Agda-2.6.1: A dependently typed functional programming language and proof assistant

Agda.Utils.Functor

Description

Utilities for functors.

Synopsis

# 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 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
 Source # The identity functor is a decoration. Instance detailsDefined in Agda.Utils.Functor MethodstraverseF :: Functor m => (a -> m b) -> Identity a -> m (Identity b) Source #distributeF :: Functor m => Identity (m a) -> m (Identity a) Source # Source # Instance detailsDefined in Agda.Syntax.Common MethodstraverseF :: Functor m => (a -> m b) -> Ranged a -> m (Ranged b) Source #distributeF :: Functor m => Ranged (m a) -> m (Ranged a) Source # Source # Instance detailsDefined in Agda.Syntax.Common MethodstraverseF :: Functor m => (a -> m b) -> Arg a -> m (Arg b) Source #distributeF :: Functor m => Arg (m a) -> m (Arg a) Source # Source # Instance detailsDefined in Agda.Syntax.Common MethodstraverseF :: Functor m => (a -> m b) -> WithOrigin a -> m (WithOrigin b) Source #distributeF :: Functor m => WithOrigin (m a) -> m (WithOrigin a) Source # Source # Instance detailsDefined in Agda.Syntax.Common MethodstraverseF :: Functor m => (a -> m b) -> WithHiding a -> m (WithHiding b) Source #distributeF :: Functor m => WithHiding (m a) -> m (WithHiding a) Source # Source # Instance detailsDefined in Agda.Syntax.Internal MethodstraverseF :: Functor m => (a -> m b) -> Abs a -> m (Abs b) Source #distributeF :: Functor m => Abs (m a) -> m (Abs a) Source # Source # Instance detailsDefined in Agda.TypeChecking.Monad.Base MethodstraverseF :: Functor m => (a -> m b) -> Open a -> m (Open b) Source #distributeF :: Functor m => Open (m a) -> m (Open a) Source # Source # Instance detailsDefined in Agda.Termination.Monad MethodstraverseF :: Functor m => (a -> m b) -> Masked a -> m (Masked b) Source #distributeF :: Functor m => Masked (m a) -> m (Masked a) Source # Source # A typical decoration is pairing with some stuff. Instance detailsDefined in Agda.Utils.Functor MethodstraverseF :: Functor m => (a0 -> m b) -> (a, a0) -> m (a, b) Source #distributeF :: Functor m => (a, m a0) -> m (a, a0) Source # Decoration (Named name) Source # Instance detailsDefined in Agda.Syntax.Common MethodstraverseF :: Functor m => (a -> m b) -> Named name a -> m (Named name b) Source #distributeF :: Functor m => Named name (m a) -> m (Named name a) Source # Source # Instance detailsDefined in Agda.Syntax.Internal MethodstraverseF :: Functor m => (a -> m b) -> Type'' t a -> m (Type'' t b) Source #distributeF :: Functor m => Type'' t (m a) -> m (Type'' t a) Source # Source # Instance detailsDefined in Agda.Syntax.Internal MethodstraverseF :: Functor m => (a -> m b) -> Dom' t a -> m (Dom' t b) Source #distributeF :: Functor m => Dom' t (m a) -> m (Dom' t a) Source # (Decoration d, Decoration t) => Decoration (Compose d t) Source # Decorations compose. (Thus, they form a category.) Instance detailsDefined in Agda.Utils.Functor MethodstraverseF :: Functor m => (a -> m b) -> Compose d t a -> m (Compose d t b) Source #distributeF :: Functor m => Compose d t (m a) -> m (Compose d t a) Source #

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

Expand

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)


($>) :: Functor f => f a -> b -> f b infixl 4 # Flipped version of <$.

#### Examples

Expand

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")


Since: base-4.7.0.0

(<&>) :: Functor m => m a -> (a -> b) -> m b infixl 1 Source #

Infix version of for.