What are Axioms of a binary tree?

Answer 1

A binary tree is a finite set of nodes which is either empty or consists of a root and two disjoint binary trees called the left subtree and the right subtree.

We can define the data structure binary tree as follows:

structure BTREE

declare CREATE( ) --> btree

ISMTBT(btree,item,btree) --> boolean

MAKEBT(btree,item,btree) --> btree

LCHILD(btree) --> btree

DATA(btree) --> item

RCHILD(btree) --> btree

for all p,r in btree, d in item let

ISMTBT(CREATE)::=true

ISMTBT(MAKEBT(p,d,r))::=false

LCHILD(MAKEBT(p,d,r))::=p; LCHILD(CREATE)::=error

DATA(MAKEBT(p,d,r))::d; DATA(CREATE)::=error

RCHILD(MAKEBT(p,d,r))::=r; RCHILD(CREATE)::=error

end

end BTREE