Data.Pair

Pair-related type constructor classes.

This module is similar to Control.Functor.Pair in the category-extras package, but it does not require a Functor superclass.

Temporarily, there is also Data.Zip, which contains the same functionality with different naming. I'm unsure which I prefer.

Pairpings

type PairTy f = forall a b. f a -> f b -> f (a, b)

Type of pair method

class Pair f where

Type constructor class for pair-like things. Here are some standard instance templates you can fill in. They're not defined in the general forms below, because they would lead to a lot of overlap.

   instance Applicative f => Pair f where
       pair = liftA2 (,)
   instance (Applicative h, Pair f) => Pair (h :. f) where
       pair = apPair
   instance (Functor g, Pair g, Pair f) => Pair (g :. f)
       where pair = ppPair
   instance (Arrow (~>), Unpair f, Pair g) => Pair (Arrw (~>) f g) where
       pair = arPair
   instance (Monoid_f h, Copair h) => Pair h where
       pair = copair

Also, if you have a type constructor that's a Functor and a Pair, here is a way to define '(*)' for Applicative:

   (<*>) = pairWith ($)

Minimum definitions for instances.

Methods

pair

Arguments

:: PairTy f

Generalized pair

Instances

Pair []

Defined in Data.Pair

Methods

pair :: PairTy []

Pair IO

Defined in Data.Pair

Methods

pair :: PairTy IO

Pair Endo

Defined in Data.Pair

Methods

pair :: PairTy Endo

Pair Id

Defined in Data.Pair

Methods

pair :: PairTy Id

Monoid u => Pair ((,) u)

Defined in Data.Pair

Methods

pair :: PairTy ((,) u)

Monoid o => Pair (Const o :: Type -> Type)

Defined in Data.Pair

Methods

pair :: PairTy (Const o)

Pair ((->) u :: Type -> Type)

Defined in Data.Pair

Methods

pair :: PairTy ((->) u)

(Pair f, Pair g) => Pair (f :*: g)

Defined in Data.Pair

Methods

pair :: PairTy (f :*: g)

(Arrow j, Monoid_f (Flip j o)) => Pair (Flip j o)

Defined in Data.Pair

Methods

pair :: PairTy (Flip j o)

(Arrow j, Unpair f, Pair g) => Pair (Arrw j f g)

Defined in Data.Pair

Methods

pair :: PairTy (Arrw j f g)

apPair :: (Applicative h, Pair f) => PairTy (h :. f)

Handy for Pair instances

ppPair :: (Functor g, Pair g, Pair f) => PairTy (g :. f)

Handy for Pair instances

arPair :: (Arrow j, Unpair f, Pair g) => PairTy (Arrw j f g)

Pairing of Arrw values. Warning: definition uses arr, so only use if your arrow has a working arr.

Unpairings

type UnpairTy f = forall a b. f (a, b) -> (f a, f b)

Type of unpair method. Generalizes unpair.

class Unpair f where

Unpairpable. Minimal instance definition: either (a) unpair or (b) both of fsts and snds. A standard template to substitute any Functor f. But watch out for effects!

    instance Functor f => Unpair f where {fsts = fmap fst; snds = fmap snd}

Minimal complete definition

Nothing

Methods

unpair

Arguments

:: UnpairTy f

generalized unpair

fsts

Arguments

:: f (a, b)

-> f a

First part of pair-like value

snds

Arguments

:: f (a, b)

-> f b

Second part of pair-like value

Instances

Unpair []

Defined in Data.Pair

Methods

unpair :: UnpairTy []

fsts :: [(a, b)] -> [a]

snds :: [(a, b)] -> [b]

Unpair Endo

Defined in Data.Pair

Methods

unpair :: UnpairTy Endo

fsts :: Endo (a, b) -> Endo a

snds :: Endo (a, b) -> Endo b

Unpair Id

Defined in Data.Pair

Methods

unpair :: UnpairTy Id

fsts :: Id (a, b) -> Id a

snds :: Id (a, b) -> Id b

Unpair ((,) a)

Defined in Data.Pair

Methods

unpair :: UnpairTy ((,) a)

fsts :: (a, (a0, b)) -> (a, a0)

snds :: (a, (a0, b)) -> (a, b)

Unpair (Const a :: Type -> Type)

Defined in Data.Pair

Methods

unpair :: UnpairTy (Const a)

fsts :: Const a (a0, b) -> Const a a0

snds :: Const a (a0, b) -> Const a b

Unpair ((->) a :: Type -> Type)

Defined in Data.Pair

Methods

unpair :: UnpairTy ((->) a)

fsts :: (a -> (a0, b)) -> a -> a0

snds :: (a -> (a0, b)) -> a -> b

Dual unpairings

class Copair f where

Dual to Unpair. Especially handy for contravariant functors (ContraFunctor) . Use this template (filling in f) :

   instance ContraFunctor f => Copair f where
     { cofsts = cofmap fst ; cosnds = cofmap snd }

Methods

cofsts

Arguments

:: f a

-> f (a, b)

Pair-like value from first part

cosnds

Arguments

:: f b

-> f (a, b)

Pair-like value from second part

Instances

Copair Endo

Defined in Data.Pair

Methods

cofsts :: Endo a -> Endo (a, b)

cosnds :: Endo b -> Endo (a, b)

Copair (Const e :: Type -> Type)

Defined in Data.Pair

Methods

cofsts :: Const e a -> Const e (a, b)

cosnds :: Const e b -> Const e (a, b)

(Copair f, Copair g) => Copair (f :*: g)

Defined in Data.Pair

Methods

cofsts :: (f :*: g) a -> (f :*: g) (a, b)

cosnds :: (f :*: g) b -> (f :*: g) (a, b)

Arrow j => Copair (Flip j o)

Defined in Data.Pair

Methods

cofsts :: Flip j o a -> Flip j o (a, b)

cosnds :: Flip j o b -> Flip j o (a, b)

(Functor h, Copair f) => Copair (h :. f)

Defined in Data.Pair

Methods

cofsts :: (h :. f) a -> (h :. f) (a, b)

cosnds :: (h :. f) b -> (h :. f) (a, b)

copair :: (Copair f, Monoid_f f) => PairTy f

Pairing of Copair values. Combines contribution of each.

Misc

pairEdit :: (Functor m, Monoid (m ((c, d) -> (c, d)))) => (m c, m d) -> m ((c, d) -> (c, d))

Turn a pair of sources into a source of pair-editors. See http://conal.net/blog/posts/pairs-sums-and-reactivity/. 'Functor'\/'Monoid' version. See also pairEditM.

pairEditM :: MonadPlus m => (m c, m d) -> m ((c, d) -> (c, d))

Turn a pair of sources into a source of pair-editors. See http://conal.net/blog/posts/pairs-sums-and-reactivity/. Monad version. See also pairEdit.