# BinaryTree SΒΆ

- S: SetCategory

BinaryTree(S) is the domain of all binary trees. A binary tree over `S`

is either empty or has a value which is an `S`

and a right and left which are both BinaryTree(`S`

).

- binaryTree: (%, S, %) -> %
`binaryTree(l, v, r)`

creates a binary tree with value`v`

and left subtree`l`

and right subtree`r`

.

- binaryTree: S -> %
`binaryTree(v)`

is an non-empty binary tree with value`v`

, and left and right empty.- child?: (%, %) -> Boolean
- from RecursiveAggregate S
- children: % -> List %
- from RecursiveAggregate S
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- copy: % -> %
- from Aggregate
- count: (S, %) -> NonNegativeInteger
- from HomogeneousAggregate S
- cyclic?: % -> Boolean
- from RecursiveAggregate S
- distance: (%, %) -> Integer
- from RecursiveAggregate S
- elt: (%, left) -> %
- from BinaryRecursiveAggregate S
- elt: (%, right) -> %
- from BinaryRecursiveAggregate S
- elt: (%, value) -> S
- from RecursiveAggregate S
- empty: () -> %
- from Aggregate
- empty?: % -> Boolean
- from Aggregate
- eq?: (%, %) -> Boolean
- from Aggregate
- eval: (%, Equation S) -> % if S has Evalable S
- from Evalable S
- eval: (%, List Equation S) -> % if S has Evalable S
- from Evalable S
- eval: (%, List S, List S) -> % if S has Evalable S
- from InnerEvalable(S, S)
- eval: (%, S, S) -> % if S has Evalable S
- from InnerEvalable(S, S)
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- latex: % -> String
- from SetCategory
- leaf?: % -> Boolean
- from RecursiveAggregate S
- leaves: % -> List S
- from RecursiveAggregate S
- left: % -> %
- from BinaryRecursiveAggregate S
- less?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- map: (S -> S, %) -> %
- from HomogeneousAggregate S
- member?: (S, %) -> Boolean
- from HomogeneousAggregate S
- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- node: (%, S, %) -> %
- from BinaryTreeCategory S
- node?: (%, %) -> Boolean
- from RecursiveAggregate S
- nodes: % -> List %
- from RecursiveAggregate S
- right: % -> %
- from BinaryRecursiveAggregate S
- sample: %
- from Aggregate
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- value: % -> S
- from RecursiveAggregate S

Evalable S if S has Evalable S

InnerEvalable(S, S) if S has Evalable S