# Control.Monad

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

### #Monad Source

`class Monad :: (Type -> Type) -> Constraint`

`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.**Applicative

### #Applicative Source

`class Applicative :: (Type -> Type) -> Constraint`

`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 identity) <*> 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 an applicative action when a condition is true.

### #unless Source

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

Perform an 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 Apply :: (Type -> Type) -> Constraint`

`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`

.

Put differently...

```
foo =
functionTakingNArguments <$> computationProducingArg1
<*> computationProducingArg2
<*> ...
<*> computationProducingArgN
```

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 Bind :: (Type -> Type) -> Constraint`

`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 laws in addition to the `Apply`

laws:

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

- Apply Superclass:
`apply f x = f >>= \f’ -> map f’ x`

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 **Data.**Functor

### #Functor Source

`class Functor :: (Type -> Type) -> Constraint`

`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 identity = identity`

- 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)
```

- Modules
- Control.
Applicative - Control.
Apply - Control.
Bind - Control.
Category - Control.
Monad - Control.
Semigroupoid - Data.
Boolean - Data.
BooleanAlgebra - Data.
Bounded - Data.
Bounded. Generic - Data.
CommutativeRing - Data.
DivisionRing - Data.
Eq - Data.
Eq. Generic - Data.
EuclideanRing - Data.
Field - Data.
Function - Data.
Functor - Data.
Generic. Rep - Data.
HeytingAlgebra - Data.
HeytingAlgebra. Generic - Data.
Monoid - Data.
Monoid. Additive - Data.
Monoid. Conj - Data.
Monoid. Disj - Data.
Monoid. Dual - Data.
Monoid. Endo - Data.
Monoid. Generic - Data.
Monoid. Multiplicative - Data.
NaturalTransformation - Data.
Ord - Data.
Ord. Generic - Data.
Ordering - Data.
Ring - Data.
Ring. Generic - Data.
Semigroup - Data.
Semigroup. First - Data.
Semigroup. Generic - Data.
Semigroup. Last - Data.
Semiring - Data.
Semiring. Generic - Data.
Show - Data.
Show. Generic - Data.
Symbol - Data.
Unit - Data.
Void - Prelude
- Record.
Unsafe - Type.
Data. Row - Type.
Data. RowList - Type.
Proxy

The

`bind`

/`>>=`

function for`Array`

works by applying a function to each element in the array, and flattening the results into a single, new array.Array's

`bind`

/`>>=`

works like a nested for loop. Each`bind`

adds another level of nesting in the loop. For example: