sym)
+ − 44
apply(simp only: Abs_eq_iff2 alphas)
+ − 45
apply(erule exE)
+ − 46
apply(erule conjE)+
+ − 47
apply(drule_tac x="p" in meta_spec)
+ − 48
apply(simp add: set_eqvt)
+ − 49
apply(blast)
+ − 50
done
+ − 51
have "(set as) \<sharp>* f as x c"
+ − 52
apply(rule fcb1)
+ − 53
apply(rule fresh1)
+ − 54
done
+ − 55
then have "q \<bullet> ((set as) \<sharp>* f as x c)"
+ − 56
by (simp add: permute_bool_def)
+ − 57
then have "set (q \<bullet> as) \<sharp>* f (q \<bullet> as) (q \<bullet> x) c"
+ − 58
apply(simp add: fresh_star_eqvt set_eqvt)
+ − 59
apply(subst (asm) perm1)
+ − 60
using inc fresh1 fr1
+ − 61
apply(auto simp add: fresh_star_def fresh_Pair)
+ − 62
done
+ − 63
then have "set (r \<bullet> bs) \<sharp>* f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 by simp
+ − 64
then have "r \<bullet> ((set bs) \<sharp>* f bs y c)"
+ − 65
apply(simp add: fresh_star_eqvt set_eqvt)
+ − 66
apply(subst (asm) perm2[symmetric])
+ − 67
using qq3 fresh2 fr1
+ − 68
apply(auto simp add: set_eqvt fresh_star_def fresh_Pair)
+ − 69
done
+ − 70
then have fcb2: "(set bs) \<sharp>* f bs y c" by (simp add: permute_bool_def)
+ − 71
have "f as x c = q \<bullet> (f as x c)"
+ − 72
apply(rule perm_supp_eq[symmetric])
+ − 73
using inc fcb1[OF fresh1] fr1 by (auto simp add: fresh_star_def)
+ − 74
also have "\<dots> = f (q \<bullet> as) (q \<bullet> x) c"
+ − 75
apply(rule perm1)
+ − 76
using inc fresh1 fr1 by (auto simp add: fresh_star_def)
+ − 77
also have "\<dots> = f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 by simp
+ − 78
also have "\<dots> = r \<bullet> (f bs y c)"
+ − 79
apply(rule perm2[symmetric])
+ − 80
using qq3 fresh2 fr1 by (auto simp add: fresh_star_def)
+ − 81
also have "... = f bs y c"
+ − 82
apply(rule perm_supp_eq)
+ − 83
using qq3 fr1 fcb2 by (auto simp add: fresh_star_def)
+ − 84
finally show ?thesis by simp
+ − 85
qed
+ − 86
+ − 87
lemma Abs_lst1_fcb2:
+ − 88
fixes a b :: "atom"
+ − 89
and x y :: "'b :: fs"
+ − 90
and c::"'c :: fs"
+ − 91
assumes e: "(Abs_lst [a] x) = (Abs_lst [b] y)"
+ − 92
and fcb1: "a \<sharp> c \<Longrightarrow> a \<sharp> f a x c"
+ − 93
and fresh: "{a, b} \<sharp>* c"
+ − 94
and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f a x c) = f (p \<bullet> a) (p \<bullet> x) c"
+ − 95
and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f b y c) = f (p \<bullet> b) (p \<bullet> y) c"
+ − 96
shows "f a x c = f b y c"
+ − 97
using e
+ − 98
apply(drule_tac Abs_lst_fcb2[where c="c" and f="\<lambda>(as::atom list) . f (hd as)"])
+ − 99
apply(simp_all)
+ − 100
using fcb1 fresh perm1 perm2
+ − 101
apply(simp_all add: fresh_star_def)
+ − 102
done
+ − 103
2861
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 104
nominal_primrec
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 105
CPS :: "lt \<Rightarrow> lt" ("_*" [250] 250)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 106
where
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 107
"atom k \<sharp> x \<Longrightarrow> (x~)* = (Abs k ((k~) $ (x~)))"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 108
| "atom k \<sharp> (x, M) \<Longrightarrow> (Abs x M)* = Abs k (k~ $ Abs x (M*))"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 109
| "atom k \<sharp> (M, N) \<Longrightarrow> atom m \<sharp> (N, k) \<Longrightarrow> atom n \<sharp> (k, m) \<Longrightarrow>
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 110
(M $ N)* = Abs k (M* $ Abs m (N* $ Abs n (m~ $ n~ $ k~)))"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 111
unfolding eqvt_def CPS_graph_def
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 112
apply (rule, perm_simp, rule, rule)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 113
apply (simp_all add: fresh_Pair_elim)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 114
apply (rule_tac y="x" in lt.exhaust)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 115
apply (auto)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 116
apply (rule_tac x="name" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 117
apply (simp_all add: fresh_at_base)[3]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 118
apply (rule_tac x="(name, lt)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 119
apply (simp add: fresh_Pair_elim fresh_at_base)[2]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 120
apply (rule_tac x="(lt1, lt2)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 121
apply (rule_tac x="(lt2, a)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 122
apply (rule_tac x="(a, aa)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 123
apply (simp add: fresh_Pair_elim fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 124
apply (simp add: Abs1_eq_iff lt.fresh fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 125
--"-"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 126
apply(rule_tac s="[[atom ka]]lst. ka~ $ Abs x (CPS_sumC M)" in trans)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 127
apply (case_tac "k = ka")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 128
apply simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 129
apply(simp (no_asm) add: Abs1_eq_iff del:eqvts)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 130
apply (simp del: eqvts add: lt.fresh fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 131
apply (simp only: lt.perm_simps(1) lt.perm_simps(3) flip_def[symmetric] lt.eq_iff(3))
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 132
apply (subst flip_at_base_simps(2))
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 133
apply simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 134
apply (intro conjI refl)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 135
apply (rule flip_fresh_fresh[symmetric])
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 136
apply (simp_all add: lt.fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 137
apply (metis fresh_eqvt_at lt.fsupp)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 138
apply (case_tac "ka = x")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 139
apply simp_all[2]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 140
apply (metis Abs_fresh_iff(3) atom_eq_iff finite_set fresh_Cons fresh_Nil fresh_atom fresh_eqvt_at fresh_finite_atom_set fresh_set lt.fsupp)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 141
apply (metis Abs_fresh_iff(3) atom_eq_iff finite_set fresh_Cons fresh_Nil fresh_atom fresh_eqvt_at fresh_finite_atom_set fresh_set lt.fsupp)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 142
--"-"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 143
apply (simp add: Abs1_eq(3))
2933
+ − 144
apply (erule Abs_lst1_fcb2)
+ − 145
apply (simp_all add: Abs_fresh_iff fresh_Nil fresh_star_def eqvt_at_def)[4]
2861
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 146
--"-"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 147
apply (rename_tac k' M N m' n')
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 148
apply (subgoal_tac "atom k \<sharp> CPS_sumC M \<and> atom k' \<sharp> CPS_sumC M \<and> atom k \<sharp> CPS_sumC N \<and> atom k' \<sharp> CPS_sumC N \<and>
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 149
atom m \<sharp> CPS_sumC N \<and> atom m' \<sharp> CPS_sumC N")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 150
prefer 2
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 151
apply (intro conjI)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 152
apply (erule fresh_eqvt_at, simp add: finite_supp, assumption)+
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 153
apply clarify
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 154
apply (case_tac "k = k'", case_tac [!] "m' = k",case_tac [!]"m = k'",case_tac[!] "m = m'")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 155
apply (simp_all add: Abs1_eq_iff lt.fresh flip_def[symmetric] fresh_at_base flip_fresh_fresh permute_eq_iff)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 156
by (metis flip_at_base_simps(3) flip_at_simps(2) flip_commute permute_flip_at)+
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 157
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 158
termination
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 159
by (relation "measure size") (simp_all add: lt.size)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 160
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 161
lemmas [simp] = fresh_Pair_elim CPS.simps(2,3)[simplified fresh_Pair_elim]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 162
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 163
lemma [simp]: "supp (M*) = supp M"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 164
by (induct rule: CPS.induct, simp_all add: lt.supp supp_at_base fresh_at_base fresh_def supp_Pair)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 165
(simp_all only: atom_eq_iff[symmetric], blast+)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 166
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 167
lemma [simp]: "x \<sharp> M* = x \<sharp> M"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 168
unfolding fresh_def by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 169
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 170
(* Will be provided automatically by nominal_primrec *)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 171
lemma CPS_eqvt[eqvt]:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 172
shows "p \<bullet> M* = (p \<bullet> M)*"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 173
apply (induct M rule: lt.induct)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 174
apply (rule_tac x="(name, p \<bullet> name, p)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 175
apply simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 176
apply (simp add: Abs1_eq_iff lt.fresh flip_def[symmetric])
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 177
apply (metis atom_eqvt flip_fresh_fresh fresh_perm atom_eq_iff fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 178
apply (rule_tac x="(name, lt, p \<bullet> name, p \<bullet> lt, p)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 179
apply simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 180
apply (metis atom_eqvt fresh_perm atom_eq_iff)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 181
apply (rule_tac x="(lt1, p \<bullet> lt1, lt2, p \<bullet> lt2, p)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 182
apply (rule_tac x="(a, lt2, p \<bullet> lt2, p)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 183
apply (rule_tac x="(a, aa, p)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 184
apply (simp)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 185
apply (simp add: Abs1_eq_iff lt.fresh flip_def[symmetric])
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 186
apply (metis atom_eqvt fresh_perm atom_eq_iff)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 187
done
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 188
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 189
nominal_primrec
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 190
convert:: "lt => lt" ("_+" [250] 250)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 191
where
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 192
"(Var x)+ = Var x"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 193
| "(Abs x M)+ = Abs x (M*)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 194
| "(M $ N)+ = M $ N"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 195
unfolding convert_graph_def eqvt_def
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 196
apply (rule, perm_simp, rule, rule)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 197
apply (erule lt.exhaust)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 198
apply (simp_all)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 199
apply blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 200
apply (simp add: Abs1_eq_iff CPS_eqvt)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 201
by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 202
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 203
termination
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 204
by (relation "measure size") (simp_all add: lt.size)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 205
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 206
lemma convert_supp[simp]:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 207
shows "supp (M+) = supp M"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 208
by (induct M rule: lt.induct, simp_all add: lt.supp)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 209
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 210
lemma convert_fresh[simp]:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 211
shows "x \<sharp> (M+) = x \<sharp> M"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 212
unfolding fresh_def by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 213
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 214
lemma convert_eqvt[eqvt]:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 215
shows "p \<bullet> (M+) = (p \<bullet> M)+"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 216
by (nominal_induct M rule: lt.strong_induct, auto simp add: CPS_eqvt)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 217
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 218
lemma [simp]:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 219
shows "isValue (p \<bullet> (M::lt)) = isValue M"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 220
by (nominal_induct M rule: lt.strong_induct) auto
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 221
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 222
lemma [eqvt]:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 223
shows "p \<bullet> isValue M = isValue (p \<bullet> M)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 224
by (induct M rule: lt.induct) (perm_simp, rule refl)+
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 225
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 226
nominal_primrec
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 227
Kapply :: "lt \<Rightarrow> lt \<Rightarrow> lt" (infixl ";" 100)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 228
where
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 229
"Kapply (Abs x M) K = K $ (Abs x M)+"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 230
| "Kapply (Var x) K = K $ Var x"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 231
| "isValue M \<Longrightarrow> isValue N \<Longrightarrow> Kapply (M $ N) K = M+ $ N+ $ K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 232
| "isValue M \<Longrightarrow> \<not>isValue N \<Longrightarrow> atom n \<sharp> M \<Longrightarrow> atom n \<sharp> K \<Longrightarrow>
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 233
Kapply (M $ N) K = N; (Abs n (M+ $ Var n $ K))"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 234
| "\<not>isValue M \<Longrightarrow> atom m \<sharp> N \<Longrightarrow> atom m \<sharp> K \<Longrightarrow> atom n \<sharp> m \<Longrightarrow> atom n \<sharp> K \<Longrightarrow>
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 235
Kapply (M $ N) K = M; (Abs m (N* $ (Abs n (Var m $ Var n $ K))))"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 236
unfolding Kapply_graph_def eqvt_def
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 237
apply (rule, perm_simp, rule, rule)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 238
apply (simp_all)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 239
apply (case_tac x)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 240
apply (rule_tac y="a" in lt.exhaust)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 241
apply (auto)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 242
apply (case_tac "isValue lt1")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 243
apply (case_tac "isValue lt2")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 244
apply (auto)[1]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 245
apply (rule_tac x="(lt1, ba)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 246
apply (simp add: fresh_Pair_elim fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 247
apply (rule_tac x="(lt2, ba)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 248
apply (rule_tac x="(a, ba)" and ?'a="name" in obtain_fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 249
apply (simp add: fresh_Pair_elim fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 250
apply (auto simp add: Abs1_eq_iff eqvts)[1]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 251
apply (rename_tac M N u K)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 252
apply (subgoal_tac "Abs n (M+ $ n~ $ K) = Abs u (M+ $ u~ $ K)")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 253
apply (simp only:)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 254
apply (auto simp add: Abs1_eq_iff flip_def[symmetric] lt.fresh fresh_at_base flip_fresh_fresh[symmetric])[1]
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 255
apply (subgoal_tac "Abs m (Na* $ Abs n (m~ $ n~ $ Ka)) = Abs ma (Na* $ Abs na (ma~ $ na~ $ Ka))")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 256
apply (simp only:)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 257
apply (simp add: Abs1_eq_iff flip_def[symmetric] lt.fresh fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 258
apply (subgoal_tac "Ka = (n \<leftrightarrow> na) \<bullet> Ka")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 259
apply (subgoal_tac "Ka = (m \<leftrightarrow> ma) \<bullet> Ka")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 260
apply (subgoal_tac "Ka = (n \<leftrightarrow> (m \<leftrightarrow> ma) \<bullet> na) \<bullet> Ka")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 261
apply (case_tac "m = ma")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 262
apply simp_all
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 263
apply rule
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 264
apply (auto simp add: flip_fresh_fresh[symmetric])
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 265
apply (metis flip_at_base_simps(3) flip_fresh_fresh permute_flip_at)+
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 266
done
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 267
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 268
termination
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 269
by (relation "measure (\<lambda>(t, _). size t)") (simp_all add: lt.size)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 270
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 271
section{* lemma related to Kapply *}
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 272
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 273
lemma [simp]: "isValue V \<Longrightarrow> V; K = K $ (V+)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 274
by (nominal_induct V rule: lt.strong_induct) auto
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 275
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 276
section{* lemma related to CPS conversion *}
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 277
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 278
lemma value_CPS:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 279
assumes "isValue V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 280
and "atom a \<sharp> V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 281
shows "V* = Abs a (a~ $ V+)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 282
using assms
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 283
proof (nominal_induct V avoiding: a rule: lt.strong_induct, simp_all add: lt.fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 284
fix name :: name and lt aa
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 285
assume a: "atom name \<sharp> aa" "\<And>b. \<lbrakk>isValue lt; atom b \<sharp> lt\<rbrakk> \<Longrightarrow> lt* = Abs b (b~ $ lt+)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 286
"atom aa \<sharp> lt \<or> aa = name"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 287
obtain ab :: name where b: "atom ab \<sharp> (name, lt, a)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 288
show "Abs name lt* = Abs aa (aa~ $ Abs name (lt*))" using a b
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 289
by (simp add: Abs1_eq_iff fresh_at_base lt.fresh)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 290
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 291
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 292
section{* first lemma CPS subst *}
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 293
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 294
lemma CPS_subst_fv:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 295
assumes *:"isValue V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 296
shows "((M[V/x])* = (M*)[V+/x])"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 297
using * proof (nominal_induct M avoiding: V x rule: lt.strong_induct)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 298
case (Var name)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 299
assume *: "isValue V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 300
obtain a :: name where a: "atom a \<sharp> (x, name, V)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 301
show "((name~)[V/x])* = (name~)*[V+/x]" using a
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 302
by (simp add: fresh_at_base * value_CPS)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 303
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 304
case (Abs name lt V x)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 305
assume *: "atom name \<sharp> V" "atom name \<sharp> x" "\<And>b ba. isValue b \<Longrightarrow> (lt[b/ba])* = lt*[b+/ba]"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 306
"isValue V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 307
obtain a :: name where a: "atom a \<sharp> (name, lt, lt[V/x], x, V)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 308
show "(Abs name lt[V/x])* = Abs name lt*[V+/x]" using * a
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 309
by (simp add: fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 310
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 311
case (App lt1 lt2 V x)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 312
assume *: "\<And>b ba. isValue b \<Longrightarrow> (lt1[b/ba])* = lt1*[b+/ba]" "\<And>b ba. isValue b \<Longrightarrow> (lt2[b/ba])* = lt2*[b+/ba]"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 313
"isValue V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 314
obtain a :: name where a: "atom a \<sharp> (lt1[V/x], lt1, lt2[V/x], lt2, V, x)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 315
obtain b :: name where b: "atom b \<sharp> (lt2[V/x], lt2, a, V, x)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 316
obtain c :: name where c: "atom c \<sharp> (a, b, V, x)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 317
show "((lt1 $ lt2)[V/x])* = (lt1 $ lt2)*[V+/x]" using * a b c
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 318
by (simp add: fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 319
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 320
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 321
lemma [simp]: "isValue V \<Longrightarrow> isValue (V+)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 322
by (nominal_induct V rule: lt.strong_induct, auto)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 323
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 324
lemma CPS_eval_Kapply:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 325
assumes a: "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 326
shows "(M* $ K) \<longrightarrow>\<^isub>\<beta>\<^sup>* (M ; K)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 327
using a
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 328
proof (nominal_induct M avoiding: K rule: lt.strong_induct, simp_all)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 329
case (Var name K)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 330
assume *: "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 331
obtain a :: name where a: "atom a \<sharp> (name, K)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 332
show "(name~)* $ K \<longrightarrow>\<^isub>\<beta>\<^sup>* K $ name~" using * a
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 333
by simp (rule evbeta', simp_all add: fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 334
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 335
fix name :: name and lt K
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 336
assume *: "atom name \<sharp> K" "\<And>b. isValue b \<Longrightarrow> lt* $ b \<longrightarrow>\<^isub>\<beta>\<^sup>* lt ; b" "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 337
obtain a :: name where a: "atom a \<sharp> (name, K, lt)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 338
then have b: "atom name \<sharp> a" using fresh_PairD(1) fresh_at_base atom_eq_iff by metis
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 339
show "Abs name lt* $ K \<longrightarrow>\<^isub>\<beta>\<^sup>* K $ Abs name (lt*)" using * a b
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 340
by simp (rule evbeta', simp_all)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 341
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 342
fix lt1 lt2 K
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 343
assume *: "\<And>b. isValue b \<Longrightarrow> lt1* $ b \<longrightarrow>\<^isub>\<beta>\<^sup>* lt1 ; b" "\<And>b. isValue b \<Longrightarrow> lt2* $ b \<longrightarrow>\<^isub>\<beta>\<^sup>* lt2 ; b" "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 344
obtain a :: name where a: "atom a \<sharp> (lt1, lt2, K)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 345
obtain b :: name where b: "atom b \<sharp> (lt1, lt2, K, a)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 346
obtain c :: name where c: "atom c \<sharp> (lt1, lt2, K, a, b)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 347
have d: "atom a \<sharp> lt1" "atom a \<sharp> lt2" "atom a \<sharp> K" "atom b \<sharp> lt1" "atom b \<sharp> lt2" "atom b \<sharp> K" "atom b \<sharp> a"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 348
"atom c \<sharp> lt1" "atom c \<sharp> lt2" "atom c \<sharp> K" "atom c \<sharp> a" "atom c \<sharp> b" using fresh_Pair a b c by simp_all
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 349
have "(lt1 $ lt2)* $ K \<longrightarrow>\<^isub>\<beta>\<^sup>* lt1* $ Abs b (lt2* $ Abs c (b~ $ c~ $ K))" using * d
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 350
by (simp add: fresh_at_base) (rule evbeta', simp_all add: fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 351
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* lt1 $ lt2 ; K" proof (cases "isValue lt1")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 352
assume e: "isValue lt1"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 353
have "lt1* $ Abs b (lt2* $ Abs c (b~ $ c~ $ K)) \<longrightarrow>\<^isub>\<beta>\<^sup>* Abs b (lt2* $ Abs c (b~ $ c~ $ K)) $ lt1+"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 354
using * d e by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 355
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* lt2* $ Abs c (lt1+ $ c~ $ K)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 356
by (rule evbeta', simp_all add: * d e, metis d(12) fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 357
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* lt1 $ lt2 ; K" proof (cases "isValue lt2")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 358
assume f: "isValue lt2"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 359
have "lt2* $ Abs c (lt1+ $ c~ $ K) \<longrightarrow>\<^isub>\<beta>\<^sup>* Abs c (lt1+ $ c~ $ K) $ lt2+" using * d e f by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 360
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* lt1+ $ lt2+ $ K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 361
by (rule evbeta', simp_all add: d e f)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 362
finally show ?thesis using * d e f by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 363
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 364
assume f: "\<not> isValue lt2"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 365
have "lt2* $ Abs c (lt1+ $ c~ $ K) \<longrightarrow>\<^isub>\<beta>\<^sup>* lt2 ; Abs c (lt1+ $ c~ $ K)" using * d e f by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 366
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* lt2 ; Abs a (lt1+ $ a~ $ K)" using Kapply.simps(4) d e evs1 f by metis
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 367
finally show ?thesis using * d e f by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 368
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 369
finally show ?thesis .
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 370
qed (metis Kapply.simps(5) isValue.simps(2) * d)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 371
finally show "(lt1 $ lt2)* $ K \<longrightarrow>\<^isub>\<beta>\<^sup>* lt1 $ lt2 ; K" .
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 372
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 373
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 374
lemma Kapply_eval:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 375
assumes a: "M \<longrightarrow>\<^isub>\<beta> N" "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 376
shows "(M; K) \<longrightarrow>\<^isub>\<beta>\<^sup>* (N; K)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 377
using assms
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 378
proof (induct arbitrary: K rule: eval.induct)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 379
case (evbeta x V M)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 380
fix K
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 381
assume a: "isValue K" "isValue V" "atom x \<sharp> V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 382
have "Abs x (M*) $ V+ $ K \<longrightarrow>\<^isub>\<beta>\<^sup>* ((M*)[V+/x] $ K)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 383
by (rule evs2,rule ev2,rule Lt.evbeta) (simp_all add: fresh_def a[simplified fresh_def] evs1)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 384
also have "... = ((M[V/x])* $ K)" by (simp add: CPS_subst_fv a)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 385
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* (M[V/x] ; K)" by (rule CPS_eval_Kapply, simp_all add: a)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 386
finally show "(Abs x M $ V ; K) \<longrightarrow>\<^isub>\<beta>\<^sup>* (M[V/x] ; K)" using a by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 387
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 388
case (ev1 V M N)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 389
fix V M N K
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 390
assume a: "isValue V" "M \<longrightarrow>\<^isub>\<beta> N" "\<And>K. isValue K \<Longrightarrow> M ; K \<longrightarrow>\<^isub>\<beta>\<^sup>* N ; K" "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 391
obtain a :: name where b: "atom a \<sharp> (V, K, M, N)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 392
show "V $ M ; K \<longrightarrow>\<^isub>\<beta>\<^sup>* V $ N ; K" proof (cases "isValue N")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 393
assume "\<not> isValue N"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 394
then show "V $ M ; K \<longrightarrow>\<^isub>\<beta>\<^sup>* V $ N ; K" using a b by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 395
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 396
assume n: "isValue N"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 397
have c: "M; Abs a (V+ $ a~ $ K) \<longrightarrow>\<^isub>\<beta>\<^sup>* Abs a (V+ $ a~ $ K) $ N+" using a b by (simp add: n)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 398
also have d: "... \<longrightarrow>\<^isub>\<beta>\<^sup>* V+ $ N+ $ K" by (rule evbeta') (simp_all add: a b n)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 399
finally show "V $ M ; K \<longrightarrow>\<^isub>\<beta>\<^sup>* V $ N ; K" using a b by (simp add: n)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 400
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 401
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 402
case (ev2 M M' N)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 403
assume *: "M \<longrightarrow>\<^isub>\<beta> M'" "\<And>K. isValue K \<Longrightarrow> M ; K \<longrightarrow>\<^isub>\<beta>\<^sup>* M' ; K" "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 404
obtain a :: name where a: "atom a \<sharp> (K, M, N, M')" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 405
obtain b :: name where b: "atom b \<sharp> (a, K, M, N, M', N+)" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 406
have d: "atom a \<sharp> K" "atom a \<sharp> M" "atom a \<sharp> N" "atom a \<sharp> M'" "atom b \<sharp> a" "atom b \<sharp> K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 407
"atom b \<sharp> M" "atom b \<sharp> N" "atom b \<sharp> M'" using a b fresh_Pair by simp_all
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 408
have "M $ N ; K \<longrightarrow>\<^isub>\<beta>\<^sup>* M' ; Abs a (N* $ Abs b (a~ $ b~ $ K))" using * d by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 409
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* M' $ N ; K" proof (cases "isValue M'")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 410
assume "\<not> isValue M'"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 411
then show ?thesis using * d by (simp_all add: evs1)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 412
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 413
assume e: "isValue M'"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 414
then have "M' ; Abs a (N* $ Abs b (a~ $ b~ $ K)) = Abs a (N* $ Abs b (a~ $ b~ $ K)) $ M'+" by simp
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 415
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* (N* $ Abs b (a~ $ b~ $ K))[M'+/a]"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 416
by (rule evbeta') (simp_all add: fresh_at_base e d)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 417
also have "... = N* $ Abs b (M'+ $ b~ $ K)" using * d by (simp add: fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 418
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* M' $ N ; K" proof (cases "isValue N")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 419
assume f: "isValue N"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 420
have "N* $ Abs b (M'+ $ b~ $ K) \<longrightarrow>\<^isub>\<beta>\<^sup>* Abs b (M'+ $ b~ $ K) $ N+"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 421
by (rule eval_trans, rule CPS_eval_Kapply) (simp_all add: d e f * evs1)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 422
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* M' $ N ; K" by (rule evbeta') (simp_all add: d e f evs1)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 423
finally show ?thesis .
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 424
next
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 425
assume "\<not> isValue N"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 426
then show ?thesis using d e
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 427
by (metis CPS_eval_Kapply Kapply.simps(4) isValue.simps(2))
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 428
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 429
finally show ?thesis .
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 430
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 431
finally show ?case .
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 432
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 433
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 434
lemma Kapply_eval_rtrancl:
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 435
assumes H: "M \<longrightarrow>\<^isub>\<beta>\<^sup>* N" and "isValue K"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 436
shows "(M;K) \<longrightarrow>\<^isub>\<beta>\<^sup>* (N;K)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 437
using H
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 438
by (induct) (metis Kapply_eval assms(2) eval_trans evs1)+
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 439
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 440
lemma
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 441
assumes "isValue V" "M \<longrightarrow>\<^isub>\<beta>\<^sup>* V"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 442
shows "M* $ (Abs x (x~)) \<longrightarrow>\<^isub>\<beta>\<^sup>* V+"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 443
proof-
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 444
obtain y::name where *: "atom y \<sharp> V" using obtain_fresh by blast
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 445
have e: "Abs x (x~) = Abs y (y~)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 446
by (simp add: Abs1_eq_iff lt.fresh fresh_at_base)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 447
have "M* $ Abs x (x~) \<longrightarrow>\<^isub>\<beta>\<^sup>* M ; Abs x (x~)"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 448
by(rule CPS_eval_Kapply,simp_all add: assms)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 449
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* (V ; Abs x (x~))" by (rule Kapply_eval_rtrancl, simp_all add: assms)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 450
also have "... = V ; Abs y (y~)" using e by (simp only:)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 451
also have "... \<longrightarrow>\<^isub>\<beta>\<^sup>* (V+)" by (simp add: assms, rule evbeta') (simp_all add: assms *)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 452
finally show "M* $ (Abs x (x~)) \<longrightarrow>\<^isub>\<beta>\<^sup>* (V+)" .
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 453
qed
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 454
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 455
end
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 456
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 457
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 458