Pair is the canonical product type: a value of type Pair a b always
contains exactly two values: one of type a; one of type b.
Pair 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 (Pair (Useless) (Useless)) ? '\u2705 ' :
. Z[k].test (Pair (['foo']) (['bar'])) ? '\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 ✅ * ', // if ‘a’ satisfies Semigroup
. 'Applicative ❌ ',
. 'Chain ✅ * ', // if ‘a’ satisfies Semigroup
. 'ChainRec ❌ ',
. 'Monad ❌ ',
. 'Alt ❌ ',
. 'Plus ❌ ',
. 'Alternative ❌ ',
. 'Foldable ✅ ',
. 'Traversable ✅ ',
. 'Extend ✅ ',
. 'Comonad ✅ ',
. 'Contravariant ❌ ' ]Pair's sole data constructor. Additionally, it serves as the Pair type representative.
> Pair (1) (2)
Pair (1) (2)fst (Pair (x) (y)) is equivalent to x.
> Pair.fst (Pair ('abc') ([1, 2, 3]))
'abc'snd (Pair (x) (y)) is equivalent to y.
> Pair.snd (Pair ('abc') ([1, 2, 3]))
[1, 2, 3]swap (Pair (x) (y)) is equivalent to Pair (y) (x).
> Pair.swap (Pair ('abc') ([1, 2, 3]))
Pair ([1, 2, 3]) ('abc')show (Pair (x) (y)) is equivalent to
'Pair (' + show (x) + ') (' + show (y) + ')'.
> show (Pair ('abc') ([1, 2, 3]))
'Pair ("abc") ([1, 2, 3])'Pair (x) (y) is equal to Pair (v) (w) iff x is equal to v
and y is equal to w according to Z.equals.
> S.equals (Pair ('abc') ([1, 2, 3])) (Pair ('abc') ([1, 2, 3]))
true
> S.equals (Pair ('abc') ([1, 2, 3])) (Pair ('abc') ([3, 2, 1]))
falsePair (x) (y) is less than or equal to Pair (v) (w) iff x is
less than v or x is equal to v and y is less than or equal to
w according to Z.lte.
> S.filter (S.lte (Pair ('b') (2)))
. ([Pair ('a') (1), Pair ('a') (2), Pair ('a') (3),
. Pair ('b') (1), Pair ('b') (2), Pair ('b') (3),
. Pair ('c') (1), Pair ('c') (2), Pair ('c') (3)])
[ Pair ('a') (1),
. Pair ('a') (2),
. Pair ('a') (3),
. Pair ('b') (1),
. Pair ('b') (2) ]compose (Pair (x) (y)) (Pair (v) (w)) is equivalent to Pair (v) (y).
> S.compose (Pair ('a') (0)) (Pair ([1, 2, 3]) ('b'))
Pair ([1, 2, 3]) (0)concat (Pair (x) (y)) (Pair (v) (w)) is equivalent to
Pair (concat (x) (v)) (concat (y) (w)).
> S.concat (Pair ('abc') ([1, 2, 3])) (Pair ('xyz') ([4, 5, 6]))
Pair ('abcxyz') ([1, 2, 3, 4, 5, 6])map (f) (Pair (x) (y)) is equivalent to Pair (x) (f (y)).
> S.map (Math.sqrt) (Pair ('abc') (256))
Pair ('abc') (16)bimap (f) (g) (Pair (x) (y)) is equivalent to Pair (f (x)) (g (y)).
> S.bimap (S.toUpper) (Math.sqrt) (Pair ('abc') (256))
Pair ('ABC') (16)ap (Pair (v) (f)) (Pair (x) (y)) is equivalent to
Pair (concat (v) (x)) (f (y)).
> S.ap (Pair ('abc') (Math.sqrt)) (Pair ('xyz') (256))
Pair ('abcxyz') (16)chain (f) (Pair (x) (y)) is equivalent to
Pair (concat (x) (fst (f (y)))) (snd (f (y))).
> S.chain (n => Pair (show (n)) (Math.sqrt (n))) (Pair ('abc') (256))
Pair ('abc256') (16)reduce (f) (x) (Pair (v) (w)) is equivalent to f (x) (w).
> S.reduce (S.concat) ([1, 2, 3]) (Pair ('abc') ([4, 5, 6]))
[1, 2, 3, 4, 5, 6]traverse (_) (f) (Pair (x) (y)) is equivalent to
map (Pair (x)) (f (y)).
> S.traverse (Array) (S.words) (Pair (123) ('foo bar baz'))
[Pair (123) ('foo'), Pair (123) ('bar'), Pair (123) ('baz')]extend (f) (Pair (x) (y)) is equivalent to
Pair (x) (f (Pair (x) (y))).
> S.extend (S.reduce (S.add) (1)) (Pair ('abc') (99))
Pair ('abc') (100)extract (Pair (x) (y)) is equivalent to y.
> S.extract (Pair ('abc') ([1, 2, 3]))
[1, 2, 3]