A variant of stack in which one other cactus stack may be attached to the top. An attached stack is called a "branch." When a branch becomes empty, it is removed. Pop is not allowed if there is a branch. A branch is only accessible through the original reference; it is not accessible through the stack. Formal Definition: The operations new to this variant of stack, branch(S, T) and notch(v), may be defined with axiomatic semantics as follows.

1. top(branch(S, T)) = top(S)
2. notch(new()) = false
3. notch(push(v, S)) = false
4. notch(branch(S, T)) = true