Standard library for Fantasy Land
npm install sanctuary-type-classesThe [Fantasy Land Specification][FL] "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.
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)
#### 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:
``javascript
// 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.bar
Members of the Foo type class whose values have a method are also
members of the Bar type class.
Each TypeClass value has a test field: a function which acceptstrue
any JavaScript value and returns if the value satisfies thefalse
type class's predicate and the predicates of all the type class's
dependencies; otherwise.
TypeClass values may be used with [sanctuary-def][type-classes]
to define parametrically polymorphic functions which verify their
type-class constraints at run time.
#### Setoid :: TypeClass
TypeClass value for [Setoid][].
`javascript
> Z.Setoid.test (null)
true
> Z.Setoid.test (Useless)
false
> Z.Setoid.test ([1, 2, 3])
true
> Z.Setoid.test ([Useless])
false
`
#### Ord :: TypeClass
TypeClass value for [Ord][].
`javascript
> Z.Ord.test (0)
true
> Z.Ord.test (Math.sqrt)
false
> Z.Ord.test ([1, 2, 3])
true
> Z.Ord.test ([Math.sqrt])
false
`
#### Semigroupoid :: TypeClass
TypeClass value for [Semigroupoid][].
`javascript
> Z.Semigroupoid.test (Math.sqrt)
true
> Z.Semigroupoid.test (0)
false
`
TypeClass value for [Category][].
`javascript
> Z.Category.test (Math.sqrt)
true
> Z.Category.test (0)
false
`
TypeClass value for [Semigroup][].
`javascript
> Z.Semigroup.test ('')
true
> Z.Semigroup.test (0)
false
`
#### Monoid :: TypeClass
TypeClass value for [Monoid][].
`javascript
> Z.Monoid.test ('')
true
> Z.Monoid.test (0)
false
`
#### Group :: TypeClass
TypeClass value for [Group][].
`javascript
> Z.Group.test (Sum (0))
true
> Z.Group.test ('')
false
`
TypeClass value for [Filterable][].
`javascript
> Z.Filterable.test ({})
true
> Z.Filterable.test ('')
false
`
#### Functor :: TypeClass
TypeClass value for [Functor][].
`javascript
> Z.Functor.test ([])
true
> Z.Functor.test ('')
false
`
TypeClass value for [Bifunctor][].
`javascript
> Z.Bifunctor.test (Pair ('foo') (64))
true
> Z.Bifunctor.test ([])
false
`
TypeClass value for [Profunctor][].
`javascript
> Z.Profunctor.test (Math.sqrt)
true
> Z.Profunctor.test ([])
false
`
#### Apply :: TypeClass
TypeClass value for [Apply][].
`javascript
> Z.Apply.test ([])
true
> Z.Apply.test ('')
false
`
TypeClass value for [Applicative][].
`javascript
> Z.Applicative.test ([])
true
> Z.Applicative.test ({})
false
`
#### Chain :: TypeClass
TypeClass value for [Chain][].
`javascript
> Z.Chain.test ([])
true
> Z.Chain.test ({})
false
`
TypeClass value for [ChainRec][].
`javascript
> Z.ChainRec.test ([])
true
> Z.ChainRec.test ({})
false
`
#### Monad :: TypeClass
TypeClass value for [Monad][].
`javascript
> Z.Monad.test ([])
true
> Z.Monad.test ({})
false
`
#### Alt :: TypeClass
TypeClass value for [Alt][].
`javascript
> Z.Alt.test ({})
true
> Z.Alt.test ('')
false
`
#### Plus :: TypeClass
TypeClass value for [Plus][].
`javascript
> Z.Plus.test ({})
true
> Z.Plus.test ('')
false
`
TypeClass value for [Alternative][].
`javascript
> Z.Alternative.test ([])
true
> Z.Alternative.test ({})
false
`
TypeClass value for [Foldable][].
`javascript
> Z.Foldable.test ({})
true
> Z.Foldable.test ('')
false
`
TypeClass value for [Traversable][].
`javascript
> Z.Traversable.test ([])
true
> Z.Traversable.test ('')
false
`
#### Extend :: TypeClass
TypeClass value for [Extend][].
`javascript
> Z.Extend.test ([])
true
> Z.Extend.test ({})
false
`
#### Comonad :: TypeClass
TypeClass value for [Comonad][].
`javascript
> Z.Comonad.test (Identity (0))
true
> Z.Comonad.test ([])
false
`
#### Contravariant :: TypeClass
TypeClass value for [Contravariant][].
`javascript
> Z.Contravariant.test (Math.sqrt)
true
> Z.Contravariant.test ([])
false
`
#### equals :: (a, b) -> Boolean
Returns true if its arguments are equal; false otherwise.
Specifically:
- Arguments with different [type identities][] are unequal.
- If the first argument has a [fantasy-land/equals][] method,fantasy-land/equals
that method is invoked to determine whether the arguments are
equal ( implementations are provided for the
following built-in types: Null, Undefined, Boolean, Number, Date,
RegExp, String, Array, Arguments, Error, Object, and Function).
- Otherwise, the arguments are equal if their
[entries][Object.entries] are equal (according to this algorithm).
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.
`javascript
> Z.equals (0, -0)
true
> Z.equals (NaN, NaN)
true
> Z.equals (Cons (1, Cons (2, Nil)), Cons (1, Cons (2, Nil)))
true
> Z.equals (Cons (1, Cons (2, Nil)), Cons (2, Cons (1, Nil)))
false
`
Returns true if its arguments are of the same type and the first isfantasy-land/lte
less than the second according to the type's [][]false
method; otherwise.
This function is derived from lte.
`javascript
> Z.lt (0, 0)
false
> Z.lt (0, 1)
true
> Z.lt (1, 0)
false
`
#### lte :: (a, b) -> Boolean
Returns true if its arguments are of the same type and the firstfantasy-land/lte
is less than or equal to the second according to the type's
[][] 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.
`javascript
> Z.lte (0, 0)
true
> Z.lte (0, 1)
true
> Z.lte (1, 0)
false
`
Returns true if its arguments are of the same type and the first isfantasy-land/lte
greater than the second according to the type's [][]false
method; otherwise.
This function is derived from lte.
`javascript
> Z.gt (0, 0)
false
> Z.gt (0, 1)
false
> Z.gt (1, 0)
true
`
#### gte :: (a, b) -> Boolean
Returns true if its arguments are of the same type and the firstfantasy-land/lte
is greater than or equal to the second according to the type's
[][] method; false otherwise.
This function is derived from lte.
`javascript
> Z.gte (0, 0)
true
> Z.gte (0, 1)
false
> Z.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.
`javascript
> Z.min (10, 2)
2
> Z.min (new Date ('1999-12-31'), new Date ('2000-01-01'))
new Date ('1999-12-31')
> Z.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.
`javascript
> Z.max (10, 2)
10
> Z.max (new Date ('1999-12-31'), new Date ('2000-01-01'))
new Date ('2000-01-01')
> Z.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.
`javascript
> Z.clamp (0, 100, 42)
42
> Z.clamp (0, 100, -1)
0
> Z.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.
`javascript`
> Z.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.
`javascript`
> Z.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.
`javascript
> Z.concat ('abc', 'def')
'abcdef'
> Z.concat ([1, 2, 3], [4, 5, 6])
[1, 2, 3, 4, 5, 6]
> Z.concat ({x: 1, y: 2}, {y: 3, z: 4})
{x: 1, y: 3, z: 4}
> Z.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.
`javascript
> Z.empty (String)
''
> Z.empty (Array)
[]
> Z.empty (Object)
{}
> Z.empty (List)
Nil
`
#### invert :: Group g => g -> g
Function wrapper for [fantasy-land/invert][].
`javascript`
> Z.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.
`javascript
> Z.filter (x => x % 2 == 1, [1, 2, 3])
[1, 3]
> Z.filter (x => x % 2 == 1, {x: 1, y: 2, z: 3})
{x: 1, z: 3}
> Z.filter (x => x % 2 == 1, Cons (1, Cons (2, Cons (3, Nil))))
Cons (1, Cons (3, Nil))
> Z.filter (x => x % 2 == 1, Nothing)
Nothing
> Z.filter (x => x % 2 == 1, Just (0))
Nothing
> Z.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.
`javascript
> Z.reject (x => x % 2 == 1, [1, 2, 3])
[2]
> Z.reject (x => x % 2 == 1, {x: 1, y: 2, z: 3})
{y: 2}
> Z.reject (x => x % 2 == 1, Cons (1, Cons (2, Cons (3, Nil))))
Cons (2, Nil)
> Z.reject (x => x % 2 == 1, Nothing)
Nothing
> Z.reject (x => x % 2 == 1, Just (0))
Just (0)
> Z.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.
`javascript
> Z.map (Math.sqrt, [1, 4, 9])
[1, 2, 3]
> Z.map (Math.sqrt, {x: 1, y: 4, z: 9})
{x: 1, y: 2, z: 3}
> Z.map (Math.sqrt, s => s.length) ('Sanctuary')
3
> Z.map (Math.sqrt, Pair ('foo') (64))
Pair ('foo') (8)
> Z.map (Math.sqrt, Nil)
Nil
> Z.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.
`javascript
> Z.flip (x => y => x + y, '!') ('foo')
'foo!'
> Z.flip ([Math.floor, Math.ceil], 1.5)
[1, 2]
> Z.flip ({floor: Math.floor, ceil: Math.ceil}, 1.5)
{floor: 1, ceil: 2}
> Z.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][].
`javascript`
> Z.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.
`javascript`
> Z.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.
`javascript`
> Z.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.
`javascript
> Z.ap ([Math.sqrt, x => x * x], [1, 4, 9, 16, 25])
[1, 2, 3, 4, 5, 1, 16, 81, 256, 625]
> Z.ap ({a: Math.sqrt, b: x => x * x}, {a: 16, b: 10, c: 1})
{a: 4, b: 100}
> Z.ap (s => n => s.slice (0, n), s => Math.ceil (s.length / 2)) ('Haskell')
'Hask'
> Z.ap (Identity (Math.sqrt), Identity (64))
Identity (8)
> Z.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.
`javascript
> Z.lift2 (x => y => Math.pow (x, y), [10], [1, 2, 3])
[10, 100, 1000]
> Z.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.
`javascript
> Z.lift3 (x => y => z => x + z + y,
. ['<', '['],
. ['>', ']'],
. ['foo', 'bar', 'baz'])
[ '
. '
. '[foo]', '[bar]', '[baz]' ]
> Z.lift3 (x => y => z => x + z + y,
. Identity ('<'),
. Identity ('>'),
. Identity ('baz'))
Identity ('
`
#### 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.
`javascript
> Z.apFirst ([1, 2], [3, 4])
[1, 1, 2, 2]
> Z.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.
`javascript
> Z.apSecond ([1, 2], [3, 4])
[3, 4, 3, 4]
> Z.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.
`javascript
> Z.of (Array, 42)
[42]
> Z.of (Function, 42) (null)
42
> Z.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.
`javascript
> Z.append (3, [1, 2])
[1, 2, 3]
> Z.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.
`javascript
> Z.prepend (1, [2, 3])
[1, 2, 3]
> Z.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.
`javascript
> Z.chain (x => [x, x], [1, 2, 3])
[1, 1, 2, 2, 3, 3]
> Z.chain (x => x % 2 == 1 ? Z.of (List, x) : Nil,
. Cons (1, Cons (2, Cons (3, Nil))))
Cons (1, Cons (3, Nil))
> Z.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.
`javascript
> Z.join ([[1], [2], [3]])
[1, 2, 3]
> Z.join ([[[1, 2, 3]]])
[[1, 2, 3]]
> Z.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.
`javascript`
> Z.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.
`javascript
> Z.alt ([1, 2, 3], [4, 5, 6])
[1, 2, 3, 4, 5, 6]
> Z.alt (Nothing, Nothing)
Nothing
> Z.alt (Nothing, Just (1))
Just (1)
> Z.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.
`javascript
> Z.zero (Array)
[]
> Z.zero (Object)
{}
> Z.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.
`javascript
> Z.reduce ((xs, x) => [x].concat (xs), [], [1, 2, 3])
[3, 2, 1]
> Z.reduce (Z.concat, '', Cons ('foo', Cons ('bar', Cons ('baz', Nil))))
'foobarbaz'
> Z.reduce (Z.concat, '', {foo: 'x', bar: 'y', baz: 'z'})
'yzx'
`
#### size :: Foldable f => f a -> Integer
Returns the number of elements of the given structure.
This function is derived from reduce.
`javascript
> Z.size ([])
0
> Z.size (['foo', 'bar', 'baz'])
3
> Z.size (Nil)
0
> Z.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 thefalse
predicate; otherwise.
This function is derived from reduce.
`javascript
> Z.all (Number.isInteger, [])
true
> Z.all (Number.isInteger, [1, 2, 3])
true
> Z.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.
`javascript
> Z.any (Number.isInteger, [])
false
> Z.any (Number.isInteger, [1, 2, 3])
true
> Z.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 thefalse
predicate; otherwise.
This function is derived from any. Z.none (pred, foldable) is!(Z.any (pred, foldable))
equivalent to .
See also all.
`javascript
> Z.none (Number.isInteger, [])
true
> Z.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 thefalse
value is an element of the structure; otherwise.
This function is derived from equals and
reduce.
`javascript
> Z.elem ('c', ['a', 'b', 'c'])
true
> Z.elem ('x', ['a', 'b', 'c'])
false
> Z.elem (3, {x: 1, y: 2, z: 3})
true
> Z.elem (8, {x: 1, y: 2, z: 3})
false
> Z.elem (0, Just (0))
true
> Z.elem (0, Just (1))
false
> Z.elem (0, Nothing)
false
`
#### intercalate :: (Monoid m, Foldable f) => (m, f m) -> m
Concatenates the elements of the given structure, separating each pair
of adjacent elements with the given separator.
This function is derived from concat, empty,
and reduce.
`javascript
> Z.intercalate (', ', [])
''
> Z.intercalate (', ', ['foo', 'bar', 'baz'])
'foo, bar, baz'
> Z.intercalate (', ', Nil)
''
> Z.intercalate (', ', Cons ('foo', Cons ('bar', Cons ('baz', Nil))))
'foo, bar, baz'
> Z.intercalate ([0, 0, 0], [])
[]
> Z.intercalate ([0, 0, 0], [[1], [2, 3], [4, 5, 6], [7, 8], [9]])
[1, 0, 0, 0, 2, 3, 0, 0, 0, 4, 5, 6, 0, 0, 0, 7, 8, 0, 0, 0, 9]
`
#### 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.
`javascript`
> Z.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.
`javascript
> Z.reverse ([1, 2, 3])
[3, 2, 1]
> Z.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.
`javascript
> Z.sort (['foo', 'bar', 'baz'])
['bar', 'baz', 'foo']
> Z.sort ([Just (2), Nothing, Just (1)])
[Nothing, Just (1), Just (2)]
> Z.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.
`javascript
> Z.sortBy (s => s.length, ['red', 'green', 'blue'])
['red', 'blue', 'green']
> Z.sortBy (s => s.length, ['black', 'white'])
['black', 'white']
> Z.sortBy (s => s.length, ['white', 'black'])
['white', 'black']
> Z.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.
`javascript
> Z.traverse (Array, x => x, [[1, 2, 3], [4, 5]])
[[1, 4], [1, 5], [2, 4], [2, 5], [3, 4], [3, 5]]
> Z.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.
`javascript
> Z.sequence (Array, Identity ([1, 2, 3]))
[Identity (1), Identity (2), Identity (3)]
> Z.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.
`javascript
> Z.extend (ss => ss.join (''), ['x', 'y', 'z'])
['xyz', 'yz', 'z']
> Z.extend (f => f ([3, 4]), Z.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.
`javascript
> Z.duplicate (Identity (1))
Identity (Identity (1))
> Z.duplicate ([1])
[[1]]
> Z.duplicate ([1, 2, 3])
[[1, 2, 3], [2, 3], [3]]
> Z.duplicate (Z.reverse) ([1, 2]) ([3, 4])
[4, 3, 2, 1]
`
#### extract :: Comonad w => w a -> a
Function wrapper for [fantasy-land/extract][].
`javascript`
> Z.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.
`javascript`
> Z.contramap (s => s.length, Math.sqrt) ('Sanctuary')
3
[Alt]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#alt
[Alternative]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#alternative
[Applicative]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#applicative
[Apply]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#apply
[Bifunctor]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#bifunctor
[Category]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#category
[Chain]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#chain
[ChainRec]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#chainrec
[Comonad]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#comonad
[Contravariant]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#contravariant
[Extend]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#extend
[FL]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0
[Filterable]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#filterable
[Foldable]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#foldable
[Functor]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#functor
[Group]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#group
[Monad]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#monad
[Monoid]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#monoid
[Ord]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#ord
[Plus]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#plus
[Profunctor]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#profunctor
[Semigroup]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#semigroup
[Semigroupoid]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#semigroupoid
[Setoid]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#setoid
[Traversable]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#traversable
[Object.entries]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Object/entriesfantasy-land/alt
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#alt-methodfantasy-land/ap
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#ap-methodfantasy-land/bimap
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#bimap-methodfantasy-land/chain
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#chain-methodfantasy-land/chainRec
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#chainrec-methodfantasy-land/compose
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#compose-methodfantasy-land/concat
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#concat-methodfantasy-land/contramap
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#contramap-methodfantasy-land/empty
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#empty-methodfantasy-land/equals
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#equals-methodfantasy-land/extend
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#extend-methodfantasy-land/extract
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#extract-methodfantasy-land/filter
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#filter-methodfantasy-land/id
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#id-methodfantasy-land/invert
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#invert-methodfantasy-land/lte
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#lte-methodfantasy-land/map
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#map-methodfantasy-land/of
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#of-methodfantasy-land/promap
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#promap-methodfantasy-land/reduce
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#reduce-methodfantasy-land/traverse
[]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#traverse-methodfantasy-land/zero`]: https://github.com/fantasyland/fantasy-land/tree/v5.0.0#zero-method
[
[stable sort]: https://en.wikipedia.org/wiki/Sorting_algorithm#Stability
[type identities]: https://github.com/sanctuary-js/sanctuary-type-identifiers/tree/v3.0.0
[type-classes]: https://github.com/sanctuary-js/sanctuary-def#type-classes