sanctuary-type-classes

sanctuary-type-classes

The Fantasy Land Specification "specifies interoperability of common algebraic structures" by defining a number of type classes. For each type class, it states laws which every member of a type must obey in order for the type to be a member of the type class. In order for the Maybe type to be considered a Functor, for example, every Maybe a value must have a fantasy-land/map method which obeys the identity and composition laws.

This project provides:

• TypeClass, a function for defining type classes;
• one TypeClass value for each Fantasy Land type class;
• lawful Fantasy Land methods for JavaScript's built-in types;
• one function for each Fantasy Land method; and
• several functions derived from these functions.

Type-class hierarchy

 Setoid   Semigroupoid  Semigroup   Foldable        Functor      Contravariant  Filterable
(equals)    (compose)    (concat)   (reduce)         (map)        (contramap)    (filter)
    |           |           |           \         / | | | | \
    |           |           |            \       /  | | | |  \
    |           |           |             \     /   | | | |   \
    |           |           |              \   /    | | | |    \
    |           |           |               \ /     | | | |     \
   Ord      Category     Monoid         Traversable | | | |      \
  (lte)       (id)       (empty)        (traverse)  / | | \       \
                            |                      /  | |  \       \
                            |                     /   / \   \       \
                            |             Profunctor /   \ Bifunctor \
                            |              (promap) /     \ (bimap)   \
                            |                      /       \           \
                          Group                   /         \           \
                         (invert)               Alt        Apply      Extend
                                               (alt)        (ap)     (extend)
                                                /           / \           \
                                               /           /   \           \
                                              /           /     \           \
                                             /           /       \           \
                                            /           /         \           \
                                          Plus    Applicative    Chain      Comonad
                                         (zero)       (of)      (chain)    (extract)
                                            \         / \         / \
                                             \       /   \       /   \
                                              \     /     \     /     \
                                               \   /       \   /       \
                                                \ /         \ /         \
                                            Alternative    Monad     ChainRec
                                                                    (chainRec)

API

TypeClass :: (String, String, Array TypeClass, a -⁠> Boolean) -⁠> TypeClass

The arguments are:

• the name of the type class, prefixed by its npm package name;
• the documentation URL of the type class;
• an array of dependencies; and
• a predicate which accepts any JavaScript value and returns true if the value satisfies the requirements of the type class; false otherwise.

Example:

//    hasMethod :: String -> a -> Boolean
const hasMethod = name => x => x != null && typeof x[name] == 'function';

//    Foo :: TypeClass
const Foo = Z.TypeClass (
  'my-package/Foo',
  'http://example.com/my-package#Foo',
  [],
  hasMethod ('foo')
);

//    Bar :: TypeClass
const Bar = Z.TypeClass (
  'my-package/Bar',
  'http://example.com/my-package#Bar',
  [Foo],
  hasMethod ('bar')
);

Types whose values have a foo method are members of the Foo type class. Members of the Foo type class whose values have a bar method are also members of the Bar type class.

Each TypeClass value has a test field: a function which accepts any JavaScript value and returns true if the value satisfies the type class's predicate and the predicates of all the type class's dependencies; false otherwise.

TypeClass values may be used with sanctuary-def to define parametrically polymorphic functions which verify their type-class constraints at run time.

Setoid :: TypeClass

TypeClass value for Setoid.

> Setoid.test (null)
true

Ord :: TypeClass

TypeClass value for Ord.

> Ord.test (0)
true

> Ord.test (Math.sqrt)
false

Semigroupoid :: TypeClass

TypeClass value for Semigroupoid.

> Semigroupoid.test (Math.sqrt)
true

> Semigroupoid.test (0)
false

Category :: TypeClass

TypeClass value for Category.

> Category.test (Math.sqrt)
true

> Category.test (0)
false

Semigroup :: TypeClass

TypeClass value for Semigroup.

> Semigroup.test ('')
true

> Semigroup.test (0)
false

Monoid :: TypeClass

TypeClass value for Monoid.

> Monoid.test ('')
true

> Monoid.test (0)
false

Group :: TypeClass

TypeClass value for Group.

> Group.test (Sum (0))
true

> Group.test ('')
false

Filterable :: TypeClass

TypeClass value for Filterable.

> Filterable.test ({})
true

> Filterable.test ('')
false

Functor :: TypeClass

TypeClass value for Functor.

> Functor.test ([])
true

> Functor.test ('')
false

Bifunctor :: TypeClass

TypeClass value for Bifunctor.

> Bifunctor.test (Pair ('foo') (64))
true

> Bifunctor.test ([])
false

Profunctor :: TypeClass

TypeClass value for Profunctor.

> Profunctor.test (Math.sqrt)
true

> Profunctor.test ([])
false

Apply :: TypeClass

TypeClass value for Apply.

> Apply.test ([])
true

> Apply.test ('')
false

Applicative :: TypeClass

TypeClass value for Applicative.

> Applicative.test ([])
true

> Applicative.test ({})
false

Chain :: TypeClass

TypeClass value for Chain.

> Chain.test ([])
true

> Chain.test ({})
false

ChainRec :: TypeClass

TypeClass value for ChainRec.

> ChainRec.test ([])
true

> ChainRec.test ({})
false

Monad :: TypeClass

TypeClass value for Monad.

> Monad.test ([])
true

> Monad.test ({})
false

Alt :: TypeClass

TypeClass value for Alt.

> Alt.test ({})
true

> Alt.test ('')
false

Plus :: TypeClass

TypeClass value for Plus.

> Plus.test ({})
true

> Plus.test ('')
false

Alternative :: TypeClass

TypeClass value for Alternative.

> Alternative.test ([])
true

> Alternative.test ({})
false

Foldable :: TypeClass

TypeClass value for Foldable.

> Foldable.test ({})
true

> Foldable.test ('')
false

Traversable :: TypeClass

TypeClass value for Traversable.

> Traversable.test ([])
true

> Traversable.test ('')
false

Extend :: TypeClass

TypeClass value for Extend.

> Extend.test ([])
true

> Extend.test ({})
false

Comonad :: TypeClass

TypeClass value for Comonad.

> Comonad.test (Identity (0))
true

> Comonad.test ([])
false

Contravariant :: TypeClass

TypeClass value for Contravariant.

> Contravariant.test (Math.sqrt)
true

> Contravariant.test ([])
false

equals :: (a, b) -⁠> Boolean

Returns true if its arguments are of the same type and equal according to the type's fantasy-land/equals method; false otherwise.

fantasy-land/equals implementations are provided for the following built-in types: Null, Undefined, Boolean, Number, Date, RegExp, String, Array, Arguments, Error, Object, and Function.

The algorithm supports circular data structures. Two arrays are equal if they have the same index paths and for each path have equal values. Two arrays which represent [1, [1, [1, [1, [1, ...]]]]], for example, are equal even if their internal structures differ. Two objects are equal if they have the same property paths and for each path have equal values.

> equals (0, -0)
true

> equals (NaN, NaN)
true

> equals (Cons (1, Cons (2, Nil)), Cons (1, Cons (2, Nil)))
true

> equals (Cons (1, Cons (2, Nil)), Cons (2, Cons (1, Nil)))
false

lt :: (a, b) -⁠> Boolean

Returns true if its arguments are of the same type and the first is less than the second according to the type's fantasy-land/lte method; false otherwise.

This function is derived from lte.

See also gt and gte.

> lt (0, 0)
false

> lt (0, 1)
true

> lt (1, 0)
false

lte :: (a, b) -⁠> Boolean

Returns true if its arguments are of the same type and the first is less than or equal to the second according to the type's fantasy-land/lte method; false otherwise.

fantasy-land/lte implementations are provided for the following built-in types: Null, Undefined, Boolean, Number, Date, String, Array, Arguments, and Object.

The algorithm supports circular data structures in the same manner as equals.

See also lt, gt, and gte.

> lte (0, 0)
true

> lte (0, 1)
true

> lte (1, 0)
false

gt :: (a, b) -⁠> Boolean

Returns true if its arguments are of the same type and the first is greater than the second according to the type's fantasy-land/lte method; false otherwise.

This function is derived from lte.

See also lt and gte.

> gt (0, 0)
false

> gt (0, 1)
false

> gt (1, 0)
true

gte :: (a, b) -⁠> Boolean

Returns true if its arguments are of the same type and the first is greater than or equal to the second according to the type's fantasy-land/lte method; false otherwise.

This function is derived from lte.

See also lt and gt.

> gte (0, 0)
true

> gte (0, 1)
false

> gte (1, 0)
true

min :: Ord a => (a, a) -⁠> a

Returns the smaller of its two arguments.

This function is derived from lte.

See also max.

> min (10, 2)
2

> min (new Date ('1999-12-31'), new Date ('2000-01-01'))
new Date ('1999-12-31')

> min ('10', '2')
'10'

max :: Ord a => (a, a) -⁠> a

Returns the larger of its two arguments.

This function is derived from lte.

See also min.

> max (10, 2)
10

> max (new Date ('1999-12-31'), new Date ('2000-01-01'))
new Date ('2000-01-01')

> max ('10', '2')
'2'

clamp :: Ord a => (a, a, a) -⁠> a

Takes a lower bound, an upper bound, and a value of the same type. Returns the value if it is within the bounds; the nearer bound otherwise.

This function is derived from min and max.

> clamp (0, 100, 42)
42

> clamp (0, 100, -1)
0

> clamp ('A', 'Z', '~')
'Z'

compose :: Semigroupoid c => (c j k, c i j) -⁠> c i k

Function wrapper for fantasy-land/compose.

fantasy-land/compose implementations are provided for the following built-in types: Function.

> compose (Math.sqrt, x => x + 1) (99)
10

id :: Category c => TypeRep c -⁠> c

Function wrapper for fantasy-land/id.

fantasy-land/id implementations are provided for the following built-in types: Function.

> id (Function) ('foo')
'foo'

concat :: Semigroup a => (a, a) -⁠> a

Function wrapper for fantasy-land/concat.

fantasy-land/concat implementations are provided for the following built-in types: String, Array, and Object.

> concat ('abc', 'def')
'abcdef'

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

> concat ({x: 1, y: 2}, {y: 3, z: 4})
{x: 1, y: 3, z: 4}

> concat (Cons ('foo', Cons ('bar', Cons ('baz', Nil))), Cons ('quux', Nil))
Cons ('foo', Cons ('bar', Cons ('baz', Cons ('quux', Nil))))

empty :: Monoid m => TypeRep m -⁠> m

Function wrapper for fantasy-land/empty.

fantasy-land/empty implementations are provided for the following built-in types: String, Array, and Object.

> empty (String)
''

> empty (Array)
[]

> empty (Object)
{}

> empty (List)
Nil

invert :: Group g => g -⁠> g

Function wrapper for fantasy-land/invert.

> invert (Sum (5))
Sum (-5)

filter :: Filterable f => (a -⁠> Boolean, f a) -⁠> f a

Function wrapper for fantasy-land/filter. Discards every element which does not satisfy the predicate.

fantasy-land/filter implementations are provided for the following built-in types: Array and Object.

See also reject.

> filter (x => x % 2 == 1, [1, 2, 3])
[1, 3]

> filter (x => x % 2 == 1, {x: 1, y: 2, z: 3})
{x: 1, z: 3}

> filter (x => x % 2 == 1, Cons (1, Cons (2, Cons (3, Nil))))
Cons (1, Cons (3, Nil))

> filter (x => x % 2 == 1, Nothing)
Nothing

> filter (x => x % 2 == 1, Just (0))
Nothing

> filter (x => x % 2 == 1, Just (1))
Just (1)

reject :: Filterable f => (a -⁠> Boolean, f a) -⁠> f a

Discards every element which satisfies the predicate.

This function is derived from filter.

> reject (x => x % 2 == 1, [1, 2, 3])
[2]

> reject (x => x % 2 == 1, {x: 1, y: 2, z: 3})
{y: 2}

> reject (x => x % 2 == 1, Cons (1, Cons (2, Cons (3, Nil))))
Cons (2, Nil)

> reject (x => x % 2 == 1, Nothing)
Nothing

> reject (x => x % 2 == 1, Just (0))
Just (0)

> reject (x => x % 2 == 1, Just (1))
Nothing

map :: Functor f => (a -⁠> b, f a) -⁠> f b

Function wrapper for fantasy-land/map.

fantasy-land/map implementations are provided for the following built-in types: Array, Object, and Function.

> map (Math.sqrt, [1, 4, 9])
[1, 2, 3]

> map (Math.sqrt, {x: 1, y: 4, z: 9})
{x: 1, y: 2, z: 3}

> map (Math.sqrt, s => s.length) ('Sanctuary')
3

> map (Math.sqrt, Pair ('foo') (64))
Pair ('foo') (8)

> map (Math.sqrt, Nil)
Nil

> map (Math.sqrt, Cons (1, Cons (4, Cons (9, Nil))))
Cons (1, Cons (2, Cons (3, Nil)))

flip :: Functor f => (f (a -⁠> b), a) -⁠> f b

Maps over the given functions, applying each to the given value.

This function is derived from map.

> flip (x => y => x + y, '!') ('foo')
'foo!'

> flip ([Math.floor, Math.ceil], 1.5)
[1, 2]

> flip ({floor: Math.floor, ceil: Math.ceil}, 1.5)
{floor: 1, ceil: 2}

> flip (Cons (Math.floor, Cons (Math.ceil, Nil)), 1.5)
Cons (1, Cons (2, Nil))

bimap :: Bifunctor f => (a -⁠> b, c -⁠> d, f a c) -⁠> f b d

Function wrapper for fantasy-land/bimap.

> bimap (s => s.toUpperCase (), Math.sqrt, Pair ('foo') (64))
Pair ('FOO') (8)

mapLeft :: Bifunctor f => (a -⁠> b, f a c) -⁠> f b c

Maps the given function over the left side of a Bifunctor.

> mapLeft (Math.sqrt, Pair (64) (9))
Pair (8) (9)

promap :: Profunctor p => (a -⁠> b, c -⁠> d, p b c) -⁠> p a d

Function wrapper for fantasy-land/promap.

fantasy-land/promap implementations are provided for the following built-in types: Function.

> promap (Math.abs, x => x + 1, Math.sqrt) (-100)
11

ap :: Apply f => (f (a -⁠> b), f a) -⁠> f b

Function wrapper for fantasy-land/ap.

fantasy-land/ap implementations are provided for the following built-in types: Array, Object, and Function.

> ap ([Math.sqrt, x => x * x], [1, 4, 9, 16, 25])
[1, 2, 3, 4, 5, 1, 16, 81, 256, 625]

> ap ({a: Math.sqrt, b: x => x * x}, {a: 16, b: 10, c: 1})
{a: 4, b: 100}

> ap (s => n => s.slice (0, n), s => Math.ceil (s.length / 2)) ('Haskell')
'Hask'

> ap (Identity (Math.sqrt), Identity (64))
Identity (8)

> ap (Cons (Math.sqrt, Cons (x => x * x, Nil)), Cons (16, Cons (100, Nil)))
Cons (4, Cons (10, Cons (256, Cons (10000, Nil))))

lift2 :: Apply f => (a -⁠> b -⁠> c, f a, f b) -⁠> f c

Lifts a -> b -> c to Apply f => f a -> f b -> f c and returns the result of applying this to the given arguments.

This function is derived from map and ap.

See also lift3.

> lift2 (x => y => Math.pow (x, y), [10], [1, 2, 3])
[10, 100, 1000]

> lift2 (x => y => Math.pow (x, y), Identity (10), Identity (3))
Identity (1000)

lift3 :: Apply f => (a -⁠> b -⁠> c -⁠> d, f a, f b, f c) -⁠> f d

Lifts a -> b -> c -> d to Apply f => f a -> f b -> f c -> f d and returns the result of applying this to the given arguments.

This function is derived from map and ap.

See also lift2.

> lift3 (x => y => z => x + z + y,
.        ['<', '['],
.        ['>', ']'],
.        ['foo', 'bar', 'baz'])
[ '<foo>', '<bar>', '<baz>',
. '<foo]', '<bar]', '<baz]',
. '[foo>', '[bar>', '[baz>',
. '[foo]', '[bar]', '[baz]' ]

> lift3 (x => y => z => x + z + y,
.        Identity ('<'),
.        Identity ('>'),
.        Identity ('baz'))
Identity ('<baz>')

apFirst :: Apply f => (f a, f b) -⁠> f a

Combines two effectful actions, keeping only the result of the first. Equivalent to Haskell's (<*) function.

This function is derived from lift2.

See also apSecond.

> apFirst ([1, 2], [3, 4])
[1, 1, 2, 2]

> apFirst (Identity (1), Identity (2))
Identity (1)

apSecond :: Apply f => (f a, f b) -⁠> f b

Combines two effectful actions, keeping only the result of the second. Equivalent to Haskell's (*>) function.

This function is derived from lift2.

See also apFirst.

> apSecond ([1, 2], [3, 4])
[3, 4, 3, 4]

> apSecond (Identity (1), Identity (2))
Identity (2)

of :: Applicative f => (TypeRep f, a) -⁠> f a

Function wrapper for fantasy-land/of.

fantasy-land/of implementations are provided for the following built-in types: Array and Function.

> of (Array, 42)
[42]

> of (Function, 42) (null)
42

> of (List, 42)
Cons (42, Nil)

append :: (Applicative f, Semigroup (f a)) => (a, f a) -⁠> f a

Returns the result of appending the first argument to the second.

This function is derived from concat and of.

See also prepend.

> append (3, [1, 2])
[1, 2, 3]

> append (3, Cons (1, Cons (2, Nil)))
Cons (1, Cons (2, Cons (3, Nil)))

prepend :: (Applicative f, Semigroup (f a)) => (a, f a) -⁠> f a

Returns the result of prepending the first argument to the second.

This function is derived from concat and of.

See also append.

> prepend (1, [2, 3])
[1, 2, 3]

> prepend (1, Cons (2, Cons (3, Nil)))
Cons (1, Cons (2, Cons (3, Nil)))

chain :: Chain m => (a -⁠> m b, m a) -⁠> m b

Function wrapper for fantasy-land/chain.

fantasy-land/chain implementations are provided for the following built-in types: Array and Function.

> chain (x => [x, x], [1, 2, 3])
[1, 1, 2, 2, 3, 3]

> chain (x => x % 2 == 1 ? of (List, x) : Nil,
.        Cons (1, Cons (2, Cons (3, Nil))))
Cons (1, Cons (3, Nil))

> chain (n => s => s.slice (0, n),
.        s => Math.ceil (s.length / 2))
.       ('Haskell')
'Hask'

join :: Chain m => m (m a) -⁠> m a

Removes one level of nesting from a nested monadic structure.

This function is derived from chain.

> join ([[1], [2], [3]])
[1, 2, 3]

> join ([[[1, 2, 3]]])
[[1, 2, 3]]

> join (Identity (Identity (1)))
Identity (1)

chainRec :: ChainRec m => (TypeRep m, (a -⁠> c, b -⁠> c, a) -⁠> m c, a) -⁠> m b

Function wrapper for fantasy-land/chainRec.

fantasy-land/chainRec implementations are provided for the following built-in types: Array.

> chainRec (
.   Array,
.   (next, done, s) => s.length == 2 ? [s + '!', s + '?'].map (done)
.                                    : [s + 'o', s + 'n'].map (next),
.   ''
. )
['oo!', 'oo?', 'on!', 'on?', 'no!', 'no?', 'nn!', 'nn?']

alt :: Alt f => (f a, f a) -⁠> f a

Function wrapper for fantasy-land/alt.

fantasy-land/alt implementations are provided for the following built-in types: Array and Object.

> alt ([1, 2, 3], [4, 5, 6])
[1, 2, 3, 4, 5, 6]

> alt (Nothing, Nothing)
Nothing

> alt (Nothing, Just (1))
Just (1)

> alt (Just (2), Just (3))
Just (2)

zero :: Plus f => TypeRep f -⁠> f a

Function wrapper for fantasy-land/zero.

fantasy-land/zero implementations are provided for the following built-in types: Array and Object.

> zero (Array)
[]

> zero (Object)
{}

> zero (Maybe)
Nothing

reduce :: Foldable f => ((b, a) -⁠> b, b, f a) -⁠> b

Function wrapper for fantasy-land/reduce.

fantasy-land/reduce implementations are provided for the following built-in types: Array and Object.

> reduce ((xs, x) => [x].concat (xs), [], [1, 2, 3])
[3, 2, 1]

> reduce (concat, '', Cons ('foo', Cons ('bar', Cons ('baz', Nil))))
'foobarbaz'

size :: Foldable f => f a -⁠> Integer

Returns the number of elements of the given structure.

This function is derived from reduce.

> size ([])
0

> size (['foo', 'bar', 'baz'])
3

> size (Nil)
0

> size (Cons ('foo', Cons ('bar', Cons ('baz', Nil))))
3

all :: Foldable f => (a -⁠> Boolean, f a) -⁠> Boolean

Returns true if all the elements of the structure satisfy the predicate; false otherwise.

This function is derived from reduce.

See also any and none.

> all (Number.isInteger, [])
true

> all (Number.isInteger, [1, 2, 3])
true

> all (Number.isInteger, [0, 0.25, 0.5, 0.75, 1])
false

any :: Foldable f => (a -⁠> Boolean, f a) -⁠> Boolean

Returns true if any element of the structure satisfies the predicate; false otherwise.

This function is derived from reduce.

See also all and none.

> any (Number.isInteger, [])
false

> any (Number.isInteger, [1, 2, 3])
true

> any (Number.isInteger, [0, 0.25, 0.5, 0.75, 1])
true

none :: Foldable f => (a -⁠> Boolean, f a) -⁠> Boolean

Returns true if none of the elements of the structure satisfies the predicate; false otherwise.

This function is derived from any. none (pred, foldable) is equivalent to !(any (pred, foldable)).

See also all.

> none (Number.isInteger, [])
true

> none (Number.isInteger, [0, 0.25, 0.5, 0.75, 1])
false

elem :: (Setoid a, Foldable f) => (a, f a) -⁠> Boolean

Takes a value and a structure and returns true if the value is an element of the structure; false otherwise.

This function is derived from equals and reduce.

> elem ('c', ['a', 'b', 'c'])
true

> elem ('x', ['a', 'b', 'c'])
false

> elem (3, {x: 1, y: 2, z: 3})
true

> elem (8, {x: 1, y: 2, z: 3})
false

> elem (0, Just (0))
true

> elem (0, Just (1))
false

> elem (0, Nothing)
false

foldMap :: (Monoid m, Foldable f) => (TypeRep m, a -⁠> m, f a) -⁠> m

Deconstructs a foldable by mapping every element to a monoid and concatenating the results.

This function is derived from concat, empty, and reduce.

> foldMap (String, f => f.name, [Math.sin, Math.cos, Math.tan])
'sincostan'

reverse :: (Applicative f, Foldable f, Monoid (f a)) => f a -⁠> f a

Reverses the elements of the given structure.

This function is derived from concat, empty, of, and reduce.

> reverse ([1, 2, 3])
[3, 2, 1]

> reverse (Cons (1, Cons (2, Cons (3, Nil))))
Cons (3, Cons (2, Cons (1, Nil)))

sort :: (Ord a, Applicative f, Foldable f, Monoid (f a)) => f a -⁠> f a

Performs a stable sort of the elements of the given structure, using lte for comparisons.

This function is derived from lte, concat, empty, of, and reduce.

See also sortBy.

> sort (['foo', 'bar', 'baz'])
['bar', 'baz', 'foo']

> sort ([Just (2), Nothing, Just (1)])
[Nothing, Just (1), Just (2)]

> sort (Cons ('foo', Cons ('bar', Cons ('baz', Nil))))
Cons ('bar', Cons ('baz', Cons ('foo', Nil)))

sortBy :: (Ord b, Applicative f, Foldable f, Monoid (f a)) => (a -⁠> b, f a) -⁠> f a

Performs a stable sort of the elements of the given structure, using lte to compare the values produced by applying the given function to each element of the structure.

This function is derived from lte, concat, empty, of, and reduce.

See also sort.

> sortBy (s => s.length, ['red', 'green', 'blue'])
['red', 'blue', 'green']

> sortBy (s => s.length, ['black', 'white'])
['black', 'white']

> sortBy (s => s.length, ['white', 'black'])
['white', 'black']

> sortBy (s => s.length, Cons ('red', Cons ('green', Cons ('blue', Nil))))
Cons ('red', Cons ('blue', Cons ('green', Nil)))

traverse :: (Applicative f, Traversable t) => (TypeRep f, a -⁠> f b, t a) -⁠> f (t b)

Function wrapper for fantasy-land/traverse.

fantasy-land/traverse implementations are provided for the following built-in types: Array and Object.

See also sequence.

> traverse (Array, x => x, [[1, 2, 3], [4, 5]])
[[1, 4], [1, 5], [2, 4], [2, 5], [3, 4], [3, 5]]

> traverse (Identity, x => Identity (x + 1), [1, 2, 3])
Identity ([2, 3, 4])

sequence :: (Applicative f, Traversable t) => (TypeRep f, t (f a)) -⁠> f (t a)

Inverts the given t (f a) to produce an f (t a).

This function is derived from traverse.

> sequence (Array, Identity ([1, 2, 3]))
[Identity (1), Identity (2), Identity (3)]

> sequence (Identity, [Identity (1), Identity (2), Identity (3)])
Identity ([1, 2, 3])

extend :: Extend w => (w a -⁠> b, w a) -⁠> w b

Function wrapper for fantasy-land/extend.

fantasy-land/extend implementations are provided for the following built-in types: Array and Function.

> extend (ss => ss.join (''), ['x', 'y', 'z'])
['xyz', 'yz', 'z']

> extend (f => f ([3, 4]), reverse) ([1, 2])
[4, 3, 2, 1]

duplicate :: Extend w => w a -⁠> w (w a)

Adds one level of nesting to a comonadic structure.

This function is derived from extend.

> duplicate (Identity (1))
Identity (Identity (1))

> duplicate ([1])
[[1]]

> duplicate ([1, 2, 3])
[[1, 2, 3], [2, 3], [3]]

> duplicate (reverse) ([1, 2]) ([3, 4])
[4, 3, 2, 1]

extract :: Comonad w => w a -⁠> a

Function wrapper for fantasy-land/extract.

> extract (Identity (42))
42

contramap :: Contravariant f => (b -⁠> a, f a) -⁠> f b

Function wrapper for fantasy-land/contramap.

fantasy-land/contramap implementations are provided for the following built-in types: Function.

> contramap (s => s.length, Math.sqrt) ('Sanctuary')
3