--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Tests/Rec_def2.thy	Thu Mar 07 11:52:08 2013 +0000
@@ -0,0 +1,47 @@
+theory Rec_def2
+imports Main
+begin
+
+datatype recf =  z
+              |  s
+              |  id nat nat
+              |  Cn nat recf "recf list"
+              |  Pr nat recf recf
+              |  Mn nat recf 
+
+function rec_exec :: "recf \<Rightarrow> nat list \<Rightarrow> nat"
+  where
+  "rec_exec z xs = 0" |
+  "rec_exec s xs = (Suc (xs ! 0))" |
+  "rec_exec (id m n) xs = (xs ! n)" |
+  "rec_exec (Cn n f gs) xs = 
+             (let ys = (map (\<lambda> a. rec_exec a xs) gs) in 
+                                  rec_exec f ys)" | 
+  "rec_exec (Pr n f g) xs = 
+     (if hd xs = 0 then 
+                  rec_exec f (tl xs)
+      else rec_exec g ((hd xs - 1) # tl xs @ [rec_exec (Pr n f g) ((hd xs - 1) # tl xs)]))" |
+  "rec_exec (Mn n f) xs = (LEAST x. rec_exec f (x # xs) = 0)"
+by pat_completeness auto
+
+termination
+apply(relation "measures [\<lambda> (r, xs). size r, (\<lambda> (r, xs). hd xs)]")
+apply(auto simp add: less_Suc_eq_le intro: trans_le_add2 list_size_estimation')
+done
+
+
+inductive terminate :: "recf \<Rightarrow> nat list \<Rightarrow> bool"
+  where
+  termi_z: "terminate z [n]"
+| termi_s: "terminate s [n]"
+| termi_id: "\<lbrakk>n < m; length xs = m\<rbrakk> \<Longrightarrow> terminate (id m n) xs"
+| termi_cn: "\<lbrakk>terminate f (map (\<lambda>g. rec_exec g xs) gs); 
+              \<forall>g \<in> set gs. terminate g xs; length xs = n\<rbrakk> \<Longrightarrow> terminate (Cn n f gs) xs"
+| termi_pr_0: "\<lbrakk>terminate f xs; length xs = n\<rbrakk> \<Longrightarrow> terminate (Pr n f g) (0 # xs)"
+| termi_pr_suc: "\<lbrakk>terminate (Pr n f gs) (x # xs);
+                  terminate g (x # rec_exec (Pr n f gs) (x # xs) # xs)\<rbrakk> 
+                  \<Longrightarrow> terminate (Pr n f gs) (Suc x # xs)"
+| termi_mn: "\<lbrakk>length xs = n; rec_exec f (r # xs) = 0;
+              \<forall> i < r. terminate f (i # xs) \<and> rec_exec f (i # xs) > 0\<rbrakk> \<Longrightarrow> terminate (Mn n f) xs"
+
+end
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