
diff -r 7d1127ac2251 -r cd82b1023932 src/HOL/Data_Structures/Tree23.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Data_Structures/Tree23.thy	Sun Oct 18 17:25:13 2015 +0200
@@ -0,0 +1,43 @@
+(* Author: Tobias Nipkow *)
+
+section \<open>2-3 Trees\<close>
+
+theory Tree23
+imports Main
+begin
+
+class height =
+fixes height :: "'a \<Rightarrow> nat"
+
+datatype 'a tree23 =
+  Leaf |
+  Node2 "'a tree23" 'a "'a tree23" |
+  Node3 "'a tree23" 'a "'a tree23" 'a "'a tree23"
+
+fun inorder :: "'a tree23 \<Rightarrow> 'a list" where
+"inorder Leaf = []" |
+"inorder(Node2 l a r) = inorder l @ a # inorder r" |
+"inorder(Node3 l a m b r) = inorder l @ a # inorder m @ b # inorder r"
+
+
+instantiation tree23 :: (type)height
+begin
+
+fun height_tree23 :: "'a tree23 \<Rightarrow> nat" where
+"height Leaf = 0" |
+"height (Node2 l _ r) = Suc(max (height l) (height r))" |
+"height (Node3 l _ m _ r) = Suc(max (height l) (max (height m) (height r)))"
+
+instance ..
+
+end
+
+text \<open>Balanced:\<close>
+
+fun bal :: "'a tree23 \<Rightarrow> bool" where
+"bal Leaf = True" |
+"bal (Node2 l _ r) = (bal l & bal r & height l = height r)" |
+"bal (Node3 l _ m _ r) =
+  (bal l & bal m & bal r & height l = height m & height m = height r)"
+
+end




