--- a/src/HOL/ex/Predicate_Compile_ex.thy Sat Oct 24 16:54:32 2009 +0200
+++ b/src/HOL/ex/Predicate_Compile_ex.thy Sat Oct 24 16:55:35 2009 +0200
@@ -31,6 +31,17 @@
values "{zs. append [0, Suc 0, 2] [17, 8] zs}"
values "{ys. append [0, Suc 0, 2] ys [0, Suc 0, 2, 17, 0,5]}"
+inductive tupled_append :: "'a list \<times> 'a list \<times> 'a list \<Rightarrow> bool"
+where
+ "tupled_append ([], xs, xs)"
+| "tupled_append (xs, ys, zs) \<Longrightarrow> tupled_append (x # xs, ys, x # zs)"
+
+code_pred tupled_append .
+
+thm tupled_append.equation
+(*
+values "{xs. tupled_append ([1,2,3], [4,5], xs)}"
+*)
inductive rev where
"rev [] []"
| "rev xs xs' ==> append xs' [x] ys ==> rev (x#xs) ys"
@@ -41,6 +52,13 @@
values "{xs. rev [0, 1, 2, 3::nat] xs}"
+inductive tupled_rev where
+ "tupled_rev ([], [])"
+| "tupled_rev (xs, xs') \<Longrightarrow> tupled_append (xs', [x], ys) \<Longrightarrow> tupled_rev (x#xs, ys)"
+
+code_pred tupled_rev .
+thm tupled_rev.equation
+
inductive partition :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> 'a list \<Rightarrow> 'a list \<Rightarrow> bool"
for f where
"partition f [] [] []"
@@ -49,8 +67,15 @@
code_pred partition .
-thm partition.equation
+inductive tupled_partition :: "('a \<Rightarrow> bool) \<Rightarrow> ('a list \<times> 'a list \<times> 'a list) \<Rightarrow> bool"
+ for f where
+ "tupled_partition f ([], [], [])"
+ | "f x \<Longrightarrow> tupled_partition f (xs, ys, zs) \<Longrightarrow> tupled_partition f (x # xs, x # ys, zs)"
+ | "\<not> f x \<Longrightarrow> tupled_partition f (xs, ys, zs) \<Longrightarrow> tupled_partition f (x # xs, ys, x # zs)"
+code_pred tupled_partition .
+
+thm tupled_partition.equation
inductive member
for xs
@@ -93,6 +118,7 @@
thm tranclp.equation
thm tranclp.rpred_equation
*)
+
inductive succ :: "nat \<Rightarrow> nat \<Rightarrow> bool" where
"succ 0 1"
| "succ m n \<Longrightarrow> succ (Suc m) (Suc n)"
@@ -141,6 +167,16 @@
(While (%s. s!0 > 0) (Seq (Ass 0 (%s. s!0 - 1)) (Ass 1 (%s. s!1 + 1))))
[3,5] t}"
+inductive tupled_exec :: "(com \<times> state \<times> state) \<Rightarrow> bool" where
+"tupled_exec (Skip, s, s)" |
+"tupled_exec (Ass x e, s, s[x := e(s)])" |
+"tupled_exec (c1, s1, s2) ==> tupled_exec (c2, s2, s3) ==> tupled_exec (Seq c1 c2, s1, s3)" |
+"b s ==> tupled_exec (c1, s, t) ==> tupled_exec (IF b c1 c2, s, t)" |
+"~b s ==> tupled_exec (c2, s, t) ==> tupled_exec (IF b c1 c2, s, t)" |
+"~b s ==> tupled_exec (While b c, s, s)" |
+"b s1 ==> tupled_exec (c, s1, s2) ==> tupled_exec (While b c, s2, s3) ==> tupled_exec (While b c, s1, s3)"
+
+code_pred tupled_exec .
subsection{* CCS *}
@@ -171,6 +207,17 @@
values 3 "{(a,q). step (par nil nil) a q}"
*)
+inductive tupled_step :: "(proc \<times> nat \<times> proc) \<Rightarrow> bool"
+where
+"tupled_step (pre n p, n, p)" |
+"tupled_step (p1, a, q) \<Longrightarrow> tupled_step (or p1 p2, a, q)" |
+"tupled_step (p2, a, q) \<Longrightarrow> tupled_step (or p1 p2, a, q)" |
+"tupled_step (p1, a, q) \<Longrightarrow> tupled_step (par p1 p2, a, par q p2)" |
+"tupled_step (p2, a, q) \<Longrightarrow> tupled_step (par p1 p2, a, par p1 q)"
+
+code_pred tupled_step .
+thm tupled_step.equation
+
subsection {* divmod *}
inductive divmod_rel :: "nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" where