# Control.MonadZero

- Package
- purescript-control
- Repository
- purescript/purescript-control

### #MonadZero Source

`class (Monad m, Alternative m) <= MonadZero m `

The `MonadZero`

type class has no members of its own; it just specifies
that the type has both `Monad`

and `Alternative`

instances.

Types which have `MonadZero`

instances should also satisfy the following
laws:

- Annihilation:
`empty >>= f = empty`

#### Instances

### #guard Source

`guard :: forall m. MonadZero m => Boolean -> m Unit`

Fail using `Plus`

if a condition does not hold, or
succeed using `Monad`

if it does.

For example:

```
import Prelude
import Control.Monad (bind)
import Control.MonadZero (guard)
import Data.Array ((..))
factors :: Int -> Array Int
factors n = do
a <- 1..n
b <- a..n
guard $ a * b == n
pure [a, b]
```

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

### #Alt Source

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

The `Alt`

type class identifies an associative operation on a type
constructor. It is similar to `Semigroup`

, except that it applies to
types of kind `* -> *`

, like `Array`

or `List`

, rather than concrete types
`String`

or `Number`

.

`Alt`

instances are required to satisfy the following laws:

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

- Distributivity:
`f <$> (x <|> y) == (f <$> x) <|> (f <$> y)`

For example, the `Array`

(`[]`

) type is an instance of `Alt`

, where
`(<|>)`

is defined to be concatenation.

#### Members

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

#### Instances

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

### #Alternative Source

`class (Applicative f, Plus f) <= Alternative f `

The `Alternative`

type class has no members of its own; it just specifies
that the type constructor has both `Applicative`

and `Plus`

instances.

Types which have `Alternative`

instances should also satisfy the following
laws:

- Distributivity:
`(f <|> g) <*> x == (f <*> x) <|> (g <*> x)`

- Annihilation:
`empty <*> f = empty`

#### Instances

## 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.**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.**Plus

### #Plus Source

`class (Alt f) <= Plus f where`

The `Plus`

type class extends the `Alt`

type class with a value that
should be the left and right identity for `(<|>)`

.

It is similar to `Monoid`

, except that it applies to types of
kind `* -> *`

, like `Array`

or `List`

, rather than concrete types like
`String`

or `Number`

.

`Plus`

instances should satisfy the following laws:

- Left identity:
`empty <|> x == x`

- Right identity:
`x <|> empty == x`

- Annihilation:
`f <$> empty == empty`

#### Members

`empty :: forall a. f a`

#### Instances

## 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)
```