--- a/Nominal/Ex/CPS/Lt.thy	Tue Feb 19 05:38:46 2013 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,121 +0,0 @@
-header {* The Call-by-Value Lambda Calculus *}
-theory Lt
-imports "../../Nominal2"
-begin
-
-atom_decl name
-
-nominal_datatype lt =
-    Var name       ("_~"  [150] 149)
-  | App lt lt         (infixl "$$" 100)
-  | Lam x::"name" t::"lt"  binds  x in t
-
-nominal_primrec
-  subst :: "lt \<Rightarrow> name \<Rightarrow> lt \<Rightarrow> lt"  ("_ [_ ::= _]" [90, 90, 90] 90)
-where
-  "(Var x)[y ::= s] = (if x = y then s else (Var x))"
-| "(App t1 t2)[y ::= s] = App (t1[y ::= s]) (t2[y ::= s])"
-| "atom x \<sharp> (y, s) \<Longrightarrow> (Lam x t)[y ::= s] = Lam x (t[y ::= s])"
-  unfolding eqvt_def subst_graph_aux_def
-  apply (simp)
-  apply(rule TrueI)
-  using [[simproc del: alpha_lst]]
-  apply(auto simp add: lt.distinct lt.eq_iff)
-  apply(rule_tac y="a" and c="(aa, b)" in lt.strong_exhaust)
-  apply blast
-  apply(simp_all add: fresh_star_def fresh_Pair_elim)
-  apply blast
-  apply (erule_tac c="(ya,sa)" in Abs_lst1_fcb2)
-  apply(simp add: Abs_fresh_iff)
-  apply(simp add: fresh_star_def fresh_Pair)
-  apply(simp add: eqvt_at_def)
-  apply(simp add: perm_supp_eq fresh_star_Pair)
-  apply(simp add: eqvt_at_def)
-  apply(simp add: perm_supp_eq fresh_star_Pair)
-done
-
-termination (eqvt) by lexicographic_order
-
-lemma forget[simp]:
-  shows "atom x \<sharp> M \<Longrightarrow> M[x ::= s] = M"
-  by (nominal_induct M avoiding: x s rule: lt.strong_induct)
-     (auto simp add: lt.fresh fresh_at_base)
-
-lemma [simp]: "supp (M[x ::= V]) <= (supp(M) - {atom x}) Un (supp V)"
-  by (nominal_induct M avoiding: x V rule: lt.strong_induct)
-     (auto simp add: lt.supp supp_at_base, blast, blast)
-
-nominal_primrec
-  isValue:: "lt => bool"
-where
-  "isValue (Var x) = True"
-| "isValue (Lam y N) = True"
-| "isValue (A $$ B) = False"
-  unfolding eqvt_def isValue_graph_aux_def
-  by (auto)
-     (erule lt.exhaust, auto)
-
-termination (eqvt)
-  by (relation "measure size") (simp_all)
-
-inductive
-  eval :: "[lt, lt] \<Rightarrow> bool" (" _ \<longrightarrow>\<^isub>\<beta> _" [80,80] 80)
-  where
-   evbeta: "\<lbrakk>atom x \<sharp> V; isValue V\<rbrakk> \<Longrightarrow> ((Lam x M) $$ V) \<longrightarrow>\<^isub>\<beta> (M[x ::= V])"
-|  ev1: "\<lbrakk>isValue V; M \<longrightarrow>\<^isub>\<beta> M' \<rbrakk> \<Longrightarrow> (V $$ M) \<longrightarrow>\<^isub>\<beta> (V $$ M')"
-|  ev2: "M \<longrightarrow>\<^isub>\<beta> M' \<Longrightarrow> (M $$ N) \<longrightarrow>\<^isub>\<beta> (M' $$ N)"
-
-equivariance eval
-
-nominal_inductive eval
-done
-
-(*lemmas [simp] = lt.supp(2)*)
-
-lemma closedev1: assumes "s \<longrightarrow>\<^isub>\<beta> t"
-  shows "supp t <= supp s"
-  using assms
-    by (induct, auto simp add: lt.supp)
-
-
-lemma [simp]: "~ ((Lam x M) \<longrightarrow>\<^isub>\<beta> N)"
-by (rule, erule eval.cases, simp_all)
-
-lemma [simp]: assumes "M \<longrightarrow>\<^isub>\<beta> N" shows "~ isValue M"
-using assms
-by (cases, auto)
-
-
-inductive
-  eval_star :: "[lt, lt] \<Rightarrow> bool" (" _ \<longrightarrow>\<^isub>\<beta>\<^sup>* _" [80,80] 80)
-  where
-   evs1: "M \<longrightarrow>\<^isub>\<beta>\<^sup>* M"
-|  evs2: "\<lbrakk>M \<longrightarrow>\<^isub>\<beta> M'; M' \<longrightarrow>\<^isub>\<beta>\<^sup>*  M'' \<rbrakk> \<Longrightarrow> M \<longrightarrow>\<^isub>\<beta>\<^sup>*  M''"
-
-lemma eval_evs: assumes *: "M \<longrightarrow>\<^isub>\<beta> M'" shows "M \<longrightarrow>\<^isub>\<beta>\<^sup>* M'"
-by (rule evs2, rule *, rule evs1)
-
-lemma eval_trans[trans]:
-  assumes "M1  \<longrightarrow>\<^isub>\<beta>\<^sup>* M2"
-      and "M2  \<longrightarrow>\<^isub>\<beta>\<^sup>*  M3"
-  shows "M1  \<longrightarrow>\<^isub>\<beta>\<^sup>* M3"
-  using assms
-  by (induct, auto intro: evs2)
-
-lemma evs3[rule_format]: assumes "M1  \<longrightarrow>\<^isub>\<beta>\<^sup>* M2"
-  shows "M2  \<longrightarrow>\<^isub>\<beta> M3 \<longrightarrow> M1  \<longrightarrow>\<^isub>\<beta>\<^sup>* M3"
-  using assms
-    by (induct, auto intro: eval_evs evs2)
-
-equivariance eval_star
-
-lemma evbeta':
-  fixes x :: name
-  assumes "isValue V" and "atom x\<sharp>V" and "N = (M[x ::= V])"
-  shows "((Lam x M) $$ V) \<longrightarrow>\<^isub>\<beta>\<^sup>* N"
-  using assms by simp (rule evs2, rule evbeta, simp_all add: evs1)
-
-end
-
-
-