sanctuary-identity

Identity is the simplest container type: a value of type Identity a
always contains exactly one value, of type a.

Identity a satisfies the following [Fantasy Land][] specifications:

``javascript
> const Useless = require ('sanctuary-useless')

> const isTypeClass = x =>
. type (x) === 'sanctuary-type-classes/TypeClass@1'

> S.map (k => k + ' '.repeat (16 - k.length) +
. (Z[k].test (Identity (Useless)) ? '\u2705 ' :
. Z[k].test (Identity (['foo'])) ? '\u2705 * ' :
. / otherwise / '\u274C '))
. (S.keys (S.unchecked.filter (isTypeClass) (Z)))
[ 'Setoid ✅ * ', // if ‘a’ satisfies Setoid
. 'Ord ✅ * ', // if ‘a’ satisfies Ord
. 'Semigroupoid ❌ ',
. 'Category ❌ ',
. 'Semigroup ✅ * ', // if ‘a’ satisfies Semigroup
. 'Monoid ❌ ',
. 'Group ❌ ',
. 'Filterable ❌ ',
. 'Functor ✅ ',
. 'Bifunctor ❌ ',
. 'Profunctor ❌ ',
. 'Apply ✅ ',
. 'Applicative ✅ ',
. 'Chain ✅ ',
. 'ChainRec ✅ ',
. 'Monad ✅ ',
. 'Alt ❌ ',
. 'Plus ❌ ',
. 'Alternative ❌ ',
. 'Foldable ✅ ',
. 'Traversable ✅ ',
. 'Extend ✅ ',
. 'Comonad ✅ ',
. 'Contravariant ❌ ' ]
`

#### Identity :: a -⁠> Identity a

Identity's sole data constructor. Additionally, it serves as the
Identity [type representative][].

`javascript
> Identity (42)
Identity (42)
`

#### Identity.fantasy-land/of :: a -⁠> Identity a

of (Identity) (x) is equivalent to Identity (x).

`javascript
> S.of (Identity) (42)
Identity (42)
`

#### Identity.fantasy-land/chainRec :: ((a -⁠> c, b -⁠> c, a) -⁠> Identity c, a) -⁠> Identity b

`javascript
> Z.chainRec (
. Identity,
. (next, done, x) => Identity (x >= 0 ? done (x * x) : next (x + 1)),
. 8
. )
Identity (64)

> Z.chainRec (
. Identity,
. (next, done, x) => Identity (x >= 0 ? done (x * x) : next (x + 1)),
. -8
. )
Identity (0)
`

#### Identity#@@show :: Showable a => Identity a ~> () -⁠> String

show (Identity (x)) is equivalent to 'Identity (' + show (x) + ')'.

`javascript
> show (Identity (['foo', 'bar', 'baz']))
'Identity (["foo", "bar", "baz"])'
`

#### Identity#fantasy-land/equals :: Setoid a => Identity a ~> Identity a -⁠> Boolean

Identity (x) is equal to Identity (y) [iff][] x is equal to y
according to [Z.equals][].

`javascript
> S.equals (Identity ([1, 2, 3])) (Identity ([1, 2, 3]))
true

> S.equals (Identity ([1, 2, 3])) (Identity ([3, 2, 1]))
false
`

#### Identity#fantasy-land/lte :: Ord a => Identity a ~> Identity a -⁠> Boolean

Identity (x) is less than or equal to Identity (y) [iff][] x is
less than or equal to y according to [Z.lte][].

`javascript
> S.filter (S.lte (Identity (1)))
. ([Identity (0), Identity (1), Identity (2)])
[Identity (0), Identity (1)]
`

#### Identity#fantasy-land/concat :: Semigroup a => Identity a ~> Identity a -⁠> Identity a

concat (Identity (x)) (Identity (y)) is equivalent to
Identity (concat (x) (y)).

`javascript
> S.concat (Identity ([1, 2, 3])) (Identity ([4, 5, 6]))
Identity ([1, 2, 3, 4, 5, 6])
`

#### Identity#fantasy-land/map :: Identity a ~> (a -⁠> b) -⁠> Identity b

map (f) (Identity (x)) is equivalent to Identity (f (x)).

`javascript
> S.map (Math.sqrt) (Identity (64))
Identity (8)
`

#### Identity#fantasy-land/ap :: Identity a ~> Identity (a -⁠> b) -⁠> Identity b

ap (Identity (f)) (Identity (x)) is equivalent to Identity (f (x)).

`javascript
> S.ap (Identity (Math.sqrt)) (Identity (64))
Identity (8)
`

#### Identity#fantasy-land/chain :: Identity a ~> (a -⁠> Identity b) -⁠> Identity b

chain (f) (Identity (x)) is equivalent to f (x).

`javascript
> S.chain (n => Identity (n + 1)) (Identity (99))
Identity (100)
`

#### Identity#fantasy-land/reduce :: Identity a ~> ((b, a) -⁠> b, b) -⁠> b

reduce (f) (x) (Identity (y)) is equivalent to f (x) (y).

`javascript
> S.reduce (S.concat) ([1, 2, 3]) (Identity ([4, 5, 6]))
[1, 2, 3, 4, 5, 6]
`

#### Identity#fantasy-land/traverse :: Applicative f => Identity a ~> (TypeRep f, a -⁠> f b) -⁠> f (Identity b)

traverse (_) (f) (Identity (x)) is equivalent to
map (Identity) (f (x)).

`javascript
> S.traverse (Array) (x => [x + 1, x + 2, x + 3]) (Identity (100))
[Identity (101), Identity (102), Identity (103)]
`

#### Identity#fantasy-land/extend :: Identity a ~> (Identity a -⁠> b) -⁠> Identity b

extend (f) (Identity (x)) is equivalent to
Identity (f (Identity (x))).

`javascript
> S.extend (S.reduce (S.add) (1)) (Identity (99))
Identity (100)
`

#### Identity#fantasy-land/extract :: Identity a ~> () -⁠> a

extract (Identity (x)) is equivalent to x.

`javascript
> S.extract (Identity (42))
42
`

[Fantasy Land]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1
[Z.equals]: https://github.com/sanctuary-js/sanctuary-type-classes/tree/v12.1.0#equals
[Z.lte`]: https://github.com/sanctuary-js/sanctuary-type-classes/tree/v12.1.0#lte
[iff]: https://en.wikipedia.org/wiki/If_and_only_if
[type representative]: https://github.com/fantasyland/fantasy-land/tree/v4.0.1#type-representatives