Agda-2.5.2: A dependently typed functional programming language and proof assistant

Safe HaskellSafe
LanguageHaskell2010

Agda.Utils.Functor

Contents

Description

Utilities for functors.

Synopsis

Documentation

($>) :: Functor f => f a -> b -> f b infixr 4 Source #

(<.>) :: 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.

(<&>) :: Functor m => m a -> (a -> b) -> m b infix 4 Source #

Infix version of for.

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.

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 Identity Source #

The identity functor is a decoration.

Methods

traverseF :: Functor m => (a -> m b) -> Identity a -> m (Identity b) Source #

distributeF :: Functor m => Identity (m a) -> m (Identity a) Source #

Decoration Ranged Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Ranged a -> m (Ranged b) Source #

distributeF :: Functor m => Ranged (m a) -> m (Ranged a) Source #

Decoration Dom Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Dom a -> m (Dom b) Source #

distributeF :: Functor m => Dom (m a) -> m (Dom a) Source #

Decoration Arg Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Arg a -> m (Arg b) Source #

distributeF :: Functor m => Arg (m a) -> m (Arg a) Source #

Decoration WithHiding Source # 

Methods

traverseF :: Functor m => (a -> m b) -> WithHiding a -> m (WithHiding b) Source #

distributeF :: Functor m => WithHiding (m a) -> m (WithHiding a) Source #

Decoration Type' Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Type' a -> m (Type' b) Source #

distributeF :: Functor m => Type' (m a) -> m (Type' a) Source #

Decoration Abs Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Abs a -> m (Abs b) Source #

distributeF :: Functor m => Abs (m a) -> m (Abs a) Source #

Decoration Local Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Local a -> m (Local b) Source #

distributeF :: Functor m => Local (m a) -> m (Local a) Source #

Decoration Open Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Open a -> m (Open b) Source #

distributeF :: Functor m => Open (m a) -> m (Open a) Source #

Decoration Masked Source # 

Methods

traverseF :: Functor m => (a -> m b) -> Masked a -> m (Masked b) Source #

distributeF :: Functor m => Masked (m a) -> m (Masked a) Source #

Decoration ((,) a) Source #

A typical decoration is pairing with some stuff.

Methods

traverseF :: Functor m => (a -> m b) -> (a, a) -> m (a, b) Source #

distributeF :: Functor m => (a, m a) -> m (a, a) Source #

Decoration (Named name) Source # 

Methods

traverseF :: 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 #

(Decoration d, Decoration t) => Decoration (Compose * * d t) Source #

Decorations compose. (Thus, they form a category.)

Methods

traverseF :: 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.

The constant functor.

Maybe. Can only be traversed into pointed functors.

Other disjoint sum types, like lists etc.

(<$>) :: 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 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)