sanctuary-either

sanctuary-either

The Either type represents values with two possibilities: a value of type Either a b is either a Left whose value is of type a or a Right whose value is of type b.

Either a b satisfies the following Fantasy Land specifications:

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

Either :: TypeRep Either

Either type representative.

Either.Left :: a -⁠> Either a b

Constructs a value of type Either a b from a value of type a.

> Left ('sqrt undefined for -1')
Left ('sqrt undefined for -1')

Either.Right :: b -⁠> Either a b

Constructs a value of type Either a b from a value of type b.

> Right (42)
Right (42)

Either.fantasy-land/of :: b -⁠> Either a b

• of (Either) (x) is equivalent to Right (x)

> S.of (Either) (42)
Right (42)

Either.fantasy-land/chainRec :: ((a -⁠> c, b -⁠> c, a) -⁠> Either d c, a) -⁠> Either d b

> Z.chainRec (
.   Either,
.   (next, done, x) =>
.     x <= 1 ? Left ('!!') : Right (x >= 1000 ? done (x) : next (x * x)),
.   1
. )
Left ('!!')

> Z.chainRec (
.   Either,
.   (next, done, x) =>
.     x <= 1 ? Left ('!!') : Right (x >= 1000 ? done (x) : next (x * x)),
.   2
. )
Right (65536)

Either#@@show :: (Showable a, Showable b) => Either a b ~> () -⁠> String

• show (Left (x)) is equivalent to 'Left (' + show (x) + ')'
• show (Right (x)) is equivalent to 'Right (' + show (x) + ')'

> show (Left ('sqrt undefined for -1'))
'Left ("sqrt undefined for -1")'

> show (Right ([1, 2, 3]))
'Right ([1, 2, 3])'

Either#fantasy-land/equals :: (Setoid a, Setoid b) => Either a b ~> Either a b -⁠> Boolean

• Left (x) is equal to Left (y) iff x is equal to y according to Z.equals
• Right (x) is equal to Right (y) iff x is equal to y according to Z.equals
• Left (x) is never equal to Right (y)

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

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

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

Either#fantasy-land/lte :: (Ord a, Ord b) => Either a b ~> Either a b -⁠> Boolean

• Left (x) is less than or equal to Left (y) iff x is less than or equal to y according to Z.lte
• Right (x) is less than or equal to Right (y) iff x is less than or equal to y according to Z.lte
• Left (x) is always less than Right (y)

> S.filter (S.lte (Left (1))) ([Left (0), Left (1), Left (2)])
[Left (0), Left (1)]

> S.filter (S.lte (Right (1))) ([Right (0), Right (1), Right (2)])
[Right (0), Right (1)]

> S.filter (S.lte (Left (1))) ([Right (0), Right (1), Right (2)])
[]

> S.filter (S.lte (Right (1))) ([Left (0), Left (1), Left (2)])
[Left (0), Left (1), Left (2)]

Either#fantasy-land/concat :: (Semigroup a, Semigroup b) => Either a b ~> Either a b -⁠> Either a b

• concat (Left (x)) (Left (y)) is equivalent to Left (concat (x) (y))
• concat (Right (x)) (Right (y)) is equivalent to Right (concat (x) (y))
• concat (Left (x)) (Right (y)) is equivalent to Right (y)
• concat (Right (x)) (Left (y)) is equivalent to Right (x)

> S.concat (Left ('abc')) (Left ('def'))
Left ('abcdef')

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

> S.concat (Left ('abc')) (Right ([1, 2, 3]))
Right ([1, 2, 3])

> S.concat (Right ([1, 2, 3])) (Left ('abc'))
Right ([1, 2, 3])

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

• map (f) (Left (x)) is equivalent to Left (x)
• map (f) (Right (x)) is equivalent to Right (f (x))

> S.map (S.add (1)) (Left ('sqrt undefined for -1'))
Left ('sqrt undefined for -1')

> S.map (S.add (1)) (Right (99))
Right (100)

Either#fantasy-land/bimap :: Either a c ~> (a -⁠> b, c -⁠> d) -⁠> Either b d

• bimap (f) (g) (Left (x)) is equivalent to Left (f (x))
• bimap (f) (g) (Right (x)) is equivalent to Right (g (x))

> S.bimap (S.toUpper) (S.add (1)) (Left ('abc'))
Left ('ABC')

> S.bimap (S.toUpper) (S.add (1)) (Right (99))
Right (100)

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

• ap (Left (x)) (Left (y)) is equivalent to Left (x)
• ap (Left (x)) (Right (y)) is equivalent to Left (x)
• ap (Right (f)) (Left (x)) is equivalent to Left (x)
• ap (Right (f)) (Right (x)) is equivalent to Right (f (x))

> S.ap (Left ('div undefined for 0')) (Left ('sqrt undefined for -1'))
Left ('div undefined for 0')

> S.ap (Left ('div undefined for 0')) (Right (99))
Left ('div undefined for 0')

> S.ap (Right (S.add (1))) (Left ('sqrt undefined for -1'))
Left ('sqrt undefined for -1')

> S.ap (Right (S.add (1))) (Right (99))
Right (100)

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

• chain (f) (Left (x)) is equivalent to Left (x)
• chain (f) (Right (x)) is equivalent to f (x)

> const sqrt = n => n < 0 ? Left ('sqrt undefined for ' + show (n))
.                         : Right (Math.sqrt (n))

> S.chain (sqrt) (Left ('div undefined for 0'))
Left ('div undefined for 0')

> S.chain (sqrt) (Right (-1))
Left ('sqrt undefined for -1')

> S.chain (sqrt) (Right (25))
Right (5)

Either#fantasy-land/alt :: Either a b ~> Either a b -⁠> Either a b

• alt (Left (y)) (Left (x)) is equivalent to Left (y)
• alt (Right (y)) (Left (x)) is equivalent to Right (y)
• alt (Left (y)) (Right (x)) is equivalent to Right (x)
• alt (Right (y)) (Right (x)) is equivalent to Right (x)

> S.alt (Left ('B')) (Left ('A'))
Left ('B')

> S.alt (Right (1)) (Left ('C'))
Right (1)

> S.alt (Left ('D')) (Right (2))
Right (2)

> S.alt (Right (4)) (Right (3))
Right (3)

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

• reduce (f) (x) (Left (y)) is equivalent to x
• reduce (f) (x) (Right (y)) is equivalent to f (x) (y)

> S.reduce (S.concat) ([1]) (Left ('sqrt undefined for -1'))
[1]

> S.reduce (S.concat) ([1]) (Right ([2]))
[1, 2]

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

• traverse (A) (f) (Left (x)) is equivalent to of (A) (Left (x))
• traverse (A) (f) (Right (x)) is equivalent to map (Right) (f (x))

> S.traverse (Array) (S.words) (Left ('sqrt undefined for -1'))
[Left ('sqrt undefined for -1')]

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

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

• extend (f) (Left (x)) is equivalent to Left (x)
• extend (f) (Right (x)) is equivalent to Right (f (Right (x)))

> S.extend (S.reduce (S.add) (1)) (Left ('sqrt undefined for -1'))
Left ('sqrt undefined for -1')

> S.extend (S.reduce (S.add) (1)) (Right (99))
Right (100)