(* 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