sanctuary-maybe

The Maybe type represents optional values: a value of type Maybe a is
either Nothing (the empty value) or a Just whose value is of type a.

Maybe 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 (Just (Useless)) ? '\u2705 ' :
. Z[k].test (Nothing) ? '\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 ✅ * ', // if ‘a’ satisfies Semigroup
. 'Group ❌ ',
. 'Filterable ✅ ',
. 'Functor ✅ ',
. 'Bifunctor ❌ ',
. 'Profunctor ❌ ',
. 'Apply ✅ ',
. 'Applicative ✅ ',
. 'Chain ✅ ',
. 'ChainRec ✅ ',
. 'Monad ✅ ',
. 'Alt ✅ ',
. 'Plus ✅ ',
. 'Alternative ✅ ',
. 'Foldable ✅ ',
. 'Traversable ✅ ',
. 'Extend ✅ ',
. 'Comonad ❌ ',
. 'Contravariant ❌ ' ]
`

#### Maybe :: TypeRep Maybe

Maybe [type representative][].

#### Maybe.Nothing :: Maybe a

The empty value of type Maybe a.

`javascript
> Nothing
Nothing
`

#### Maybe.Just :: a -⁠> Maybe a

Constructs a value of type Maybe a from a value of type a.

`javascript
> Just (42)
Just (42)
`

#### Maybe.fantasy-land/empty :: () -⁠> Maybe a

- empty (Maybe) is equivalent to Nothing

`javascript
> S.empty (Maybe)
Nothing
`

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

- of (Maybe) (x) is equivalent to Just (x)

`javascript
> S.of (Maybe) (42)
Just (42)
`

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

`javascript
> Z.chainRec (
. Maybe,
. (next, done, x) =>
. x <= 1 ? Nothing : Just (x >= 1000 ? done (x) : next (x * x)),
. 1
. )
Nothing

> Z.chainRec (
. Maybe,
. (next, done, x) =>
. x <= 1 ? Nothing : Just (x >= 1000 ? done (x) : next (x * x)),
. 2
. )
Just (65536)
`

#### Maybe.fantasy-land/zero :: () -⁠> Maybe a

- zero (Maybe) is equivalent to Nothing

`javascript
> S.zero (Maybe)
Nothing
`

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

- show (Nothing) is equivalent to 'Nothing'
- show (Just (x)) is equivalent to 'Just (' + show (x) + ')'

`javascript
> show (Nothing)
'Nothing'

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

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

- Nothing is equal to Nothing
- Just (x) is equal to Just (y) [iff][] x is equal to y
according to [Z.equals][]
- Nothing is never equal to Just (x)

`javascript
> S.equals (Nothing) (Nothing)
true

> S.equals (Just ([1, 2, 3])) (Just ([1, 2, 3]))
true

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

> S.equals (Just ([1, 2, 3])) (Nothing)
false
`

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

- Nothing is (less than or) equal to Nothing
- Just (x) is less than or equal to Just (y) [iff][] x is less
than or equal to y according to [Z.lte][]
- Nothing is always less than Just (x)

`javascript
> S.filter (S.lte (Nothing)) ([Nothing, Just (0), Just (1), Just (2)])
[Nothing]

> S.filter (S.lte (Just (1))) ([Nothing, Just (0), Just (1), Just (2)])
[Nothing, Just (0), Just (1)]
`

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

- concat (Nothing) (Nothing) is equivalent to Nothing
- concat (Just (x)) (Just (y)) is equivalent to
Just (concat (x) (y))
- concat (Nothing) (Just (x)) is equivalent to Just (x)
- concat (Just (x)) (Nothing) is equivalent to Just (x)

`javascript
> S.concat (Nothing) (Nothing)
Nothing

> S.concat (Just ([1, 2, 3])) (Just ([4, 5, 6]))
Just ([1, 2, 3, 4, 5, 6])

> S.concat (Nothing) (Just ([1, 2, 3]))
Just ([1, 2, 3])

> S.concat (Just ([1, 2, 3])) (Nothing)
Just ([1, 2, 3])
`

#### Maybe#fantasy-land/filter :: Maybe a ~> (a -⁠> Boolean) -⁠> Maybe a

- filter (p) (Nothing) is equivalent to Nothing
- filter (p) (Just (x)) is equivalent to p (x) ? Just (x) : Nothing

`javascript
> S.filter (isFinite) (Nothing)
Nothing

> S.filter (isFinite) (Just (Infinity))
Nothing

> S.filter (isFinite) (Just (Number.MAX_SAFE_INTEGER))
Just (9007199254740991)
`

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

- map (f) (Nothing) is equivalent to Nothing
- map (f) (Just (x)) is equivalent to Just (f (x))

`javascript
> S.map (Math.sqrt) (Nothing)
Nothing

> S.map (Math.sqrt) (Just (9))
Just (3)
`

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

- ap (Nothing) (Nothing) is equivalent to Nothing
- ap (Nothing) (Just (x)) is equivalent to Nothing
- ap (Just (f)) (Nothing) is equivalent to Nothing
- ap (Just (f)) (Just (x)) is equivalent to Just (f (x))

`javascript
> S.ap (Nothing) (Nothing)
Nothing

> S.ap (Nothing) (Just (9))
Nothing

> S.ap (Just (Math.sqrt)) (Nothing)
Nothing

> S.ap (Just (Math.sqrt)) (Just (9))
Just (3)
`

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

- chain (f) (Nothing) is equivalent to Nothing
- chain (f) (Just (x)) is equivalent to f (x)

`javascript
> const head = xs => xs.length === 0 ? Nothing : Just (xs[0])

> S.chain (head) (Nothing)
Nothing

> S.chain (head) (Just ([]))
Nothing

> S.chain (head) (Just (['foo', 'bar', 'baz']))
Just ('foo')
`

#### Maybe#fantasy-land/alt :: Maybe a ~> Maybe a -⁠> Maybe a

- alt (Nothing) (Nothing) is equivalent to Nothing
- alt (Just (x)) (Nothing) is equivalent to Just (x)
- alt (Nothing) (Just (x)) is equivalent to Just (x)
- alt (Just (y)) (Just (x)) is equivalent to Just (x)

`javascript
> S.alt (Nothing) (Nothing)
Nothing

> S.alt (Just (1)) (Nothing)
Just (1)

> S.alt (Nothing) (Just (2))
Just (2)

> S.alt (Just (4)) (Just (3))
Just (3)
`

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

- reduce (f) (x) (Nothing) is equivalent to x
- reduce (f) (x) (Just (y)) is equivalent to f (x) (y)

`javascript
> S.reduce (S.concat) ('abc') (Nothing)
'abc'

> S.reduce (S.concat) ('abc') (Just ('xyz'))
'abcxyz'
`

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

- traverse (A) (f) (Nothing) is equivalent to of (A) (Nothing)
- traverse (A) (f) (Just (x)) is equivalent to map (Just) (f (x))

`javascript
> S.traverse (Array) (S.words) (Nothing)
[Nothing]

> S.traverse (Array) (S.words) (Just ('foo bar baz'))
[Just ('foo'), Just ('bar'), Just ('baz')]
`

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

- extend (f) (Nothing) is equivalent to Nothing
- extend (f) (Just (x)) is equivalent to Just (f (Just (x)))

`javascript
> S.extend (S.reduce (S.add) (1)) (Nothing)
Nothing

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

[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