# Collection S¶

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S: Type

A collection is a homogeneous aggregate which can be built from a list of members. The operation used to build the aggregate is generically named construct. However, each collection provides its own special function with the same name as the data type, except with an initial lower case letter, e.g. list for List, flexibleArray for FlexibleArray, and so on.

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

- =: (%, %) -> Boolean if % has finiteAggregate and S has BasicType or S has SetCategory
from BasicType

- ~=: (%, %) -> Boolean if % has finiteAggregate and S has BasicType or S has SetCategory
from BasicType

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

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

- construct: List S -> %
`construct([x, y, ..., z])`

returns the collection of elements`x, y, ..., z`

ordered as given. Equivalently written as`[x, y, ..., z]\$D`

, where`D`

is the domain.`D`

may be omitted for those of type List.

- convert: % -> InputForm if S has ConvertibleTo InputForm
from ConvertibleTo InputForm

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

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

- eval: (%, Equation S) -> % if S has SetCategory and S has Evalable S
from Evalable S

- eval: (%, List Equation S) -> % if S has SetCategory and S has Evalable S
from Evalable S

- eval: (%, List S, List S) -> % if S has SetCategory and S has Evalable S
from InnerEvalable(S, S)

- eval: (%, S, S) -> % if S has SetCategory and S has Evalable S
from InnerEvalable(S, S)

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

- find: (S -> Boolean, %) -> Union(S, failed)
`find(p, u)`

returns the first`x`

in`u`

such that`p(x)`

is`true`

, and “failed” otherwise.

- hash: % -> SingleInteger if S has SetCategory
from SetCategory

- hashUpdate!: (HashState, %) -> HashState if S has SetCategory
from SetCategory

- latex: % -> String if S has SetCategory
from SetCategory

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

- map!: (S -> S, %) -> % if % has shallowlyMutable
from HomogeneousAggregate S

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

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

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

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

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

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

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

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

- reduce: ((S, S) -> S, %) -> S if % has finiteAggregate
`reduce(f, u)`

reduces the binary operation`f`

across`u`

. For example, if`u`

is`[x, y, ..., z]`

then`reduce(f, u)`

returns`f(..f(f(x, y), ...), z)`

. Note: if`u`

has one element`x`

,`reduce(f, u)`

returns`x`

. Error: if`u`

is empty.

- reduce: ((S, S) -> S, %, S) -> S if % has finiteAggregate
`reduce(f, u, x)`

reduces the binary operation`f`

across`u`

, where`x`

is the identity operation of`f`

. Same as`reduce(f, u)`

if`u`

has 2 or more elements. Returns`f(y, x)`

if`u`

has one element`y`

. Returns`x`

if`u`

is empty. For example,`reduce(+, u, 0)`

returns the sum of the elements of`u`

.

- reduce: ((S, S) -> S, %, S, S) -> S if % has finiteAggregate and S has BasicType
`reduce(f, u, x, z)`

reduces the binary operation`f`

across`u`

, stopping when an “absorbing element”`z`

is encountered. As for`reduce(f, u, x)`

,`x`

is the identity element of`f`

. Same as`reduce(f, u, x)`

when`u`

contains no element`z`

. Thus the third argument`x`

is returned when`u`

is empty.

- remove: (S -> Boolean, %) -> % if % has finiteAggregate
`remove(p, u)`

returns a copy of`u`

removing all elements`x`

such that`p(x)`

is`true`

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

.

- remove: (S, %) -> % if % has finiteAggregate and S has BasicType
`remove(x, u)`

returns a copy of`u`

with all elements equal to`x`

removed. Note:`remove(x, u) = [y for y in u | y ~= x]`

.

- removeDuplicates: % -> % if % has finiteAggregate and S has BasicType
`removeDuplicates(u)`

returns a copy of`u`

with all duplicates removed.

- select: (S -> Boolean, %) -> % if % has finiteAggregate
`select(p, u)`

returns a copy of`u`

containing only those elements such`p(x)`

is`true`

. Note:`select(p, u) = [x for x in u | p(x)]`

.

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

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

CoercibleTo OutputForm if S has CoercibleTo OutputForm

ConvertibleTo InputForm if S has ConvertibleTo InputForm

Evalable S if S has SetCategory and S has Evalable S

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

SetCategory if S has SetCategory