Agda.Utils.Functor

Composition: pure function after functorial (monadic) function.

The true pure for loop. for is a misnomer, it should be forA.

A decoration is a functor that is traversable into any functor.

The Functor superclass is given because of the limitations of the Haskell class system. traverseF actually implies functoriality.

Minimal complete definition: traverseF or distributeF.

Any decoration is traversable with traverse = traverseF. Just like any Traversable is a functor, so is any decoration, given by just traverseF, a functor.

Any decoration is a lens. set is a special case of dmap.

An infix synonym for fmap.

The name of this operator is an allusion to Prelude.$. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas Prelude.$ is function application, <$> is function application lifted over a Functor.

Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> NothingNothing

>>> show <$> Just 3Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17Left 17

>>> show <$> Right 17Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3][2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)(2,True)

Flipped version of <$.

Examples

Replace the contents of a Maybe Int with a constant String:

>>> Nothing $> "foo"Nothing

>>> Just 90210 $> "foo"Just "foo"

Replace the contents of an Either Int Int with a constant String, resulting in an Either Int String:

>>> Left 8675309 $> "foo"Left 8675309

>>> Right 8675309 $> "foo"Right "foo"

Replace each element of a list with a constant String:

>>> [1,2,3] $> "foo"["foo","foo","foo"]

Replace the second element of a pair with a constant String:

>>> (1,2) $> "foo"(1,"foo")

Flipped version of <$>.

(<&>) = flip fmap

Examples

Apply (+1) to a list, a Just and a Right:

>>> Just 2 <&> (+1)Just 3

>>> [1,2,3] <&> (+1)[2,3,4]

>>> Right 3 <&> (+1)Right 4