# StreamAggregate SΒΆ

- S: Type

A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is Stream. From streams, a number of infinite structures such as power series can be built.

- <: (%, %) -> Boolean if S has OrderedSet and % has finiteAggregate
- from PartialOrder
- <=: (%, %) -> Boolean if S has OrderedSet and % has finiteAggregate
- from PartialOrder
- =: (%, %) -> Boolean if S has SetCategory or S has BasicType and % has finiteAggregate
- from BasicType
- >: (%, %) -> Boolean if S has OrderedSet and % has finiteAggregate
- from PartialOrder
- >=: (%, %) -> Boolean if S has OrderedSet and % has finiteAggregate
- from PartialOrder
- ~=: (%, %) -> Boolean if S has SetCategory or S has BasicType and % has finiteAggregate
- from BasicType
- child?: (%, %) -> Boolean if S has BasicType
- from RecursiveAggregate S
- children: % -> List %
- from RecursiveAggregate S
- coerce: % -> OutputForm if S has CoercibleTo OutputForm
- from CoercibleTo OutputForm
- concat: (%, %) -> %
- from LinearAggregate S
- concat: (%, S) -> %
- from LinearAggregate S
- concat: (S, %) -> %
- from LinearAggregate S
- concat: List % -> %
- from LinearAggregate S
- construct: List S -> %
- from Collection S
- convert: % -> InputForm if S has ConvertibleTo InputForm
- from ConvertibleTo InputForm
- copy: % -> %
- from Aggregate
- copyInto!: (%, %, Integer) -> % if % has shallowlyMutable and % has finiteAggregate
- from LinearAggregate S
- count: (S, %) -> NonNegativeInteger if S has BasicType and % has finiteAggregate
- from HomogeneousAggregate S
- cycleEntry: % -> %
- from UnaryRecursiveAggregate S
- cycleLength: % -> NonNegativeInteger
- from UnaryRecursiveAggregate S
- cycleTail: % -> %
- from UnaryRecursiveAggregate S
- cyclic?: % -> Boolean
- from RecursiveAggregate S
- delete: (%, Integer) -> %
- from LinearAggregate S
- delete: (%, UniversalSegment Integer) -> %
- from LinearAggregate S
- distance: (%, %) -> Integer
- from RecursiveAggregate S
- elt: (%, first) -> S
- from UnaryRecursiveAggregate S
- elt: (%, Integer) -> S
- from Eltable(Integer, S)
- elt: (%, Integer, S) -> S
- from EltableAggregate(Integer, S)
- elt: (%, last) -> S
- from UnaryRecursiveAggregate S
- elt: (%, rest) -> %
- from UnaryRecursiveAggregate S
- elt: (%, UniversalSegment Integer) -> %
- from Eltable(UniversalSegment Integer, %)
- elt: (%, value) -> S
- from RecursiveAggregate S
- empty: () -> %
- from Aggregate
- empty?: % -> Boolean
- from Aggregate
- entries: % -> List S
- from IndexedAggregate(Integer, S)
- entry?: (S, %) -> Boolean if S has BasicType and % has finiteAggregate
- from IndexedAggregate(Integer, S)
- eq?: (%, %) -> Boolean
- from Aggregate
- eval: (%, Equation S) -> % if S has Evalable S and S has SetCategory
- from Evalable S
- eval: (%, List Equation S) -> % if S has Evalable S and S has SetCategory
- from Evalable S
- eval: (%, List S, List S) -> % if S has Evalable S and S has SetCategory
- from InnerEvalable(S, S)
- eval: (%, S, S) -> % if S has Evalable S and S has SetCategory
- from InnerEvalable(S, S)

- explicitlyFinite?: % -> Boolean
`explicitlyFinite?(s)`

tests if the stream has a finite number of elements, and`false`

otherwise. Note: for many datatypes,`explicitlyFinite?(s) = not possiblyInfinite?(s)`

.- find: (S -> Boolean, %) -> Union(S, failed)
- from Collection S
- first: % -> S
- from IndexedAggregate(Integer, S)
- first: (%, NonNegativeInteger) -> %
- from UnaryRecursiveAggregate S
- hash: % -> SingleInteger if S has SetCategory
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState if S has SetCategory
- from SetCategory
- index?: (Integer, %) -> Boolean
- from IndexedAggregate(Integer, S)
- indices: % -> List Integer
- from IndexedAggregate(Integer, S)
- insert: (%, %, Integer) -> %
- from LinearAggregate S
- insert: (S, %, Integer) -> %
- from LinearAggregate S
- last: % -> S
- from UnaryRecursiveAggregate S
- last: (%, NonNegativeInteger) -> %
- from UnaryRecursiveAggregate S
- latex: % -> String if S has SetCategory
- from SetCategory
- leaf?: % -> Boolean
- from RecursiveAggregate S
- leaves: % -> List S
- from RecursiveAggregate S
- leftTrim: (%, S) -> % if S has BasicType and % has finiteAggregate
- from LinearAggregate S
- less?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- map: ((S, S) -> S, %, %) -> %
- from LinearAggregate S
- map: (S -> S, %) -> %
- from HomogeneousAggregate S
- max: (%, %) -> % if S has OrderedSet and % has finiteAggregate
- from OrderedSet
- maxIndex: % -> Integer
- from IndexedAggregate(Integer, S)
- member?: (S, %) -> Boolean if S has BasicType and % has finiteAggregate
- from HomogeneousAggregate S
- merge: (%, %) -> % if S has OrderedSet and % has finiteAggregate
- from LinearAggregate S
- min: (%, %) -> % if S has OrderedSet and % has finiteAggregate
- from OrderedSet
- minIndex: % -> Integer
- from IndexedAggregate(Integer, S)
- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- new: (NonNegativeInteger, S) -> %
- from LinearAggregate S
- node?: (%, %) -> Boolean if S has BasicType
- from RecursiveAggregate S
- nodes: % -> List %
- from RecursiveAggregate S
- position: (S, %) -> Integer if S has BasicType and % has finiteAggregate
- from LinearAggregate S
- position: (S, %, Integer) -> Integer if S has BasicType and % has finiteAggregate
- from LinearAggregate S

- possiblyInfinite?: % -> Boolean
`possiblyInfinite?(s)`

tests if the stream`s`

could possibly have an infinite number of elements. Note: for many datatypes,`possiblyInfinite?(s) = not explictlyFinite?(s)`

.- qelt: (%, Integer) -> S
- from EltableAggregate(Integer, S)
- reduce: ((S, S) -> S, %, S, S) -> S if S has BasicType and % has finiteAggregate
- from Collection S
- remove: (S, %) -> % if S has BasicType and % has finiteAggregate
- from Collection S
- removeDuplicates: % -> % if S has BasicType and % has finiteAggregate
- from Collection S
- rest: % -> %
- from UnaryRecursiveAggregate S
- rest: (%, NonNegativeInteger) -> %
- from UnaryRecursiveAggregate S
- reverse!: % -> % if % has shallowlyMutable and % has finiteAggregate
- from LinearAggregate S
- rightTrim: (%, S) -> % if S has BasicType and % has finiteAggregate
- from LinearAggregate S
- sample: %
- from Aggregate
- second: % -> S
- from UnaryRecursiveAggregate S
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- smaller?: (%, %) -> Boolean if S has Comparable and % has finiteAggregate or S has OrderedSet and % has finiteAggregate
- from Comparable
- sort!: % -> % if S has OrderedSet and % has shallowlyMutable and % has finiteAggregate
- from LinearAggregate S
- sort!: ((S, S) -> Boolean, %) -> % if % has shallowlyMutable and % has finiteAggregate
- from LinearAggregate S
- sort: % -> % if S has OrderedSet and % has finiteAggregate
- from LinearAggregate S
- sorted?: % -> Boolean if S has OrderedSet and % has finiteAggregate
- from LinearAggregate S
- tail: % -> %
- from UnaryRecursiveAggregate S
- third: % -> S
- from UnaryRecursiveAggregate S
- trim: (%, S) -> % if S has BasicType and % has finiteAggregate
- from LinearAggregate S
- value: % -> S
- from RecursiveAggregate S

BasicType if S has SetCategory or S has BasicType and % has finiteAggregate

CoercibleTo OutputForm if S has CoercibleTo OutputForm

Comparable if S has Comparable and % has finiteAggregate or S has OrderedSet and % has finiteAggregate

ConvertibleTo InputForm if S has ConvertibleTo InputForm

Eltable(UniversalSegment Integer, %)

Evalable S if S has Evalable S and S has SetCategory

InnerEvalable(S, S) if S has Evalable S and S has SetCategory

OrderedSet if S has OrderedSet and % has finiteAggregate

PartialOrder if S has OrderedSet and % has finiteAggregate

SetCategory if S has SetCategory