Control.XApplicative

This module describes an intermediate type class between a functor and an indexed monad XMonad - an indexed applicative.

XApplicative

class (forall p q. Functor (f p q)) => XApplicative f where

A poly-kinded type-parameterized (indexed) functor with application, with operations to

• embed pure expressions (xpure), and
• sequence computations and combine their results (<*>: and xliftA2).

These functors have kind r -> r -> Type -> Type, where the kind equality of the of the first and the second type parameters is implied from chaining.

A minimal complete definition must include implementations of xpure and of either <*>: or xliftA2. If it defines both, then they must behave the same as their default definitions:

(<*>:) = xliftA2 id

liftA2 f x y = f <$> x <*>: y

The definition must satisfy the same laws as Applicative:

Identity

xpure id <*>: v = v

Composition

xpure (.) <*>: u <*>: v <*>: w = u <*>: (v <*>: w)

Homomorphism

xpure f <*>: xpure x = xpure (f x)

Interchange

u <*>: xpure y = xpure ($ y) <*>: u

The other methods have the following default definitions:

• u *>: v = (id <$ u) <*>: v

• u <*: v = xliftA2 const u v

The Functor instance for f p q will satisfy

• fmap f x = xpure f <*>: x

If f is also an XMonad, it should satisfy

• xpure = xreturn

• m1 <*>: m2 = m1 >>=: (x1 -> m2 >>=: (x2 -> xreturn (x1 x2)))

• (*>:) = (>>:)

Minimal complete definition

xpure, ((<*>:) | xliftA2)

Methods

xpure :: a -> f p p a

Lift a value.

(<*>:) :: f p q (a -> b) -> f q r a -> f p r b infixl 4

Sequential application.

xliftA2 :: (a -> b -> c) -> f p q a -> f q r b -> f p r c

Lift a binary function to type-parameterized actions.

If fmap is an expensive operation, it is likely better to use xliftA2 than to fmap over the structure and then use <*>:.

(*>:) :: f p q a -> f q r b -> f p r b infixl 4

Sequence actions, discarding the value of the first argument.

(<*:) :: f p q a -> f q r b -> f p r a infixl 4

Sequence actions, discarding the value of the second argument.

Instances

XApplicative (XFree f :: k -> k -> Type -> Type)

Defined in Control.XFreer

Methods

xpure :: a -> XFree f p p a

(<*>:) :: XFree f p q (a -> b) -> XFree f q r a -> XFree f p r b

xliftA2 :: (a -> b -> c) -> XFree f p q a -> XFree f q r b -> XFree f p r c

(*>:) :: XFree f p q a -> XFree f q r b -> XFree f p r b

(<*:) :: XFree f p q a -> XFree f q r b -> XFree f p r a

Functions

(<**>:) :: XApplicative f => f p q a -> f q r (a -> b) -> f p r b infixl 4

A variant of <*>: with the arguments reversed.

xliftA :: XApplicative f => (a -> b) -> f p q a -> f p q b

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

xliftA3 :: XApplicative f => (a -> b -> c -> d) -> f p q a -> f q r b -> f r l c -> f p l d

Lift a ternary function to actions.