# Stream SΒΆ

- S: Type

A stream is an implementation of a possibly infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.

- <: (%, %) -> 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

- coerce: List S -> %
`coerce(l)`

converts a list`l`

to a stream.- complete: % -> %
- from LazyStreamAggregate S
- concat: (%, %) -> %
- from LinearAggregate S
- concat: (%, S) -> %
- from LinearAggregate S
- concat: (S, %) -> %
- from LinearAggregate S
- concat: List % -> %
- from LinearAggregate S

- cons: (S, %) -> %
`cons(a, s)`

returns a stream whose`first`

is`a`

and whose`rest`

is`s`

. Note:`cons(a, s) = concat(a, s)`

.- construct: List S -> %
- from Collection S
- convert: % -> InputForm if S has ConvertibleTo InputForm
- from ConvertibleTo InputForm
- copy: % -> %
- from Aggregate
- 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

- delay: () -> % -> %
`delay(f)`

creates a stream with a lazy evaluation defined by function`f`

. Caution: This function can only be called in compiled code.- 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)
- explicitEntries?: % -> Boolean
- from LazyStreamAggregate S
- explicitlyEmpty?: % -> Boolean
- from LazyStreamAggregate S
- explicitlyFinite?: % -> Boolean
- from StreamAggregate S
- extend: (%, Integer) -> %
- from LazyStreamAggregate S

- filterUntil: (S -> Boolean, %) -> %
`filterUntil(p, s)`

returns`[x0, x1, ..., x(n)]`

where`s = [x0, x1, x2, ..]`

and`n`

is the smallest index such that`p(xn) = true`

.

- filterWhile: (S -> Boolean, %) -> %
`filterWhile(p, s)`

returns`[x0, x1, ..., x(n-1)]`

where`s = [x0, x1, x2, ..]`

and`n`

is the smallest index such that`p(xn) = false`

.- find: (S -> Boolean, %) -> Union(S, failed)
- from Collection S

- findCycle: (NonNegativeInteger, %) -> Record(cycle?: Boolean, prefix: NonNegativeInteger, period: NonNegativeInteger)
`findCycle(n, st)`

determines if st is periodic within`n`

.- first: % -> S
- from IndexedAggregate(Integer, S)
- first: (%, NonNegativeInteger) -> %
- from UnaryRecursiveAggregate S
- frst: % -> S
- from LazyStreamAggregate 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
- lazy?: % -> Boolean
- from LazyStreamAggregate S
- lazyEvaluate: % -> %
- from LazyStreamAggregate S
- 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
- numberOfComputedEntries: % -> NonNegativeInteger
- from LazyStreamAggregate 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
- from StreamAggregate 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 -> Boolean, %) -> %
- from LazyStreamAggregate S
- remove: (S, %) -> % if S has BasicType and % has finiteAggregate
- from Collection S
- removeDuplicates: % -> % if S has BasicType and % has finiteAggregate
- from Collection S

- repeating: List S -> %
`repeating(l)`

is a repeating stream whose period is the list`l`

.

- repeating?: (List S, %) -> Boolean if S has SetCategory
`repeating?(l, s)`

returns`true`

if a stream`s`

is periodic with period`l`

, and`false`

otherwise.- rest: % -> %
- from UnaryRecursiveAggregate S
- rest: (%, NonNegativeInteger) -> %
- from UnaryRecursiveAggregate S
- rightTrim: (%, S) -> % if S has BasicType and % has finiteAggregate
- from LinearAggregate S
- rst: % -> %
- from LazyStreamAggregate S
- sample: %
- from Aggregate
- second: % -> S
- from UnaryRecursiveAggregate S
- select: (S -> Boolean, %) -> %
- from LazyStreamAggregate S

- setrest!: (%, Integer, %) -> %
`setrest!(x, n, y)`

sets rest(`x`

,`n`

) to`y`

. The function will expand cycles if necessary.

- showAll?: () -> Boolean if S has SetCategory
`showAll?()`

returns`true`

if all computed entries of streams will be displayed.

- showAllElements: % -> OutputForm if S has SetCategory
`showAllElements(s)`

creates an output form which displays all computed elements.

- showElements: (NonNegativeInteger, %) -> OutputForm if S has SetCategory
`showElements(n, st)`

computes and creates and output form of the first`n`

entries of st.- 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 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

- stream: () -> S -> %
`stream(f)`

creates an infinite stream all of whose elements are equal to`f()`

. Note:`stream(f) = [f(), f(), f(), ...]`

.

- stream: (S -> S, S) -> %
`stream(f, x)`

creates an infinite stream whose first element is`x`

and whose`n`

th element (`n > 1`

) is`f`

applied to the previous element. Note:`stream(f, x) = [x, f(x), f(f(x)), ...]`

.- 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