# LazyStreamAggregate S¶

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S: Type

LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function ‘empty?’ will cause lazy evaluation if necessary to determine if there are entries. Functions which call ‘empty?’, e.g. ‘first’ and ‘rest’, will also cause lazy evaluation if necessary. Elements of LazyStreamAggregate are computed only when strictly needed. Lazy computation means that potential errors are delayed, so errors are detected later than in case of normal (eager) evaluation used by other aggregates. In some cases computation that would signal error when using eager evaluation can succeed when using lazy evaluation.

- #: % -> NonNegativeInteger if % has finiteAggregate
from Aggregate

- <=: (%, %) -> 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 or S has Hashable 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 or S has Hashable and % has finiteAggregate
from BasicType

- any?: (S -> Boolean, %) -> Boolean if % has finiteAggregate
from HomogeneousAggregate S

- child?: (%, %) -> Boolean if S has BasicType
from RecursiveAggregate S

- children: % -> List %
from RecursiveAggregate S

- coerce: % -> OutputForm if S has CoercibleTo OutputForm
from CoercibleTo OutputForm

- complete: % -> %
`complete(st)`

causes all entries of ‘st’ to be computed. this function should only be called on streams which are known to be finite.

- concat!: (%, %) -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- concat!: (%, S) -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- concat!: List % -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- 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

- copyInto!: (%, %, Integer) -> % if % has finiteAggregate and % has shallowlyMutable
from LinearAggregate S

- count: (S -> Boolean, %) -> NonNegativeInteger if % has finiteAggregate
from HomogeneousAggregate S

- count: (S, %) -> NonNegativeInteger if S has BasicType and % has finiteAggregate
from HomogeneousAggregate S

- cycleEntry: % -> %
from UnaryRecursiveAggregate S

- cycleLength: % -> NonNegativeInteger
from UnaryRecursiveAggregate S

- cycleSplit!: % -> % if % has shallowlyMutable
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
- 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

- entries: % -> List S
from IndexedAggregate(Integer, S)

- entry?: (S, %) -> Boolean if S has BasicType and % has finiteAggregate
from IndexedAggregate(Integer, S)

- 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)

- every?: (S -> Boolean, %) -> Boolean if % has finiteAggregate
from HomogeneousAggregate S

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

returns`true`

if the stream`s`

has explicitly computed entries, and`false`

otherwise.

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

returns`true`

if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.

- explicitlyFinite?: % -> Boolean
from StreamAggregate S

- extend: (%, Integer) -> %
`extend(st, n)`

causes entries to be computed, if necessary, so that ‘st’ will have at least`'n'`

explicit entries or so that all entries of ‘st’ will be computed if ‘st’ is finite with length`<=`

`n`

.

- fill!: (%, S) -> % if % has shallowlyMutable
from IndexedAggregate(Integer, S)

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

- first: % -> S
from IndexedAggregate(Integer, S)

- first: (%, NonNegativeInteger) -> %
from LinearAggregate S

- frst: % -> S
`frst(s)`

returns the first element of stream`s`

. Caution: this function should only be called after a`empty?`

test has been made since there is no error check.

- hash: % -> SingleInteger if S has Hashable and % has finiteAggregate
from Hashable

- hashUpdate!: (HashState, %) -> HashState if S has Hashable and % has finiteAggregate
from Hashable

- 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
`lazy?(s)`

returns`true`

if the first node of the stream`s`

is a lazy evaluation mechanism which could produce an additional entry to`s`

.

- lazyEvaluate: % -> %
`lazyEvaluate(s)`

causes one lazy evaluation of stream`s`

. Caution: the first node must be a lazy evaluation mechanism (satisfies`lazy?(s) = true`

) as there is no error check. Note: a call to this function may or may not produce an explicit first entry

- 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, %) -> % if % has shallowlyMutable
from HomogeneousAggregate S

- map: ((S, S) -> S, %, %) -> %
from LinearAggregate S

- map: (S -> S, %) -> %
from HomogeneousAggregate S

- max: % -> S if S has OrderedSet and % has finiteAggregate
from HomogeneousAggregate S

- max: (%, %) -> % if S has OrderedSet and % has finiteAggregate
from OrderedSet

- max: ((S, S) -> Boolean, %) -> S if % has finiteAggregate
from HomogeneousAggregate S

- maxIndex: % -> Integer
from IndexedAggregate(Integer, S)

- member?: (S, %) -> Boolean if S has BasicType and % has finiteAggregate
from HomogeneousAggregate S

- members: % -> List S if % has finiteAggregate
from HomogeneousAggregate S

- merge: (%, %) -> % if S has OrderedSet and % has finiteAggregate
from LinearAggregate S

- merge: ((S, S) -> Boolean, %, %) -> % if % has finiteAggregate
from LinearAggregate S

- min: % -> S if S has OrderedSet and % has finiteAggregate
from HomogeneousAggregate 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
`numberOfComputedEntries(st)`

returns the number of explicitly computed entries of stream`st`

which exist immediately prior to the time this function is called.

- parts: % -> List S if % has finiteAggregate
from HomogeneousAggregate S

- position: (S -> Boolean, %) -> Integer if % has finiteAggregate
from LinearAggregate 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)

- qsetelt!: (%, Integer, S) -> S if % has shallowlyMutable
from EltableAggregate(Integer, S)

- qsetfirst!: (%, S) -> S if % has shallowlyMutable
from UnaryRecursiveAggregate S

- qsetrest!: (%, %) -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- reduce: ((S, S) -> S, %) -> S if % has finiteAggregate
from Collection S

- reduce: ((S, S) -> S, %, S) -> S if % has finiteAggregate
from Collection S

- reduce: ((S, S) -> S, %, S, S) -> S if S has BasicType and % has finiteAggregate
from Collection S

- remove: (S -> Boolean, %) -> %
`remove(f, st)`

returns a stream consisting of those elements of stream st which do not satisfy the predicate`f`

. Note:`remove(f, st) = [x for x in st | not f(x)]`

.- 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 finiteAggregate and % has shallowlyMutable
from LinearAggregate S

- reverse: % -> % if % has finiteAggregate
from LinearAggregate S

- rightTrim: (%, S) -> % if S has BasicType and % has finiteAggregate
from LinearAggregate S

- rst: % -> %
`rst(s)`

returns a pointer to the next node of stream`s`

. Caution: this function should only be called after a`empty?`

test has been made since there is no error check.

- second: % -> S
from UnaryRecursiveAggregate S

- select: (S -> Boolean, %) -> %
`select(f, st)`

returns a stream consisting of those elements of stream st satisfying the predicate`f`

. Note:`select(f, st) = [x for x in st | f(x)]`

.

- setchildren!: (%, List %) -> % if % has shallowlyMutable
from RecursiveAggregate S

- setelt!: (%, first, S) -> S if % has shallowlyMutable
from UnaryRecursiveAggregate S

- setelt!: (%, Integer, S) -> S if % has shallowlyMutable
from EltableAggregate(Integer, S)

- setelt!: (%, last, S) -> S if % has shallowlyMutable
from UnaryRecursiveAggregate S

- setelt!: (%, rest, %) -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- setelt!: (%, UniversalSegment Integer, S) -> S if % has shallowlyMutable
from LinearAggregate S

- setelt!: (%, value, S) -> S if % has shallowlyMutable
from RecursiveAggregate S

- setfirst!: (%, S) -> S if % has shallowlyMutable
from UnaryRecursiveAggregate S

- setlast!: (%, S) -> S if % has shallowlyMutable
from UnaryRecursiveAggregate S

- setrest!: (%, %) -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- setvalue!: (%, S) -> S if % has shallowlyMutable
from RecursiveAggregate S

- size?: (%, NonNegativeInteger) -> Boolean
from Aggregate

- smaller?: (%, %) -> Boolean if S has OrderedSet and % has finiteAggregate or % has finiteAggregate and S has Comparable
from Comparable

- sort!: % -> % if S has OrderedSet and % has finiteAggregate and % has shallowlyMutable
from LinearAggregate S

- sort!: ((S, S) -> Boolean, %) -> % if % has finiteAggregate and % has shallowlyMutable
from LinearAggregate S

- sort: % -> % if S has OrderedSet and % has finiteAggregate
from LinearAggregate S

- sort: ((S, S) -> Boolean, %) -> % if % has finiteAggregate
from LinearAggregate S

- sorted?: % -> Boolean if S has OrderedSet and % has finiteAggregate
from LinearAggregate S

- sorted?: ((S, S) -> Boolean, %) -> Boolean if % has finiteAggregate
from LinearAggregate S

- split!: (%, NonNegativeInteger) -> % if % has shallowlyMutable
from UnaryRecursiveAggregate S

- swap!: (%, Integer, Integer) -> Void if % has shallowlyMutable
from IndexedAggregate(Integer, 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 BasicType and % has finiteAggregate or S has SetCategory or S has Hashable and % has finiteAggregate

CoercibleTo OutputForm if S has CoercibleTo OutputForm

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

ConvertibleTo InputForm if S has ConvertibleTo InputForm

Eltable(UniversalSegment Integer, %)

Evalable S if S has Evalable S and S has SetCategory

Hashable if S has Hashable and % has finiteAggregate

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