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 {* The Call-by-Value Lambda Calculus *}
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 2
theory 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
+ − 3
imports Nominal2
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 6
atom_decl 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
+ − 7
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 8
nominal_datatype 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
+ − 9
Var name ("_~" [150] 149)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 10
| Abs x::"name" t::"lt" bind x in t
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 11
| App lt 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
+ − 12
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 13
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
+ − 14
subst :: "lt \<Rightarrow> lt \<Rightarrow> name \<Rightarrow> lt" ("_[_'/_]" [200,0,0] 190)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 15
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
+ − 16
"(y~)[L/x] = (if y = x then L else 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
+ − 17
| "atom y\<sharp>L \<Longrightarrow> atom y\<sharp>x \<Longrightarrow> (Abs y M)[L/x] = Abs y (M[L/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
+ − 18
| "(M $ N)[L/x] = M[L/x] $ N[L/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
+ − 19
unfolding eqvt_def subst_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
+ − 20
apply(perm_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
+ − 21
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
+ − 22
apply(rule_tac y="a" and c="(aa, b)" in lt.strong_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
+ − 23
apply(simp_all add: fresh_star_def fresh_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
+ − 24
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
+ − 25
apply (erule Abs_lst1_fcb)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 26
apply (simp_all add: Abs_fresh_iff)[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
+ − 27
apply(drule_tac a="atom (ya)" in fresh_eqvt_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
+ − 28
apply(simp add: finite_supp fresh_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
+ − 29
apply(simp_all add: fresh_Pair Abs_fresh_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
+ − 30
apply(subgoal_tac "(atom y \<rightleftharpoons> atom ya) \<bullet> La = La")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 31
apply(subgoal_tac "(atom y \<rightleftharpoons> atom ya) \<bullet> xa = xa")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 32
apply(simp add: atom_eqvt eqvt_at_def Abs1_eq_iff swap_commute)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 33
apply (simp_all add: swap_fresh_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
+ − 34
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
+ − 35
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 36
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
+ − 37
by (relation "measure (\<lambda>(t, _, _). size t)")
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 38
(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
+ − 39
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 40
lemma subst_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
+ − 41
shows "p\<bullet>(M[V/(x::name)]) = (p\<bullet>M)[(p\<bullet>V)/(p\<bullet>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
+ − 42
by (induct M V x rule: subst.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
+ − 43
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 44
lemma forget[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
+ − 45
shows "atom x \<sharp> M \<Longrightarrow> M[s/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
+ − 46
by (nominal_induct M avoiding: x s 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
+ − 47
(auto simp 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
+ − 48
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 49
lemma [simp]: "supp ( M[V/(x::name)] ) <= (supp(M) - {atom x}) Un (supp 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
+ − 50
by (nominal_induct M avoiding: x V 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
+ − 51
(auto simp add: lt.supp supp_at_base, blast, 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
+ − 52
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 53
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
+ − 54
isValue:: "lt => bool"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 55
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
+ − 56
"isValue (Var x) = True"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 57
| "isValue (Abs y N) = True"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 58
| "isValue (A $ B) = False"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 59
unfolding eqvt_def isValue_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
+ − 60
by (perm_simp, 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
+ − 61
(erule lt.exhaust, 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
+ − 62
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 63
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
+ − 64
by (relation "measure 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
+ − 65
(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
+ − 66
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 67
lemma is_Value_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
+ − 68
shows "p\<bullet>(isValue (M::lt)) = 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
+ − 69
by (induct M rule: lt.induct) (simp_all add: 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
+ − 70
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 71
inductive
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 72
eval :: "[lt, lt] \<Rightarrow> bool" (" _ \<longrightarrow>\<^isub>\<beta> _" [80,80] 80)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 73
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
+ − 74
evbeta: "\<lbrakk>atom x\<sharp>V; isValue V\<rbrakk> \<Longrightarrow> ((Abs x M) $ V) \<longrightarrow>\<^isub>\<beta> (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
+ − 75
| ev1: "\<lbrakk>isValue V; M \<longrightarrow>\<^isub>\<beta> M' \<rbrakk> \<Longrightarrow> (V $ M) \<longrightarrow>\<^isub>\<beta> (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
+ − 76
| ev2: "M \<longrightarrow>\<^isub>\<beta> M' \<Longrightarrow> (M $ N) \<longrightarrow>\<^isub>\<beta> (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
+ − 77
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 78
equivariance 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
+ − 79
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 80
nominal_inductive 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
+ − 81
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
+ − 82
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 83
(*lemmas [simp] = lt.supp(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
+ − 84
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 85
lemma closedev1: assumes "s \<longrightarrow>\<^isub>\<beta> t"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 86
shows "supp t <= supp s"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 87
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
+ − 88
by (induct, auto simp 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
+ − 89
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 90
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 91
lemma [simp]: "~ ((Abs x M) \<longrightarrow>\<^isub>\<beta> 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
+ − 92
by (rule, erule eval.cases, 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
+ − 93
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 94
lemma [simp]: assumes "M \<longrightarrow>\<^isub>\<beta> N" shows "~ 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
+ − 95
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
+ − 96
by (cases, 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
+ − 97
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 98
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 99
inductive
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 100
eval_star :: "[lt, lt] \<Rightarrow> bool" (" _ \<longrightarrow>\<^isub>\<beta>\<^sup>* _" [80,80] 80)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the proofs, CPS2,3 just have the function and need eqvt_rhs to finish the obligations.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
+ − 101
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
+ − 102
evs1: "M \<longrightarrow>\<^isub>\<beta>\<^sup>* 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
+ − 103
| evs2: "\<lbrakk>M \<longrightarrow>\<^isub>\<beta> M'; M' \<longrightarrow>\<^isub>\<beta>\<^sup>* M'' \<rbrakk> \<Longrightarrow> M \<longrightarrow>\<^isub>\<beta>\<^sup>* 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
+ − 104
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
lemma eval_evs: assumes *: "M \<longrightarrow>\<^isub>\<beta> M'" shows "M \<longrightarrow>\<^isub>\<beta>\<^sup>* 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
+ − 106
by (rule evs2, rule *, rule 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
+ − 107
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
lemma eval_trans[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
+ − 109
assumes "M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M2"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
and "M2 \<longrightarrow>\<^isub>\<beta>\<^sup>* M3"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
shows "M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M3"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
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
+ − 113
by (induct, auto intro: evs2)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
lemma evs3[rule_format]: assumes "M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M2"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
shows "M2 \<longrightarrow>\<^isub>\<beta> M3 \<longrightarrow> M1 \<longrightarrow>\<^isub>\<beta>\<^sup>* M3"
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
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
+ − 118
by (induct, auto intro: eval_evs evs2)
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
equivariance eval_star
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
lemma evbeta':
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
fixes x :: 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
+ − 124
assumes "isValue V" and "atom x\<sharp>V" and "N = (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
+ − 125
shows "((Abs x M) $ V) \<longrightarrow>\<^isub>\<beta>\<^sup>* 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
+ − 126
using assms by simp (rule evs2, rule evbeta, 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
+ − 127
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
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
+ − 129
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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
5635a968fd3f
Added the CPS translation experiments. CPS1 comes with all the 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