<

Comparison (<) of comparable types, as a constraint.

"Smaller than". Type-level version of (<).

Example

>>> :kind! Eval ("a" < "b")
Eval ("a" < "b") :: Bool
= 'True

Proof that the first argument is strictly less than the second argument.

Less-than relation relation. Defined in terms of <= and /=.

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Examples

Perform a computation with Maybe and replace the result with a constant value if it is Just:

>>> 'a' <$ Just 2
Just 'a'

>>> 'a' <$ Nothing
Nothing

An infix synonym for fmap. The name of this operator is an allusion to $. Note the similarities between their types:

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

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

Examples

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

>>> show <$> Nothing
Nothing

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

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

>>> show <$> Left 17
Left 17

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

Sequence actions, discarding the value of the second argument.

Sequential application. A few functors support an implementation of <*> that is more efficient than the default one.

Example

Used in combination with (<$>), (<*>) can be used to build a record.

>>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}

>>> produceFoo :: Applicative f => f Foo

>>> produceBar :: Applicative f => f Bar

>>> produceBaz :: Applicative f => f Baz

>>> mkState :: Applicative f => f MyState

>>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

An associative operation.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

Strict version of <$>.

Right-to-left composition of Kleisli arrows. (>=>), with the arguments flipped. Note how this operator resembles function composition (.):

(.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

A variant of <*> with the arguments reversed.