# Data.Bifunctor

#### Description

Since: base-4.8.0.0

class Bifunctor p where Source

A bifunctor is a type constructor that takes two type arguments and is a functor in both arguments. That is, unlike with `Functor`, a type constructor such as `Either` does not need to be partially applied for a `Bifunctor` instance, and the methods in this class permit mapping functions over the `Left` value or the `Right` value, or both at the same time.

Formally, the class `Bifunctor` represents a bifunctor from `Hask` -> `Hask`.

Intuitively it is a bifunctor where both the first and second arguments are covariant.

You can define a `Bifunctor` by either defining `bimap` or by defining both `first` and `second`.

If you supply `bimap`, you should ensure that:

`bimap id id ≡ id`

If you supply `first` and `second`, ensure:

```first id ≡ id
second id ≡ id
```

If you supply both, you should also ensure:

`bimap f g ≡ first f . second g`

These ensure by parametricity:

```bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g
```

Since: base-4.8.0.0

#### Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d Source

Map over both arguments at the same time.

`bimap f g ≡ first f . second g`
##### Examples
Expand
```>>> bimap toUpper (+1) ('j', 3)
('J',4)
```
```>>> bimap toUpper (+1) (Left 'j')
Left 'J'
```
```>>> bimap toUpper (+1) (Right 3)
Right 4
```

first :: (a -> b) -> p a c -> p b c Source

Map covariantly over the first argument.

`first f ≡ bimap f id`
##### Examples
Expand
```>>> first toUpper ('j', 3)
('J',3)
```
```>>> first toUpper (Left 'j')
Left 'J'
```

second :: (b -> c) -> p a b -> p a c Source

Map covariantly over the second argument.

`second ≡ bimap id`
##### Examples
Expand
```>>> second (+1) ('j', 3)
('j',4)
```
```>>> second (+1) (Right 3)
Right 4
```
##### Instances
Instances details
Bifunctor Either

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d Source

first :: (a -> b) -> Either a c -> Either b c Source

second :: (b -> c) -> Either a b -> Either a c Source

Bifunctor (,)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) Source

first :: (a -> b) -> (a, c) -> (b, c) Source

second :: (b -> c) -> (a, b) -> (a, c) Source

Bifunctor Arg

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source

first :: (a -> b) -> Arg a c -> Arg b c Source

second :: (b -> c) -> Arg a b -> Arg a c Source

Bifunctor ((,,) x1)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) Source

first :: (a -> b) -> (x1, a, c) -> (x1, b, c) Source

second :: (b -> c) -> (x1, a, b) -> (x1, a, c) Source

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d Source

first :: (a -> b) -> Const a c -> Const b c Source

second :: (b -> c) -> Const a b -> Const a c Source

Bifunctor (K1 i :: Type -> Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d Source

first :: (a -> b) -> K1 i a c -> K1 i b c Source

second :: (b -> c) -> K1 i a b -> K1 i a c Source

Bifunctor ((,,,) x1 x2)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) Source

first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) Source

second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) Source

Bifunctor ((,,,,) x1 x2 x3)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) Source

first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) Source

second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) Source

Bifunctor ((,,,,,) x1 x2 x3 x4)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) Source

first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) Source

second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) Source

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)

Since: base-4.8.0.0

Instance details

Defined in Data.Bifunctor

#### Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) Source

first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) Source

second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) Source

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