src/HOL/ex/BT.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/BT.thy	Thu Jun 29 16:16:24 1995 +0200
@@ -0,0 +1,50 @@
+(*  Title: 	HOL/ex/BT.thy
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   1995  University of Cambridge
+
+Binary trees (based on the ZF version)
+*)
+
+BT = List +
+
+datatype 'a bt = Lf  |  Br 'a ('a bt) ('a bt)
+  
+consts
+    n_nodes	:: "'a bt => nat"
+    n_leaves   	:: "'a bt => nat"
+    reflect 	:: "'a bt => 'a bt"
+    bt_map      :: "('a=>'b) => ('a bt => 'b bt)"
+    preorder    :: "'a bt => 'a list"
+    inorder     :: "'a bt => 'a list"
+    postorder   :: "'a bt => 'a list"
+
+primrec n_nodes bt
+  n_nodes_Lf "n_nodes (Lf) = 0"
+  n_nodes_Br "n_nodes (Br a t1 t2) = Suc(n_nodes t1 + n_nodes t2)"
+
+primrec n_leaves bt
+  n_leaves_Lf "n_leaves (Lf) = Suc 0"
+  n_leaves_Br "n_leaves (Br a t1 t2) = n_leaves t1 + n_leaves t2"
+
+primrec reflect bt
+  reflect_Lf "reflect (Lf) = Lf"
+  reflect_Br "reflect (Br a t1 t2) = Br a (reflect t2) (reflect t1)"
+
+primrec bt_map bt
+  bt_map_Lf  "bt_map f Lf = Lf"
+  bt_map_Br  "bt_map f (Br a t1 t2) = Br (f a) (bt_map f t1) (bt_map f t2)"
+
+primrec preorder bt
+  preorder_Lf "preorder (Lf) = []"
+  preorder_Br "preorder (Br a t1 t2) = [a] @ (preorder t1) @ (preorder t2)"
+
+primrec inorder bt
+  inorder_Lf "inorder (Lf) = []"
+  inorder_Br "inorder (Br a t1 t2) = (inorder t1) @ [a] @ (inorder t2)"
+
+primrec postorder bt
+  postorder_Lf "postorder (Lf) = []"
+  postorder_Br "postorder (Br a t1 t2) = (postorder t1) @ (postorder t2) @ [a]"
+
+end