| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Agda.Utils.Functor
Description
Utilities for functors.
Synopsis
- (<.>) :: Functor m => (b -> c) -> (a -> m b) -> a -> m c
- for :: Functor m => m a -> (a -> b) -> m b
- class Functor t => Decoration (t :: Type -> Type) where
- traverseF :: Functor m => (a -> m b) -> t a -> m (t b)
- distributeF :: Functor m => t (m a) -> m (t a)
- dmap :: Decoration t => (a -> b) -> t a -> t b
- dget :: Decoration t => t a -> a
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- ($>) :: Functor f => f a -> b -> f b
- (<&>) :: Functor f => f a -> (a -> b) -> f b
Documentation
(<.>) :: Functor m => (b -> c) -> (a -> m b) -> a -> m c infixr 9 Source #
Composition: pure function after functorial (monadic) function.
for :: Functor m => m a -> (a -> b) -> m b Source #
The true pure for loop.
for is a misnomer, it should be forA.
class Functor t => Decoration (t :: Type -> Type) where Source #
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.
Minimal complete definition
Nothing
Methods
traverseF :: Functor m => (a -> m b) -> t a -> m (t b) Source #
traverseF is the defining property.
distributeF :: Functor m => t (m a) -> m (t a) Source #
Decorations commute into any functor.
Instances
| Decoration Arg Source # | |
| Decoration Ranged Source # | |
| Decoration WithHiding Source # | |
Defined in Agda.Syntax.Common Methods traverseF :: Functor m => (a -> m b) -> WithHiding a -> m (WithHiding b) Source # distributeF :: Functor m => WithHiding (m a) -> m (WithHiding a) Source # | |
| Decoration WithOrigin Source # | |
Defined in Agda.Syntax.Common Methods traverseF :: Functor m => (a -> m b) -> WithOrigin a -> m (WithOrigin b) Source # distributeF :: Functor m => WithOrigin (m a) -> m (WithOrigin a) Source # | |
| Decoration Abs Source # | |
| Decoration Masked Source # | |
| Decoration Open Source # | |
| Decoration Identity Source # | The identity functor is a decoration. |
| Decoration (Named name) Source # | |
| Decoration (Dom' t) Source # | |
| Decoration (Type'' t) Source # | |
| Decoration (Blocked' t) Source # | |
| Decoration ((,) a) Source # | A typical decoration is pairing with some stuff. |
Defined in Agda.Utils.Functor | |
| (Decoration d, Decoration t) => Decoration (Compose d t) Source # | Decorations compose. (Thus, they form a category.) |
dmap :: Decoration t => (a -> b) -> t a -> t b Source #
Any decoration is traversable with traverse = traverseF.
Just like any Traversable is a functor, so is
any decoration, given by just traverseF, a functor.
dget :: Decoration t => t a -> a Source #
Any decoration is a lens. set is a special case of dmap.
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
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, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> 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 <$> (2,2)(2,True)
($>) :: Functor f => f a -> b -> f b infixl 4 #
Flipped version of <$.
Examples
Replace the contents of a Maybe IntString:
>>>Nothing $> "foo"Nothing>>>Just 90210 $> "foo"Just "foo"
Replace the contents of an Either Int IntString, 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")
Since: base-4.7.0.0