# Prelude

- Package
- purescript-prelude
- Repository
- purescript/purescript-prelude

## Re-exports from **Control.**Applicative

### #Applicative Source

`class (Apply f) <= Applicative f where`

The `Applicative`

type class extends the `Apply`

type class
with a `pure`

function, which can be used to create values of type `f a`

from values of type `a`

.

Where `Apply`

provides the ability to lift functions of two or
more arguments to functions whose arguments are wrapped using `f`

, and
`Functor`

provides the ability to lift functions of one
argument, `pure`

can be seen as the function which lifts functions of
*zero* arguments. That is, `Applicative`

functors support a lifting
operation for any number of function arguments.

Instances must satisfy the following laws in addition to the `Apply`

laws:

- Identity:
`(pure id) <*> v = v`

- Composition:
`pure (<<<) <*> f <*> g <*> h = f <*> (g <*> h)`

- Homomorphism:
`(pure f) <*> (pure x) = pure (f x)`

- Interchange:
`u <*> (pure y) = (pure (_ $ y)) <*> u`

#### Members

`pure :: forall a. a -> f a`

#### Instances

### #when Source

`when :: forall m. Applicative m => Boolean -> m Unit -> m Unit`

Perform a applicative action when a condition is true.

### #unless Source

`unless :: forall m. Applicative m => Boolean -> m Unit -> m Unit`

Perform a applicative action unless a condition is true.

### #liftA1 Source

`liftA1 :: forall f a b. Applicative f => (a -> b) -> f a -> f b`

`liftA1`

provides a default implementation of `(<$>)`

for any
`Applicative`

functor, without using `(<$>)`

as provided
by the `Functor`

-`Applicative`

superclass
relationship.

`liftA1`

can therefore be used to write `Functor`

instances
as follows:

```
instance functorF :: Functor F where
map = liftA1
```

## Re-exports from **Control.**Apply

### #Apply Source

`class (Functor f) <= Apply f where`

The `Apply`

class provides the `(<*>)`

which is used to apply a function
to an argument under a type constructor.

`Apply`

can be used to lift functions of two or more arguments to work on
values wrapped with the type constructor `f`

. It might also be understood
in terms of the `lift2`

function:

```
lift2 :: forall f a b c. Apply f => (a -> b -> c) -> f a -> f b -> f c
lift2 f a b = f <$> a <*> b
```

`(<*>)`

is recovered from `lift2`

as `lift2 ($)`

. That is, `(<*>)`

lifts
the function application operator `($)`

to arguments wrapped with the
type constructor `f`

.

Instances must satisfy the following law in addition to the `Functor`

laws:

- Associative composition:
`(<<<) <$> f <*> g <*> h = f <*> (g <*> h)`

Formally, `Apply`

represents a strong lax semi-monoidal endofunctor.

#### Members

`apply :: forall a b. f (a -> b) -> f a -> f b`

#### Instances

## Re-exports from **Control.**Bind

### #Bind Source

`class (Apply m) <= Bind m where`

The `Bind`

type class extends the `Apply`

type class with a
"bind" operation `(>>=)`

which composes computations in sequence, using
the return value of one computation to determine the next computation.

The `>>=`

operator can also be expressed using `do`

notation, as follows:

```
x >>= f = do y <- x
f y
```

where the function argument of `f`

is given the name `y`

.

Instances must satisfy the following law in addition to the `Apply`

laws:

- Associativity:
`(x >>= f) >>= g = x >>= (\k -> f k >>= g)`

Associativity tells us that we can regroup operations which use `do`

notation so that we can unambiguously write, for example:

```
do x <- m1
y <- m2 x
m3 x y
```

#### Members

`bind :: forall a b. m a -> (a -> m b) -> m b`

#### Instances

### #(<=<) Source

Operator alias for Control.Bind.composeKleisliFlipped *(right-associative / precedence 1)*

## Re-exports from **Control.**Category

### #Category Source

`class (Semigroupoid a) <= Category a where`

`Category`

s consist of objects and composable morphisms between them, and
as such are `Semigroupoids`

, but unlike `semigroupoids`

must have an identity element.

Instances must satisfy the following law in addition to the
`Semigroupoid`

law:

- Identity:
`id <<< p = p <<< id = p`

#### Members

`id :: forall t. a t t`

#### Instances

## Re-exports from **Control.**Monad

### #Monad Source

`class (Applicative m, Bind m) <= Monad m `

The `Monad`

type class combines the operations of the `Bind`

and
`Applicative`

type classes. Therefore, `Monad`

instances represent type
constructors which support sequential composition, and also lifting of
functions of arbitrary arity.

Instances must satisfy the following laws in addition to the
`Applicative`

and `Bind`

laws:

- Left Identity:
`pure x >>= f = f x`

- Right Identity:
`x >>= pure = x`

#### Instances

### #liftM1 Source

`liftM1 :: forall m a b. Monad m => (a -> b) -> m a -> m b`

`liftM1`

provides a default implementation of `(<$>)`

for any
`Monad`

, without using `(<$>)`

as provided by the
`Functor`

-`Monad`

superclass relationship.

`liftM1`

can therefore be used to write `Functor`

instances
as follows:

```
instance functorF :: Functor F where
map = liftM1
```

## Re-exports from **Control.**Semigroupoid

### #Semigroupoid Source

`class Semigroupoid a where`

A `Semigroupoid`

is similar to a `Category`

but does not
require an identity element `id`

, just composable morphisms.

`Semigroupoid`

s must satisfy the following law:

- Associativity:
`p <<< (q <<< r) = (p <<< q) <<< r`

One example of a `Semigroupoid`

is the function type constructor `(->)`

,
with `(<<<)`

defined as function composition.

#### Members

`compose :: forall b c d. a c d -> a b c -> a b d`

#### Instances

### #(>>>) Source

Operator alias for Control.Semigroupoid.composeFlipped *(right-associative / precedence 9)*

## Re-exports from **Data.**Boolean

## Re-exports from **Data.**BooleanAlgebra

### #BooleanAlgebra Source

`class (HeytingAlgebra a) <= BooleanAlgebra a `

The `BooleanAlgebra`

type class represents types that behave like boolean
values.

Instances should satisfy the following laws in addition to the
`HeytingAlgebra`

law:

- Excluded middle:
`a || not a = tt`

#### Instances

`BooleanAlgebra Boolean`

`BooleanAlgebra Unit`

`(BooleanAlgebra b) => BooleanAlgebra (a -> b)`

## Re-exports from **Data.**Bounded

### #Bounded Source

## Re-exports from **Data.**CommutativeRing

### #CommutativeRing Source

`class (Ring a) <= CommutativeRing a `

The `CommutativeRing`

class is for rings where multiplication is
commutative.

Instances must satisfy the following law in addition to the `Ring`

laws:

- Commutative multiplication:
`a * b = b * a`

#### Instances

## Re-exports from **Data.**Eq

### #Eq Source

`class Eq a where`

The `Eq`

type class represents types which support decidable equality.

`Eq`

instances should satisfy the following laws:

- Reflexivity:
`x == x = true`

- Symmetry:
`x == y = y == x`

- Transitivity: if
`x == y`

and`y == z`

then`x == z`

**Note:** The `Number`

type is not an entirely law abiding member of this
class due to the presence of `NaN`

, since `NaN /= NaN`

. Additionally,
computing with `Number`

can result in a loss of precision, so sometimes
values that should be equivalent are not.

#### Members

#### Instances

## Re-exports from **Data.**EuclideanRing

### #EuclideanRing Source

`class (CommutativeRing a) <= EuclideanRing a where`

The `EuclideanRing`

class is for commutative rings that support division.
The mathematical structure this class is based on is sometimes also called
a *Euclidean domain*.

Instances must satisfy the following laws in addition to the `Ring`

laws:

- Integral domain:
`one /= zero`

, and if`a`

and`b`

are both nonzero then so is their product`a * b`

- Euclidean function
`degree`

:- Nonnegativity: For all nonzero
`a`

,`degree a >= 0`

- Quotient/remainder: For all
`a`

and`b`

, where`b`

is nonzero, let`q = a / b`

and`r = a `mod` b`

; then`a = q*b + r`

, and also either`r = zero`

or`degree r < degree b`

- Nonnegativity: For all nonzero
- Submultiplicative euclidean function:
- For all nonzero
`a`

and`b`

,`degree a <= degree (a * b)`

- For all nonzero

The behaviour of division by `zero`

is unconstrained by these laws,
meaning that individual instances are free to choose how to behave in this
case. Similarly, there are no restrictions on what the result of
`degree zero`

is; it doesn't make sense to ask for `degree zero`

in the
same way that it doesn't make sense to divide by `zero`

, so again,
individual instances may choose how to handle this case.

For any `EuclideanRing`

which is also a `Field`

, one valid choice
for `degree`

is simply `const 1`

. In fact, unless there's a specific
reason not to, `Field`

types should normally use this definition of
`degree`

.

The `Unit`

instance is provided for backwards compatibility, but it is
not law-abiding, because `Unit`

fails to form an integral domain. This
instance will be removed in a future release.

#### Members

#### Instances

### #lcm Source

`lcm :: forall a. Eq a => EuclideanRing a => a -> a -> a`

The *least common multiple* of two values.

### #gcd Source

`gcd :: forall a. Eq a => EuclideanRing a => a -> a -> a`

The *greatest common divisor* of two values.

## Re-exports from **Data.**Field

### #Field Source

`class (EuclideanRing a) <= Field a `

The `Field`

class is for types that are commutative fields.

Instances must satisfy the following law in addition to the
`EuclideanRing`

laws:

- Non-zero multiplicative inverse:
`a `mod` b = zero`

for all`a`

and`b`

The `Unit`

instance is provided for backwards compatibility, but it is
not law-abiding, because `Unit`

does not obey the `EuclideanRing`

laws.
This instance will be removed in a future release.

#### Instances

## Re-exports from **Data.**Function

### #flip Source

`flip :: forall a b c. (a -> b -> c) -> b -> a -> c`

Flips the order of the arguments to a function of two arguments.

```
flip const 1 2 = const 2 1 = 2
```

### #const Source

`const :: forall a b. a -> b -> a`

Returns its first argument and ignores its second.

```
const 1 "hello" = 1
```

### #($) Source

Operator alias for Data.Function.apply *(right-associative / precedence 0)*

Applies a function to an argument: the reverse of `(#)`

.

```
length $ groupBy productCategory $ filter isInStock $ products
```

is equivalent to:

```
length (groupBy productCategory (filter isInStock products))
```

Or another alternative equivalent, applying chain of composed functions to a value:

```
length <<< groupBy productCategory <<< filter isInStock $ products
```

### #(#) Source

Operator alias for Data.Function.applyFlipped *(left-associative / precedence 1)*

Applies an argument to a function: the reverse of `($)`

.

```
products # filter isInStock # groupBy productCategory # length
```

is equivalent to:

```
length (groupBy productCategory (filter isInStock products))
```

Or another alternative equivalent, applying a value to a chain of composed functions:

```
products # filter isInStock >>> groupBy productCategory >>> length
```

## Re-exports from **Data.**Functor

### #Functor Source

`class Functor f where`

A `Functor`

is a type constructor which supports a mapping operation
`map`

.

`map`

can be used to turn functions `a -> b`

into functions
`f a -> f b`

whose argument and return types use the type constructor `f`

to represent some computational context.

Instances must satisfy the following laws:

- Identity:
`map id = id`

- Composition:
`map (f <<< g) = map f <<< map g`

#### Members

`map :: forall a b. (a -> b) -> f a -> f b`

#### Instances

### #void Source

`void :: forall f a. Functor f => f a -> f Unit`

The `void`

function is used to ignore the type wrapped by a
`Functor`

, replacing it with `Unit`

and keeping only the type
information provided by the type constructor itself.

`void`

is often useful when using `do`

notation to change the return type
of a monadic computation:

```
main = forE 1 10 \n -> void do
print n
print (n * n)
```

### #flap Source

`flap :: forall f a b. Functor f => f (a -> b) -> a -> f b`

Apply a value in a computational context to a value in no context.

Generalizes `flip`

.

```
longEnough :: String -> Bool
hasSymbol :: String -> Bool
hasDigit :: String -> Bool
password :: String
validate :: String -> List Bool
validate = flap [longEnough, hasSymbol, hasDigit]
```

```
flap (-) 3 4 == 1
threeve <$> Just 1 <@> 'a' <*> Just true == Just (threeve 1 'a' true)
```

## Re-exports from **Data.**HeytingAlgebra

### #HeytingAlgebra Source

`class HeytingAlgebra a where`

The `HeytingAlgebra`

type class represents types that are bounded lattices with
an implication operator such that the following laws hold:

- Associativity:
`a || (b || c) = (a || b) || c`

`a && (b && c) = (a && b) && c`

- Commutativity:
`a || b = b || a`

`a && b = b && a`

- Absorption:
`a || (a && b) = a`

`a && (a || b) = a`

- Idempotent:
`a || a = a`

`a && a = a`

- Identity:
`a || ff = a`

`a && tt = a`

- Implication:
`a `implies` a = tt`

`a && (a `implies` b) = a && b`

`b && (a `implies` b) = b`

`a `implies` (b && c) = (a `implies` b) && (a `implies` c)`

- Complemented:
`not a = a `implies` ff`

#### Members

#### Instances

`HeytingAlgebra Boolean`

`HeytingAlgebra Unit`

`(HeytingAlgebra b) => HeytingAlgebra (a -> b)`

## Re-exports from **Data.**NaturalTransformation

### #type (~>) Source

Operator alias for Data.NaturalTransformation.NaturalTransformation *(right-associative / precedence 4)*

## Re-exports from **Data.**Ord

### #Ord Source

## Re-exports from **Data.**Ordering

### #Ordering Source

`data Ordering`

The `Ordering`

data type represents the three possible outcomes of
comparing two values:

`LT`

- The first value is *less than* the second.
`GT`

- The first value is *greater than* the second.
`EQ`

- The first value is *equal to* the second.

#### Constructors

#### Instances

## Re-exports from **Data.**Ring

### #Ring Source

## Re-exports from **Data.**Semigroup

### #Semigroup Source

`class Semigroup a where`

The `Semigroup`

type class identifies an associative operation on a type.

Instances are required to satisfy the following law:

- Associativity:
`(x <> y) <> z = x <> (y <> z)`

One example of a `Semigroup`

is `String`

, with `(<>)`

defined as string
concatenation.

#### Members

`append :: a -> a -> a`

#### Instances

## Re-exports from **Data.**Semiring

### #Semiring Source

`class Semiring a where`

The `Semiring`

class is for types that support an addition and
multiplication operation.

Instances must satisfy the following laws:

- Commutative monoid under addition:
- Associativity:
`(a + b) + c = a + (b + c)`

- Identity:
`zero + a = a + zero = a`

- Commutative:
`a + b = b + a`

- Associativity:
- Monoid under multiplication:
- Associativity:
`(a * b) * c = a * (b * c)`

- Identity:
`one * a = a * one = a`

- Associativity:
- Multiplication distributes over addition:
- Left distributivity:
`a * (b + c) = (a * b) + (a * c)`

- Right distributivity:
`(a + b) * c = (a * c) + (b * c)`

- Left distributivity:
- Annihilation:
`zero * a = a * zero = zero`

**Note:** The `Number`

and `Int`

types are not fully law abiding
members of this class hierarchy due to the potential for arithmetic
overflows, and in the case of `Number`

, the presence of `NaN`

and
`Infinity`

values. The behaviour is unspecified in these cases.

#### Members

#### Instances

## Re-exports from **Data.**Show

### #Show Source

`class Show a where`

The `Show`

type class represents those types which can be converted into
a human-readable `String`

representation.

While not required, it is recommended that for any expression `x`

, the
string `show x`

be executable PureScript code which evaluates to the same
value as the expression `x`

.

#### Members

#### Instances

## Re-exports from **Data.**Unit

## Re-exports from **Data.**Void

- Modules
- Control.
Applicative - Control.
Apply - Control.
Bind - Control.
Category - Control.
Monad - Control.
Semigroupoid - Data.
Boolean - Data.
BooleanAlgebra - Data.
Bounded - Data.
CommutativeRing - Data.
Eq - Data.
EuclideanRing - Data.
Field - Data.
Function - Data.
Functor - Data.
HeytingAlgebra - Data.
NaturalTransformation - Data.
Ord - Data.
Ord. Unsafe - Data.
Ordering - Data.
Ring - Data.
Semigroup - Data.
Semiring - Data.
Show - Data.
Unit - Data.
Void - Prelude

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