sanctuary

❑ Sanctuary

Sanctuary is a JavaScript functional programming library inspired by [Haskell][] and [PureScript][]. It’s stricter than [Ramda][], and provides a similar suite of functions.

Sanctuary promotes programs composed of simple, pure functions. Such programs are easier to comprehend, test, and maintain – they are also a pleasure to write.

Sanctuary provides two data types, [Maybe][] and [Either][], both of which are compatible with [Fantasy Land][]. Thanks to these data types even Sanctuary functions that may fail, such as head, are composable.

Sanctuary makes it possible to write safe code without null checks. In JavaScript it’s trivial to introduce a possible run-time type error:

words[0].toUpperCase()

If words is [] we’ll get a familiar error at run-time:

TypeError: Cannot read property 'toUpperCase' of undefined

Sanctuary gives us a fighting chance of avoiding such errors. We might write:

S.map (S.toUpper) (S.head (words))

Sanctuary is designed to work in Node.js and in ES5-compatible browsers.

❑ Folktale

[Folktale][], like Sanctuary, is a standard library for functional programming in JavaScript. It is well designed and well documented. Whereas Sanctuary treats JavaScript as a member of the ML language family, Folktale embraces JavaScript’s object-oriented programming model. Programming with Folktale resembles programming with Scala.

❑ Ramda

[Ramda][] provides several functions that return problematic values such as undefined, Infinity, or NaN when applied to unsuitable inputs. These are known as [partial functions][]. Partial functions necessitate the use of guards or null checks. In order to safely use R.head, for example, one must ensure that the array is non-empty:

if (R.isEmpty (xs)) {
  // ...
} else {
  return f (R.head (xs));
}

Using the Maybe type renders such guards (and null checks) unnecessary. Changing functions such as R.head to return Maybe values was proposed in [ramda/ramda#683][], but was considered too much of a stretch for JavaScript programmers. Sanctuary was released the following month, in January 2015, as a companion library to Ramda.

In addition to broadening in scope in the years since its release, Sanctuary’s philosophy has diverged from Ramda’s in several respects.

❑ Totality

Every Sanctuary function is defined for every value that is a member of the function’s input type. Such functions are known as [total functions][]. Ramda, on the other hand, contains a number of [partial functions][].

❑ Information preservation

Certain Sanctuary functions preserve more information than their Ramda counterparts. Examples:

|> R.tail ([])                      |> S.tail ([])
[]                                  Nothing

|> R.tail (['foo'])                 |> S.tail (['foo'])
[]                                  Just ([])

|> R.replace (/^x/) ('') ('abc')    |> S.stripPrefix ('x') ('abc')
'abc'                               Nothing

|> R.replace (/^x/) ('') ('xabc')   |> S.stripPrefix ('x') ('xabc')
'abc'                               Just ('abc')

❑ Invariants

Sanctuary performs rigorous [type checking][] of inputs and outputs, and throws a descriptive error if a type error is encountered. This allows bugs to be caught and fixed early in the development cycle.

Ramda operates on the [garbage in, garbage out][GIGO] principle. Functions are documented to take arguments of particular types, but these invariants are not enforced. The problem with this approach in a language as permissive as JavaScript is that there’s no guarantee that garbage input will produce garbage output ([ramda/ramda#1413][]). Ramda performs ad hoc type checking in some such cases ([ramda/ramda#1419][]).

Sanctuary can be configured to operate in garbage in, garbage out mode. Ramda cannot be configured to enforce its invariants.

❑ Currying

Sanctuary functions are curried. There is, for example, exactly one way to apply S.reduce to S.add, 0, and xs:

• S.reduce (S.add) (0) (xs)

Ramda functions are also curried, but in a complex manner. There are four ways to apply R.reduce to R.add, 0, and xs:

• R.reduce (R.add) (0) (xs)
• R.reduce (R.add) (0, xs)
• R.reduce (R.add, 0) (xs)
• R.reduce (R.add, 0, xs)

Ramda supports all these forms because curried functions enable partial application, one of the library’s tenets, but f(x)(y)(z) is considered too unfamiliar and too unattractive to appeal to JavaScript programmers.

Sanctuary’s developers prefer a simple, unfamiliar construct to a complex, familiar one. Familiarity can be acquired; complexity is intrinsic.

The lack of breathing room in f(x)(y)(z) impairs readability. The simple solution to this problem, proposed in [#438][], is to include a space when applying a function: f (x) (y) (z).

Ramda also provides a special placeholder value, [R.__][], that removes the restriction that a function must be applied to its arguments in order. The following expressions are equivalent:

• R.reduce (R.__, 0, xs) (R.add)
• R.reduce (R.add, R.__, xs) (0)
• R.reduce (R.__, 0) (R.add) (xs)
• R.reduce (R.__, 0) (R.add, xs)
• R.reduce (R.__, R.__, xs) (R.add) (0)
• R.reduce (R.__, R.__, xs) (R.add, 0)

❑ Variadic functions

Ramda provides several functions that take any number of arguments. These are known as [variadic functions][]. Additionally, Ramda provides several functions that take variadic functions as arguments. Although natural in a dynamically typed language, variadic functions are at odds with the type notation Ramda and Sanctuary both use, leading to some indecipherable type signatures such as this one:

R.lift :: (*... -> *...) -> ([*]... -> [*])

Sanctuary has no variadic functions, nor any functions that take variadic functions as arguments. Sanctuary provides two “lift” functions, each with a helpful type signature:

S.lift2 :: Apply f => (a -> b -> c) -> f a -> f b -> f c
S.lift3 :: Apply f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

❑ Implicit context

Ramda provides [R.bind][] and [R.invoker][] for working with methods. Additionally, many Ramda functions use Function#call or Function#apply to preserve context. Sanctuary makes no allowances for this.

❑ Transducers

Several Ramda functions act as transducers. Sanctuary provides no support for transducers.

❑ Modularity

Whereas Ramda has no dependencies, Sanctuary has a modular design: [sanctuary-def][] provides type checking, [sanctuary-type-classes][] provides Fantasy Land functions and type classes, [sanctuary-show][] provides string representations, and algebraic data types are provided by [sanctuary-either][], [sanctuary-maybe][], and [sanctuary-pair][]. Not only does this approach reduce the complexity of Sanctuary itself, but it allows these components to be reused in other contexts.

❑ Types

Sanctuary uses Haskell-like type signatures to describe the types of values, including functions. 'foo', for example, is a member of String; [1, 2, 3] is a member of Array Number. The double colon (::) is used to mean “is a member of”, so one could write:

'foo' :: String
[1, 2, 3] :: Array Number

An identifier may appear to the left of the double colon:

Math.PI :: Number

The arrow (->) is used to express a function’s type:

Math.abs :: Number -> Number

That states that Math.abs is a unary function that takes an argument of type Number and returns a value of type Number.

Some functions are parametrically polymorphic: their types are not fixed. Type variables are used in the representations of such functions:

S.I :: a -> a

a is a type variable. Type variables are not capitalized, so they are differentiable from type identifiers (which are always capitalized). By convention type variables have single-character names. The signature above states that S.I takes a value of any type and returns a value of the same type. Some signatures feature multiple type variables:

S.K :: a -> b -> a

It must be possible to replace all occurrences of a with a concrete type. The same applies for each other type variable. For the function above, the types with which a and b are replaced may be different, but needn’t be.

Since all Sanctuary functions are curried (they accept their arguments one at a time), a binary function is represented as a unary function that returns a unary function: * -> * -> *. This aligns neatly with Haskell, which uses curried functions exclusively. In JavaScript, though, we may wish to represent the types of functions with arities less than or greater than one. The general form is (<input-types>) -> <output-type>, where <input-types> comprises zero or more comma–space (, ) -separated type representations:

• () -> String
• (a, b) -> a
• (a, b, c) -> d

Number -> Number can thus be seen as shorthand for (Number) -> Number.

Sanctuary embraces types. JavaScript doesn’t support algebraic data types, but these can be simulated by providing a group of data constructors that return values with the same set of methods. A value of the Either type, for example, is created via the Left constructor or the Right constructor.

It’s necessary to extend Haskell’s notation to describe implicit arguments to the methods provided by Sanctuary’s types. In x.map(y), for example, the map method takes an implicit argument x in addition to the explicit argument y. The type of the value upon which a method is invoked appears at the beginning of the signature, separated from the arguments and return value by a squiggly arrow (~>). The type of the fantasy-land/map method of the Maybe type is written Maybe a ~> (a -> b) -> Maybe b. One could read this as:

When the fantasy-land/map method is invoked on a value of type Maybe a (for any type a) with an argument of type a -> b (for any type b), it returns a value of type Maybe b.

The squiggly arrow is also used when representing non-function properties. Maybe a ~> Boolean, for example, represents a Boolean property of a value of type Maybe a.

Sanctuary supports type classes: constraints on type variables. Whereas a -> a implicitly supports every type, Functor f => (a -> b) -> f a -> f b requires that f be a type that satisfies the requirements of the Functor type class. Type-class constraints appear at the beginning of a type signature, separated from the rest of the signature by a fat arrow (=>).

❑ Type checking

Sanctuary functions are defined via [sanctuary-def][] to provide run-time type checking. This is tremendously useful during development: type errors are reported immediately, avoiding circuitous stack traces (at best) and silent failures due to type coercion (at worst). For example:

S.add (2) (true);
// ! TypeError: Invalid value
//
//   add :: FiniteNumber -> FiniteNumber -> FiniteNumber
//                          ^^^^^^^^^^^^
//                               1
//
//   1)  true :: Boolean
//
//   The value at position 1 is not a member of ‘FiniteNumber’.
//
//   See https://github.com/sanctuary-js/sanctuary-def/tree/v0.22.0#FiniteNumber for information about the FiniteNumber type.

Compare this to the behaviour of Ramda’s unchecked equivalent:

R.add (2) (true);
// => 3

There is a performance cost to run-time type checking. Type checking is disabled by default if process.env.NODE_ENV is 'production'. If this rule is unsuitable for a given program, one may use create to create a Sanctuary module based on a different rule. For example:

const S = sanctuary.create ({
  checkTypes: localStorage.getItem ('SANCTUARY_CHECK_TYPES') === 'true',
  env: sanctuary.env,
});

Occasionally one may wish to perform an operation that is not type safe, such as mapping over an object with heterogeneous values. This is possible via selective use of unchecked functions.

❑ Installation

npm install sanctuary will install Sanctuary for use in Node.js.

To add Sanctuary to a website, add the following <script> element, replacing X.Y.Z with a version number greater than or equal to 2.0.2:

<script src="https://cdn.jsdelivr.net/gh/sanctuary-js/[email protected]/dist/bundle.js"></script>

Optionally, define aliases for various modules:

const S = window.sanctuary;
const $ = window.sanctuaryDef;
// ...

❑ API

❑ Configure

create :: { checkTypes :: Boolean, env :: Array Type } -⁠> Module

Takes an options record and returns a Sanctuary module. checkTypes specifies whether to enable type checking. The module’s polymorphic functions (such as I) require each value associated with a type variable to be a member of at least one type in the environment.

A well-typed application of a Sanctuary function will produce the same result regardless of whether type checking is enabled. If type checking is enabled, a badly typed application will produce an exception with a descriptive error message.

The following snippet demonstrates defining a custom type and using create to produce a Sanctuary module that is aware of that type:

const {create, env} = require ('sanctuary');
const $ = require ('sanctuary-def');
const type = require ('sanctuary-type-identifiers');

//    Identity :: a -> Identity a
const Identity = x => {
  const identity = Object.create (Identity$prototype);
  identity.value = x;
  return identity;
};

//    identityTypeIdent :: String
const identityTypeIdent = 'my-package/Identity@1';

const Identity$prototype = {
  '@@type': identityTypeIdent,
  '@@show': function() { return `Identity (${S.show (this.value)})`; },
  'fantasy-land/map': function(f) { return Identity (f (this.value)); },
};

//    IdentityType :: Type -> Type
const IdentityType = $.UnaryType
  ('Identity')
  ('http://example.com/my-package#Identity')
  ([])
  (x => type (x) === identityTypeIdent)
  (identity => [identity.value]);

const S = create ({
  checkTypes: process.env.NODE_ENV !== 'production',
  env: env.concat ([IdentityType ($.Unknown)]),
});

S.map (S.sub (1)) (Identity (43));
// => Identity (42)

See also env.

env :: Array Type

The Sanctuary module’s environment ((S.create ({checkTypes, env})).env is a reference to env). Useful in conjunction with create.

> S.env
[ $.AnyFunction,
. $.Arguments,
. $.Array ($.Unknown),
. $.Array2 ($.Unknown) ($.Unknown),
. $.Boolean,
. $.Buffer,
. $.Date,
. $.Descending ($.Unknown),
. $.Either ($.Unknown) ($.Unknown),
. $.Error,
. $.Fn ($.Unknown) ($.Unknown),
. $.HtmlElement,
. $.Identity ($.Unknown),
. $.JsMap ($.Unknown) ($.Unknown),
. $.JsSet ($.Unknown),
. $.Maybe ($.Unknown),
. $.Module,
. $.Null,
. $.Number,
. $.Object,
. $.Pair ($.Unknown) ($.Unknown),
. $.RegExp,
. $.StrMap ($.Unknown),
. $.String,
. $.Symbol,
. $.Type,
. $.TypeClass,
. $.Undefined ]

unchecked :: Module

A complete Sanctuary module that performs no type checking. This is useful as it permits operations that Sanctuary’s type checking would disallow, such as mapping over an object with heterogeneous values.

See also create.

> S.unchecked.map (S.show) ({x: 'foo', y: true, z: 42})
{x: '"foo"', y: 'true', z: '42'}

Opting out of type checking may cause type errors to go unnoticed.

> S.unchecked.add (2) ('2')
'22'

❑ Classify

type :: Any -⁠> { namespace :: Maybe String, name :: String, version :: NonNegativeInteger }

Returns the result of parsing the [type identifier][] of the given value.

> S.type (S.Just (42))
{namespace: Just ('sanctuary-maybe'), name: 'Maybe', version: 1}

> S.type ([1, 2, 3])
{namespace: Nothing, name: 'Array', version: 0}

is :: Type -⁠> Any -⁠> Boolean

Returns true [iff][] the given value is a member of the specified type. See [$.test][] for details.

> S.is ($.Array ($.Integer)) ([1, 2, 3])
true

> S.is ($.Array ($.Integer)) ([1, 2, 3.14])
false

❑ Showable

show :: Any -⁠> String

Alias of [show][].

> S.show (-0)
'-0'

> S.show (['foo', 'bar', 'baz'])
'["foo", "bar", "baz"]'

> S.show ({x: 1, y: 2, z: 3})
'{"x": 1, "y": 2, "z": 3}'

> S.show (S.Left (S.Right (S.Just (S.Nothing))))
'Left (Right (Just (Nothing)))'

❑ Fantasy Land

Sanctuary is compatible with the [Fantasy Land][] specification.

equals :: Setoid a => a -⁠> a -⁠> Boolean

Curried version of [Z.equals][] that requires two arguments of the same type.

To compare values of different types first use create to create a Sanctuary module with type checking disabled, then use that module’s equals function.

> S.equals (0) (-0)
true

> S.equals (NaN) (NaN)
true

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

> S.equals (S.Just ([1, 2, 3])) (S.Just ([1, 2, 4]))
false

lt :: Ord a => a -⁠> a -⁠> Boolean

Returns true [iff][] the second argument is less than the first according to [Z.lt][].

> S.filter (S.lt (3)) ([1, 2, 3, 4, 5])
[1, 2]

lte :: Ord a => a -⁠> a -⁠> Boolean

Returns true [iff][] the second argument is less than or equal to the first according to [Z.lte][].

> S.filter (S.lte (3)) ([1, 2, 3, 4, 5])
[1, 2, 3]

gt :: Ord a => a -⁠> a -⁠> Boolean

Returns true [iff][] the second argument is greater than the first according to [Z.gt][].

> S.filter (S.gt (3)) ([1, 2, 3, 4, 5])
[4, 5]

gte :: Ord a => a -⁠> a -⁠> Boolean

Returns true [iff][] the second argument is greater than or equal to the first according to [Z.gte][].

> S.filter (S.gte (3)) ([1, 2, 3, 4, 5])
[3, 4, 5]

min :: Ord a => a -⁠> a -⁠> a

Returns the smaller of its two arguments (according to [Z.lte][]).

See also max.

> S.min (10) (2)
2

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

> S.min ('10') ('2')
'10'

max :: Ord a => a -⁠> a -⁠> a

Returns the larger of its two arguments (according to [Z.lte][]).

See also min.

> S.max (10) (2)
10

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

> S.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.

See also min and max.

> S.clamp (0) (100) (42)
42

> S.clamp (0) (100) (-1)
0

> S.clamp ('A') ('Z') ('~')
'Z'

id :: Category c => TypeRep c -⁠> c

[Type-safe][sanctuary-def] version of [Z.id][].

> S.id (Function) (42)
42

concat :: Semigroup a => a -⁠> a -⁠> a

Curried version of [Z.concat][].

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

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

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

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

> S.concat (Sum (18)) (Sum (24))
Sum (42)

empty :: Monoid a => TypeRep a -⁠> a

[Type-safe][sanctuary-def] version of [Z.empty][].

> S.empty (String)
''

> S.empty (Array)
[]

> S.empty (Object)
{}

> S.empty (Sum)
Sum (0)

invert :: Group g => g -⁠> g

[Type-safe][sanctuary-def] version of [Z.invert][].

> S.invert (Sum (5))
Sum (-5)

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

Curried version of [Z.filter][]. Discards every element that does not satisfy the predicate.

See also reject.

> S.filter (S.odd) ([1, 2, 3])
[1, 3]

> S.filter (S.odd) ({x: 1, y: 2, z: 3})
{x: 1, z: 3}

> S.filter (S.odd) (S.Nothing)
Nothing

> S.filter (S.odd) (S.Just (0))
Nothing

> S.filter (S.odd) (S.Just (1))
Just (1)

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

Curried version of [Z.reject][]. Discards every element that satisfies the predicate.

See also filter.

> S.reject (S.odd) ([1, 2, 3])
[2]

> S.reject (S.odd) ({x: 1, y: 2, z: 3})
{y: 2}

> S.reject (S.odd) (S.Nothing)
Nothing

> S.reject (S.odd) (S.Just (0))
Just (0)

> S.reject (S.odd) (S.Just (1))
Nothing

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

Curried version of [Z.map][].

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

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

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

> S.map (Math.sqrt) (S.Right (9))
Right (3)

> S.map (Math.sqrt) (S.Pair (99980001) (99980001))
Pair (99980001) (9999)

Replacing Functor f => f with Function x produces the B combinator from combinatory logic (i.e. compose):

Functor f => (a -> b) -> f a -> f b
(a -> b) -> Function x a -> Function x b
(a -> c) -> Function x a -> Function x c
(b -> c) -> Function x b -> Function x c
(b -> c) -> Function a b -> Function a c
(b -> c) -> (a -> b) -> (a -> c)

> S.map (Math.sqrt) (S.add (1)) (99)
10

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

Curried version of [Z.flip][]. Maps over the given functions, applying each to the given value.

Replacing Functor f => f with Function x produces the C combinator from combinatory logic:

Functor f => f (a -> b) -> a -> f b
Function x (a -> b) -> a -> Function x b
Function x (a -> c) -> a -> Function x c
Function x (b -> c) -> b -> Function x c
Function a (b -> c) -> b -> Function a c
(a -> b -> c) -> b -> a -> c

> S.flip (S.concat) ('!') ('foo')
'foo!'

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

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

> S.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

Curried version of [Z.bimap][].

> S.bimap (S.toUpper) (Math.sqrt) (S.Pair ('foo') (64))
Pair ('FOO') (8)

> S.bimap (S.toUpper) (Math.sqrt) (S.Left ('foo'))
Left ('FOO')

> S.bimap (S.toUpper) (Math.sqrt) (S.Right (64))
Right (8)

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

Curried version of [Z.mapLeft][]. Maps the given function over the left side of a Bifunctor.

> S.mapLeft (S.toUpper) (S.Pair ('foo') (64))
Pair ('FOO') (64)

> S.mapLeft (S.toUpper) (S.Left ('foo'))
Left ('FOO')

> S.mapLeft (S.toUpper) (S.Right (64))
Right (64)

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

Curried version of [Z.promap][].

> S.promap (Math.abs) (S.add (1)) (Math.sqrt) (-100)
11

alt :: Alt f => f a -⁠> f a -⁠> f a

Curried version of [Z.alt][] with arguments flipped to facilitate partial application.

> S.alt (S.Just ('default')) (S.Nothing)
Just ('default')

> S.alt (S.Just ('default')) (S.Just ('hello'))
Just ('hello')

> S.alt (S.Right (0)) (S.Left ('X'))
Right (0)

> S.alt (S.Right (0)) (S.Right (1))
Right (1)

zero :: Plus f => TypeRep f -⁠> f a

[Type-safe][sanctuary-def] version of [Z.zero][].

> S.zero (Array)
[]

> S.zero (Object)
{}

> S.zero (S.Maybe)
Nothing

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

Takes a curried binary function, an initial value, and a [Foldable][], and applies the function to the initial value and the Foldable’s first value, then applies the function to the result of the previous application and the Foldable’s second value. Repeats this process until each of the Foldable’s values has been used. Returns the initial value if the Foldable is empty; the result of the final application otherwise.

See also reduce_.

> S.reduce (S.add) (0) ([1, 2, 3, 4, 5])
15

> S.reduce (xs => x => S.prepend (x) (xs)) ([]) ([1, 2, 3, 4, 5])
[5, 4, 3, 2, 1]

reduce_ :: Foldable f => (a -⁠> b -⁠> b) -⁠> b -⁠> f a -⁠> b

Variant of reduce that takes a reducing function with arguments flipped.

> S.reduce_ (S.append) ([]) (Cons (1) (Cons (2) (Cons (3) (Nil))))
[1, 2, 3]

> S.reduce_ (S.prepend) ([]) (Cons (1) (Cons (2) (Cons (3) (Nil))))
[3, 2, 1]

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

Curried version of [Z.traverse][].

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

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

> S.traverse (S.Maybe) (S.parseInt (16)) (['A', 'B', 'C'])
Just ([10, 11, 12])

> S.traverse (S.Maybe) (S.parseInt (16)) (['A', 'B', 'C', 'X'])
Nothing

> S.traverse (S.Maybe) (S.parseInt (16)) ({a: 'A', b: 'B', c: 'C'})
Just ({a: 10, b: 11, c: 12})

> S.traverse (S.Maybe) (S.parseInt (16)) ({a: 'A', b: 'B', c: 'C', x: 'X'})
Nothing

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

Curried version of [Z.sequence][]. Inverts the given t (f a) to produce an f (t a).

> S.sequence (Array) (S.Just ([1, 2, 3]))
[Just (1), Just (2), Just (3)]

> S.sequence (S.Maybe) ([S.Just (1), S.Just (2), S.Just (3)])
Just ([1, 2, 3])

> S.sequence (S.Maybe) ([S.Just (1), S.Just (2), S.Nothing])
Nothing

> S.sequence (S.Maybe) ({a: S.Just (1), b: S.Just (2), c: S.Just (3)})
Just ({a: 1, b: 2, c: 3})

> S.sequence (S.Maybe) ({a: S.Just (1), b: S.Just (2), c: S.Nothing})
Nothing

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

Curried version of [Z.ap][].

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

> S.ap ({x: Math.sqrt, y: S.add (1), z: S.sub (1)}) ({w: 4, x: 4, y: 4})
{x: 2, y: 5}

> S.ap (S.Just (Math.sqrt)) (S.Just (64))
Just (8)

Replacing Apply f => f with Function x produces the S combinator from combinatory logic:

Apply f => f (a -> b) -> f a -> f b
Function x (a -> b) -> Function x a -> Function x b
Function x (a -> c) -> Function x a -> Function x c
Function x (b -> c) -> Function x b -> Function x c
Function a (b -> c) -> Function a b -> Function a c
(a -> b -> c) -> (a -> b) -> (a -> c)

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

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

Promotes a curried binary function to a function that operates on two [Apply][]s.

> S.lift2 (S.add) (S.Just (2)) (S.Just (3))
Just (5)

> S.lift2 (S.add) (S.Just (2)) (S.Nothing)
Nothing

> S.lift2 (S.and) (S.Just (true)) (S.Just (true))
Just (true)

> S.lift2 (S.and) (S.Just (true)) (S.Just (false))
Just (false)

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

Promotes a curried ternary function to a function that operates on three [Apply][]s.

> S.lift3 (S.reduce) (S.Just (S.add)) (S.Just (0)) (S.Just ([1, 2, 3]))
Just (6)

> S.lift3 (S.reduce) (S.Just (S.add)) (S.Just (0)) (S.Nothing)
Nothing

apFirst :: Apply f => f a -⁠> f b -⁠> f a

Curried version of [Z.apFirst][]. Combines two effectful actions, keeping only the result of the first. Equivalent to Haskell’s (<*) function.

See also apSecond.

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

> S.apFirst (S.Just (1)) (S.Just (2))
Just (1)

apSecond :: Apply f => f a -⁠> f b -⁠> f b

Curried version of [Z.apSecond][]. Combines two effectful actions, keeping only the result of the second. Equivalent to Haskell’s (*>) function.

See also apFirst.

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

> S.apSecond (S.Just (1)) (S.Just (2))
Just (2)

of :: Applicative f => TypeRep f -⁠> a -⁠> f a

Curried version of [Z.of][].

> S.of (Array) (42)
[42]

> S.of (Function) (42) (null)
42

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

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

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

Curried version of [Z.chain][].

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

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

> S.chain (S.parseInt (10)) (S.Just ('123'))
Just (123)

> S.chain (S.parseInt (10)) (S.Just ('XXX'))
Nothing

join :: Chain m => m (m a) -⁠> m a

[Type-safe][sanctuary-def] version of [Z.join][]. Removes one level of nesting from a nested monadic structure.

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

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

> S.join (S.Just (S.Just (1)))
Just (1)

> S.join (S.Pair ('foo') (S.Pair ('bar') ('baz')))
Pair ('foobar') ('baz')

Replacing Chain m => m with Function x produces the W combinator from combinatory logic:

Chain m => m (m a) -> m a
Function x (Function x a) -> Function x a
(x -> x -> a) -> (x -> a)

> S.join (S.concat) ('abc')
'abcabc'

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

Performs a chain-like computation with constant stack usage. Similar to [Z.chainRec][], but curried and more convenient due to the use of the Either type to indicate completion (via a Right).

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

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

Curried version of [Z.extend][].

> S.extend (S.joinWith ('')) (['x', 'y', 'z'])
['xyz', 'yz', 'z']

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

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

[Type-safe][sanctuary-def] version of [Z.duplicate][]. Adds one level of nesting to a comonadic structure.

> S.duplicate (S.Just (1))
Just (Just (1))

> S.duplicate ([1])
[[1]]

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

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

extract :: Comonad w => w a -⁠> a

[Type-safe][sanctuary-def] version of [Z.extract][].

> S.extract (S.Pair ('foo') ('bar'))
'bar'

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

[Type-safe][sanctuary-def] version of [Z.contramap][].

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

❑ Combinator

I :: a -⁠> a

The I combinator. Returns its argument. Equivalent to Haskell’s id function.

> S.I ('foo')
'foo'

K :: a -⁠> b -⁠> a

The K combinator. Takes two values and returns the first. Equivalent to Haskell’s const function.

> S.K ('foo') ('bar')
'foo'

> S.map (S.K (42)) (S.range (0) (5))
[42, 42, 42, 42, 42]

T :: a -⁠> (a -⁠> b) -⁠> b

The T ([thrush][]) combinator. Takes a value and a function, and returns the result of applying the function to the value. Equivalent to Haskell’s (&) function.

> S.T (42) (S.add (1))
43

> S.map (S.T (100)) ([S.add (1), Math.sqrt])
[101, 10]

❑ Function

curry2 :: ((a, b) -⁠> c) -⁠> a -⁠> b -⁠> c

Curries the given binary function.

> S.map (S.curry2 (Math.pow) (10)) ([1, 2, 3])
[10, 100, 1000]

curry3 :: ((a, b, c) -⁠> d) -⁠> a -⁠> b -⁠> c -⁠> d

Curries the given ternary function.

> const replaceString = S.curry3 ((what, replacement, string) =>
.   string.replace (what, replacement)
. )

> replaceString ('banana') ('orange') ('banana icecream')
'orange icecream'

curry4 :: ((a, b, c, d) -⁠> e) -⁠> a -⁠> b -⁠> c -⁠> d -⁠> e

Curries the given quaternary function.

> const createRect = S.curry4 ((x, y, width, height) =>
.   ({x, y, width, height})
. )

> createRect (0) (0) (10) (10)
{x: 0, y: 0, width: 10, height: 10}

curry5 :: ((a, b, c, d, e) -⁠> f) -⁠> a -⁠> b -⁠> c -⁠> d -⁠> e -⁠> f

Curries the given quinary function.

> const toUrl = S.curry5 ((protocol, creds, hostname, port, pathname) =>
.   protocol + '//' +
.   S.maybe ('') (S.flip (S.concat) ('@')) (creds) +
.   hostname +
.   S.maybe ('') (S.concat (':')) (port) +
.   pathname
. )

> toUrl ('https:') (S.Nothing) ('example.com') (S.Just ('443')) ('/foo/bar')
'https://example.com:443/foo/bar'

❑ Composition

compose :: Semigroupoid s => s b c -⁠> s a b -⁠> s a c

Curried version of [Z.compose][].

When specialized to Function, compose composes two unary functions, from right to left (this is the B combinator from combinatory logic).

The generalized type signature indicates that compose is compatible with any [Semigroupoid][].

See also pipe.

> S.compose (Math.sqrt) (S.add (1)) (99)
10

pipe :: Foldable f => f (Any -⁠> Any) -⁠> a -⁠> b

Takes a sequence of functions assumed to be unary and a value of any type, and returns the result of applying the sequence of transformations to the initial value.

In general terms, pipe performs left-to-right composition of a sequence of functions. pipe ([f, g, h]) (x) is equivalent to h (g (f (x))).

> S.pipe ([S.add (1), Math.sqrt, S.sub (1)]) (99)
9

pipeK :: (Foldable f, Chain m) => f (Any -⁠> m Any) -⁠> m a -⁠> m b

Takes a sequence of functions assumed to be unary that return values with a [Chain][], and a value of that Chain, and returns the result of applying the sequence of transformations to the initial value.

In general terms, pipeK performs left-to-right [Kleisli][] composition of an sequence of functions. pipeK ([f, g, h]) (x) is equivalent to chain (h) (chain (g) (chain (f) (x))).

> S.pipeK ([S.tail, S.tail, S.head]) (S.Just ([1, 2, 3, 4]))
Just (3)

on :: (b -⁠> b -⁠> c) -⁠> (a -⁠> b) -⁠> a -⁠> a -⁠> c

Takes a binary function f, a unary function g, and two values x and y. Returns f (g (x)) (g (y)).

This is the P combinator from combinatory logic.

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

❑ Pair

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.

The implementation is provided by [sanctuary-pair][].

Pair :: a -⁠> b -⁠> Pair a b

Pair’s sole data constructor. Additionally, it serves as the Pair [type representative][].

> S.Pair ('foo') (42)
Pair ('foo') (42)

pair :: (a -⁠> b -⁠> c) -⁠> Pair a b -⁠> c

Case analysis for the Pair a b type.

> S.pair (S.concat) (S.Pair ('foo') ('bar'))
'foobar'

fst :: Pair a b -⁠> a

fst (Pair (x) (y)) is equivalent to x.

> S.fst (S.Pair ('foo') (42))
'foo'

snd :: Pair a b -⁠> b

snd (Pair (x) (y)) is equivalent to y.

> S.snd (S.Pair ('foo') (42))
42

swap :: Pair a b -⁠> Pair b a

swap (Pair (x) (y)) is equivalent to Pair (y) (x).

> S.swap (S.Pair ('foo') (42))
Pair (42) ('foo')

❑ 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.

The implementation is provided by [sanctuary-maybe][].

Maybe :: TypeRep Maybe

Maybe [type representative][].

Nothing :: Maybe a

The empty value of type Maybe a.

> S.Nothing
Nothing

Just :: a -⁠> Maybe a

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

> S.Just (42)
Just (42)

isNothing :: Maybe a -⁠> Boolean

Returns true if the given Maybe is Nothing; false if it is a Just.

> S.isNothing (S.Nothing)
true

> S.isNothing (S.Just (42))
false

isJust :: Maybe a -⁠> Boolean

Returns true if the given Maybe is a Just; false if it is Nothing.

> S.isJust (S.Just (42))
true

> S.isJust (S.Nothing)
false

maybe :: b -⁠> (a -⁠> b) -⁠> Maybe a -⁠> b

Takes a value of any type, a function, and a Maybe. If the Maybe is a Just, the return value is the result of applying the function to the Just’s value. Otherwise, the first argument is returned.

See also maybe_ and fromMaybe.

> S.maybe (0) (S.prop ('length')) (S.Just ('refuge'))
6

> S.maybe (0) (S.prop ('length')) (S.Nothing)
0

maybe_ :: (() -⁠> b) -⁠> (a -⁠> b) -⁠> Maybe a -⁠> b

Variant of maybe that takes a thunk so the default value is only computed if required.

> function fib(n) { return n <= 1 ? n : fib (n - 2) + fib (n - 1); }

> S.maybe_ (() => fib (30)) (Math.sqrt) (S.Just (1000000))
1000

> S.maybe_ (() => fib (30)) (Math.sqrt) (S.Nothing)
832040

fromMaybe :: a -⁠> Maybe a -⁠> a

Takes a default value and a Maybe, and returns the Maybe’s value if the Maybe is a Just; the default value otherwise.

See also maybe, fromMaybe_, and maybeToNullable.

> S.fromMaybe (0) (S.Just (42))
42

> S.fromMaybe (0) (S.Nothing)
0

fromMaybe_ :: (() -⁠> a) -⁠> Maybe a -⁠> a

Variant of fromMaybe that takes a thunk so the default value is only computed if required.

> function fib(n) { return n <= 1 ? n : fib (n - 2) + fib (n - 1); }

> S.fromMaybe_ (() => fib (30)) (S.Just (1000000))
1000000

> S.fromMaybe_ (() => fib (30)) (S.Nothing)
832040

justs :: (Filterable f, Functor f) => f (Maybe a) -⁠> f a

Discards each element that is Nothing, and unwraps each element that is a Just. Related to Haskell’s catMaybes function.

See also lefts and rights.

> S.justs ([S.Just ('foo'), S.Nothing, S.Just ('baz')])
['foo', 'baz']

mapMaybe :: (Filterable f, Functor f) => (a -⁠> Maybe b) -⁠> f a -⁠> f b

Takes a function and a structure, applies the function to each element of the structure, and returns the “successful” results. If the result of applying the function to an element is Nothing, the result is discarded; if the result is a Just, the Just’s value is included.

> S.mapMaybe (S.head) ([[], [1, 2, 3], [], [4, 5, 6], []])
[1, 4]

> S.mapMaybe (S.head) ({x: [1, 2, 3], y: [], z: [4, 5, 6]})
{x: 1, z: 4}

maybeToNullable :: Maybe a -⁠> Nullable a

Returns the given Maybe’s value if the Maybe is a Just; null otherwise. [Nullable][] is defined in [sanctuary-def][].

See also fromMaybe.

> S.maybeToNullable (S.Just (42))
42

> S.maybeToNullable (S.Nothing)
null

maybeToEither :: a -⁠> Maybe b -⁠> Either a b

Converts a Maybe to an Either. Nothing becomes a Left (containing the first argument); a Just becomes a Right.

See also eitherToMaybe.

> S.maybeToEither ('Expecting an integer') (S.parseInt (10) ('xyz'))
Left ('Expecting an integer')

> S.maybeToEither ('Expecting an integer') (S.parseInt (10) ('42'))
Right (42)

❑ 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.

The implementation is provided by [sanctuary-either][].

Either :: TypeRep Either

Either [type representative][].

Left :: a -⁠> Either a b

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

> S.Left ('Cannot divide by zero')
Left ('Cannot divide by zero')

Right :: b -⁠> Either a b

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

> S.Right (42)
Right (42)

isLeft :: Either a b -⁠> Boolean

Returns true if the given Either is a Left; false if it is a Right.

> S.isLeft (S.Left ('Cannot divide by zero'))
true

> S.isLeft (S.Right (42))
false

isRight :: Either a b -⁠> Boolean

Returns true if the given Either is a Right; false if it is a Left.

> S.isRight (S.Right (42))
true

> S.isRight (S.Left ('Cannot divide by zero'))
false

either :: (a -⁠> c) -⁠> (b -⁠> c) -⁠> Either a b -⁠> c

Takes two functions and an Either, and returns the result of applying the first function to the Left’s value, if the Either is a Left, or the result of applying the second function to the Right’s value, if the Either is a Right.

See also fromLeft and fromRight.

> S.either (S.toUpper) (S.show) (S.Left ('Cannot divide by zero'))
'CANNOT DIVIDE BY ZERO'

> S.either (S.toUpper) (S.show) (S.Right (42))
'42'

fromLeft :: a -⁠> Either a b -⁠> a

Takes a default value and an Either, and returns the Left value if the Either is a Left; the default value otherwise.

See also either and fromRight.

> S.fromLeft ('abc') (S.Left ('xyz'))
'xyz'

> S.fromLeft ('abc') (S.Right (123))
'abc'

fromRight :: b -⁠> Either a b -⁠> b

Takes a default value and an Either, and returns the Right value if the Either is a Right; the default value otherwise.

See also either and fromLeft.

> S.fromRight (123) (S.Right (789))
789

> S.fromRight (123) (S.Left ('abc'))
123

fromEither :: b -⁠> Either a b -⁠> b

Takes a default value and an Either, and returns the Right value if the Either is a Right; the default value otherwise.

The behaviour of fromEither is likely to change in a future release. Please use fromRight instead.

> S.fromEither (0) (S.Right (42))
42

> S.fromEither (0) (S.Left (42))
0

lefts :: (Filterable f, Functor f) => f (Either a b) -⁠> f a

Discards each element that is a Right, and unwraps each element that is a Left.

See also rights.

> S.lefts ([S.Right (20), S.Left ('foo'), S.Right (10), S.Left ('bar')])
['foo', 'bar']

rights :: (Filterable f, Functor f) => f (Either a b) -⁠> f b

Discards each element that is a Left, and unwraps each element that is a Right.

See also lefts.

> S.rights ([S.Right (20), S.Left ('foo'), S.Right (10), S.Left ('bar')])
[20, 10]

tagBy :: (a -⁠> Boolean) -⁠> a -⁠> Either a a

Takes a predicate and a value, and returns a Right of the value if it satisfies the predicate; a Left of the value otherwise.

> S.tagBy (S.odd) (0)
Left (0)

> S.tagBy (S.odd) (1)
Right (1)

encase :: Throwing e a b -⁠> a -⁠> Either e b

Takes a function that may throw and returns a pure function.

> S.encase (JSON.parse) ('["foo","bar","baz"]')
Right (['foo', 'bar', 'baz'])

> S.encase (JSON.parse) ('[')
Left (new SyntaxError ('Unexpected end of JSON input'))

eitherToMaybe :: Either a b -⁠> Maybe b

Converts an Either to a Maybe. A Left becomes Nothing; a Right becomes a Just.

See also maybeToEither.

> S.eitherToMaybe (S.Left ('Cannot divide by zero'))
Nothing

> S.eitherToMaybe (S.Right (42))
Just (42)

❑ Logic

and :: Boolean -⁠> Boolean -⁠> Boolean

Boolean “and”.

> S.and (false) (false)
false

> S.and (false) (true)
false

> S.and (true) (false)
false

> S.and (true) (true)
true

or :: Boolean -⁠> Boolean -⁠> Boolean

Boolean “or”.

> S.or (false) (false)
false

> S.or (false) (true)
true

> S.or (true) (false)
true

> S.or (true) (true)
true

not :: Boolean -⁠> Boolean

Boolean “not”.

See also complement.

> S.not (false)
true

> S.not (true)
false

complement :: (a -⁠> Boolean) -⁠> a -⁠> Boolean

Takes a unary predicate and a value of any type, and returns the logical negation of applying the predicate to the value.

See also not.

> Number.isInteger (42)
true

> S.complement (Number.isInteger) (42)
false

boolean :: a -⁠> a -⁠> Boolean -⁠> a

Case analysis for the Boolean type. boolean (x) (y) (b) evaluates to x if b is false; to y if b is true.

> S.boolean ('no') ('yes') (false)
'no'

> S.boolean ('no') ('yes') (true)
'yes'

ifElse :: (a -⁠> Boolean) -⁠> (a -⁠> b) -⁠> (a -⁠> b) -⁠> a -⁠> b

Takes a unary predicate, a unary “if” function, a unary “else” function, and a value of any type, and returns the result of applying the “if” function to the value if the value satisfies the predicate; the result of applying the “else” function to the value otherwise.

See also when and unless.

> S.ifElse (x => x < 0) (Math.abs) (Math.sqrt) (-1)
1

> S.ifElse (x => x < 0) (Math.abs) (Math.sqrt) (16)
4

when :: (a -⁠> Boolean) -⁠> (a -⁠> a) -⁠> a -⁠> a

Takes a unary predicate, a unary function, and a value of any type, and returns the result of applying the function to the value if the value satisfies the predicate; the value otherwise.

See also unless and ifElse.

> S.when (x => x >= 0) (Math.sqrt) (16)
4

> S.when (x => x >= 0) (Math.sqrt) (-1)
-1

unless :: (a -⁠> Boolean) -⁠> (a -⁠> a) -⁠> a -⁠> a

Takes a unary predicate, a unary function, and a value of any type, and returns the result of applying the function to the value if the value does not satisfy the predicate; the value otherwise.

See also when and ifElse.

> S.unless (x => x < 0) (Math.sqrt) (16)
4

> S.unless (x => x < 0) (Math.sqrt) (-1)
-1

❑ Array

array :: b -⁠> (a -⁠> Array a -⁠> b) -⁠> Array a -⁠> b

Case analysis for the Array a type.

> S.array (S.Nothing) (head => tail => S.Just (head)) ([])
Nothing

> S.array (S.Nothing) (head => tail => S.Just (head)) ([1, 2, 3])
Just (1)

> S.array (S.Nothing) (head => tail => S.Just (tail)) ([])
Nothing

> S.array (S.Nothing) (head => tail => S.Just (tail)) ([1, 2, 3])
Just ([2, 3])

head :: Foldable f => f a -⁠> Maybe a

Returns Just the first element of the given structure if the structure contains at least one element; Nothing otherwise.

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

> S.head ([])
Nothing

> S.head (Cons (1) (Cons (2) (Cons (3) (Nil))))
Just (1)

> S.head (Nil)
Nothing

last :: Foldable f => f a -⁠> Maybe a

Returns Just the last element of the given structure if the structure contains at least one element; Nothing otherwise.

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

> S.last ([])
Nothing

> S.last (Cons (1) (Cons (2) (Cons (3) (Nil))))
Just (3)

> S.last (Nil)
Nothing

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

Returns Just all but the first of the given structure’s elements if the structure contains at least one element; Nothing otherwise.

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

> S.tail ([])
Nothing

> S.tail (Cons (1) (Cons (2) (Cons (3) (Nil))))
Just (Cons (2) (Cons (3) (Nil)))

> S.tail (Nil)
Nothing

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

Returns Just all but the last of the given structure’s elements if the structure contains at least one element; Nothing otherwise.

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

> S.init ([])
Nothing

> S.init (Cons (1) (Cons (2) (Cons (3) (Nil))))
Just (Cons (1) (Cons (2) (Nil)))

> S.init (Nil)
Nothing

take :: (Applicative f, Foldable f, Monoid (f a)) => Integer -⁠> f a -⁠> Maybe (f a)

Returns Just the first N elements of the given structure if N is non-negative and less than or equal to the size of the structure; Nothing otherwise.

> S.take (0) (['foo', 'bar'])
Just ([])

> S.take (1) (['foo', 'bar'])
Just (['foo'])

> S.take (2) (['foo', 'bar'])
Just (['foo', 'bar'])

> S.take (3) (['foo', 'bar'])
Nothing

> S.take (3) (Cons (1) (Cons (2) (Cons (3) (Cons (4) (Cons (5) (Nil))))))
Just (Cons (1) (Cons (2) (Cons (3) (Nil))))

drop :: (Applicative f, Foldable f, Monoid (f a)) => Integer -⁠> f a -⁠> Maybe (f a)

Returns Just all but the first N elements of the given structure if N is non-negative and less than or equal to the size of the structure; Nothing otherwise.

> S.drop (0) (['foo', 'bar'])
Just (['foo', 'bar'])

> S.drop (1) (['foo', 'bar'])
Just (['bar'])

> S.drop (2) (['foo', 'bar'])
Just ([])

> S.drop (3) (['foo', 'bar'])
Nothing

> S.drop (3) (Cons (1) (Cons (2) (Cons (3) (Cons (4) (Cons (5) (Nil))))))
Just (Cons (4) (Cons (5) (Nil)))

takeLast :: (Applicative f, Foldable f, Monoid (f a)) => Integer -⁠> f a -⁠> Maybe (f a)

Returns Just the last N elements of the given structure if N is non-negative and less than or equal to the size of the structure; Nothing otherwise.

> S.takeLast (0) (['foo', 'bar'])
Just ([])

> S.takeLast (1) (['foo', 'bar'])
Just (['bar'])

> S.takeLast (2) (['foo', 'bar'])
Just (['foo', 'bar'])

> S.takeLast (3) (['foo', 'bar'])
Nothing

> S.takeLast (3) (Cons (1) (Cons (2) (Cons (3) (Cons (4) (Nil)))))
Just (Cons (2) (Cons (3) (Cons (4) (Nil))))

dropLast :: (Applicative f, Foldable f, Monoid (f a)) => Integer -⁠> f a -⁠> Maybe (f a)

Returns Just all but the last N elements of the given structure if N is non-negative and less than or equal to the size of the structure; Nothing otherwise.

> S.dropLast (0) (['foo', 'bar'])
Just (['foo', 'bar'])

> S.dropLast (1) (['foo', 'bar'])
Just (['foo'])

> S.dropLast (2) (['foo', 'bar'])
Just ([])

> S.dropLast (3) (['foo', 'bar'])
Nothing

> S.dropLast (3) (Cons (1) (Cons (2) (Cons (3) (Cons (4) (Nil)))))
Just (Cons (1) (Nil))

takeWhile :: (a -⁠> Boolean) -⁠> Array a -⁠> Array a

Discards the first element that does not satisfy the predicate, and all subsequent elements.

See also dropWhile.

> S.takeWhile (S.odd) ([3, 3, 3, 7, 6, 3, 5, 4])
[3, 3, 3, 7]

> S.takeWhile (S.even) ([3, 3, 3, 7, 6, 3, 5, 4])
[]

dropWhile :: (a -⁠> Boolean) -⁠> Array a -⁠> Array a

Retains the first element that does not satisfy the predicate, and all subsequent elements.

See also takeWhile.

> S.dropWhile (S.odd) ([3, 3, 3, 7, 6, 3, 5, 4])
[6, 3, 5, 4]

> S.dropWhile (S.even) ([3, 3, 3, 7, 6, 3, 5, 4])
[3, 3, 3, 7, 6, 3, 5, 4]

size :: Foldable f => f a -⁠> NonNegativeInteger

Returns the number of elements of the given structure.

> S.size ([])
0

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

> S.size (Nil)
0

> S.size (Cons ('foo') (Cons ('bar') (Cons ('baz') (Nil))))
3

> S.size (S.Nothing)
0

> S.size (S.Just ('quux'))
1

> S.size (S.Pair ('ignored!') ('counted!'))
1

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

Returns true [iff][] all the elements of the structure satisfy the predicate.

See also any and none.

> S.all (S.odd) ([])
true

> S.all (S.odd) ([1, 3, 5])
true

> S.all (S.odd) ([1, 2, 3])
false

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

Returns true [iff][] any element of the structure satisfies the predicate.

See also all and none.

> S.any (S.odd) ([])
false

> S.any (S.odd) ([2, 4, 6])
false

> S.any (S.odd) ([1, 2, 3])
true

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

Returns true [iff][] none of the elements of the structure satisfies the predicate.

Properties:

• forall p :: a -> Boolean, xs :: Foldable f => f a. S.none (p) (xs) = S.not (S.any (p) (xs))

• forall p :: a -> Boolean, xs :: Foldable f => f a. S.none (p) (xs) = S.all (S.complement (p)) (xs)

See also all and any.

> S.none (S.odd) ([])
true

> S.none (S.odd) ([2, 4, 6])
true

> S.none (S.odd) ([1, 2, 3])
false

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

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

See also prepend.

> S.append (3) ([1, 2])
[1, 2, </script></input-types></output-type></input-types>

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