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1. fmap :: Functor f => (a -> b) -> f a -> f b

   basement	Basement.Compat.Base

   fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`). Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

   Examples

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

   >>> fmap show Nothing
   Nothing
   
   >>> fmap show (Just 3)
   Just "3"
   

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

   >>> fmap show (Left 17)
   Left 17
   
   >>> fmap show (Right 17)
   Right "17"
   

   Double each element of a list:

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

   Apply even to the second element of a pair:

   >>> fmap even (2,2)
   (2,True)
   

   It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap). It explains why fmap can be used with tuples containing values of different types as in the following example:

   >>> fmap even ("hello", 1.0, 4)
   ("hello",1.0,True)
   

2. gmapM :: (Data a, Monad m) => (forall d . Data d => d -> m d) -> a -> m a

   basement	Basement.Compat.Base

   A generic monadic transformation that maps over the immediate subterms The default definition instantiates the type constructor c in the type of gfoldl to the monad datatype constructor, defining injection and projection using return and >>=.

3. gmapMo :: (Data a, MonadPlus m) => (forall d . Data d => d -> m d) -> a -> m a

   basement	Basement.Compat.Base

   Transformation of one immediate subterm with success

4. gmapMp :: (Data a, MonadPlus m) => (forall d . Data d => d -> m d) -> a -> m a

   basement	Basement.Compat.Base

   Transformation of at least one immediate subterm does not fail

5. gmapQ :: Data a => (forall d . Data d => d -> u) -> a -> [u]

   basement	Basement.Compat.Base

   A generic query that processes the immediate subterms and returns a list of results. The list is given in the same order as originally specified in the declaration of the data constructors.

6. gmapQi :: Data a => Int -> (forall d . Data d => d -> u) -> a -> u

   basement	Basement.Compat.Base

   A generic query that processes one child by index (zero-based)

7. gmapQl :: Data a => (r -> r' -> r) -> r -> (forall d . Data d => d -> r') -> a -> r

   basement	Basement.Compat.Base

   A generic query with a left-associative binary operator

8. gmapQr :: forall r r' . Data a => (r' -> r -> r) -> r -> (forall d . Data d => d -> r') -> a -> r

   basement	Basement.Compat.Base

   A generic query with a right-associative binary operator

9. gmapT :: Data a => (forall b . Data b => b -> b) -> a -> a

   basement	Basement.Compat.Base

   A generic transformation that maps over the immediate subterms The default definition instantiates the type constructor c in the type of gfoldl to an identity datatype constructor, using the isomorphism pair as injection and projection.

10. bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d

    basement	Basement.Compat.Bifunctor

    Map over both arguments at the same time.

    bimap f g ≡ first f . second g
    

    Examples

    >>> bimap toUpper (+1) ('j', 3)
    ('J',4)
    

    >>> bimap toUpper (+1) (Left 'j')
    Left 'J'
    

    >>> bimap toUpper (+1) (Right 3)
    Right 4
    

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