Copyright	Copyright (C) 2015 Kyle Carter
License	BSD3
Maintainer	Kyle Carter <kylcarte@indiana.edu>
Stability	experimental
Portability	RankNTypes
Safe Haskell	None
Language	Haskell2010

Data.Type.Sum

Description

Sum is a type combinators for representing disjoint sums of indices (as :: [k]) of a single functor @(f :: k -> *). Contrast to the many-functors-one-index FSum

Synopsis

Documentation

data Sum f :: [k] -> * where Source #

Constructors

InL :: !(f a) -> Sum f (a :< as)
InR :: !(Sum f as) -> Sum f (a :< as)

Instances

(Witness p q (f a1), Witness p q (Sum a f ((:<) a b as))) => Witness p q (Sum a f ((:<) a a1 ((:<) a b as))) Source #
Associated Types type WitnessC (p :: Constraint) (q :: Constraint) (Sum a f ((:<) a a1 ((:<) a b as))) :: Constraint Source # Methods (\\) :: p => (q -> r) -> Sum a f ((a :< a1) ((a :< b) as)) -> r Source #
Witness p q (f a) => Witness p q (Sum k f ((:) k a ([] k))) Source #
Associated Types type WitnessC (p :: Constraint) (q :: Constraint) (Sum k f ((:) k a ([] k))) :: Constraint Source # Methods (\\) :: p => (q -> r) -> Sum k f ((k ': a) [k]) -> r Source #
IxTraversable1 k [k] (Index k) (Sum k) Source #
Methods itraverse1 :: Applicative h => (forall a. i b a -> f a -> h (g a)) -> t f b -> h (t g b) Source #
IxFoldable1 k [k] (Index k) (Sum k) Source #
Methods ifoldMap1 :: Monoid m => (forall a. i b a -> f a -> m) -> t f b -> m Source #
IxFunctor1 k [k] (Index k) (Sum k) Source #
Methods imap1 :: (forall a. i b a -> f a -> g a) -> t f b -> t g b Source #
Traversable1 [k] k (Sum k) Source #
Methods traverse1 :: Applicative h => (forall a. f a -> h (g a)) -> t f b -> h (t g b) Source #
Foldable1 [k] k (Sum k) Source #
Methods foldMap1 :: Monoid m => (forall a. f a -> m) -> t f b -> m Source #
Functor1 [k] k (Sum k) Source #
Methods map1 :: (forall a. f a -> g a) -> t f b -> t g b Source #
Read1 k f => Read1 [k] (Sum k f) Source #
Methods readsPrec1 :: Int -> ReadS (Some (Sum k f) f) Source #
Show1 k f => Show1 [k] (Sum k f) Source #
Methods showsPrec1 :: Int -> f a -> ShowS Source # show1 :: f a -> String Source #
Ord1 k f => Ord1 [k] (Sum k f) Source #
Methods compare1 :: f a -> f a -> Ordering Source # (<#) :: f a -> f a -> Bool Source # (>#) :: f a -> f a -> Bool Source # (<=#) :: f a -> f a -> Bool Source # (>=#) :: f a -> f a -> Bool Source #
Eq1 k f => Eq1 [k] (Sum k f) Source #
Methods eq1 :: f a -> f a -> Bool Source # neq1 :: f a -> f a -> Bool Source #
ListC ((<$>) Constraint * Eq ((<$>) * k f as)) => Eq (Sum k f as) Source #
Methods (==) :: Sum k f as -> Sum k f as -> Bool # (/=) :: Sum k f as -> Sum k f as -> Bool #
(ListC ((<$>) Constraint * Eq ((<$>) * k f as)), ListC ((<$>) Constraint * Ord ((<$>) * k f as))) => Ord (Sum k f as) Source #
Methods compare :: Sum k f as -> Sum k f as -> Ordering # (<) :: Sum k f as -> Sum k f as -> Bool # (<=) :: Sum k f as -> Sum k f as -> Bool # (>) :: Sum k f as -> Sum k f as -> Bool # (>=) :: Sum k f as -> Sum k f as -> Bool # max :: Sum k f as -> Sum k f as -> Sum k f as # min :: Sum k f as -> Sum k f as -> Sum k f as #
ListC ((<$>) Constraint * Show ((<$>) * k f as)) => Show (Sum k f as) Source #
Methods showsPrec :: Int -> Sum k f as -> ShowS # show :: Sum k f as -> String # showList :: [Sum k f as] -> ShowS #
type WitnessC p q (Sum a f ((:<) a a1 ((:<) a b as))) Source #
type WitnessC p q (Sum a f ((:<) a a1 ((:<) a b as))) = (Witness p q (f a1), Witness p q (Sum a f ((:<) a b as)))
type WitnessC p q (Sum k f ((:) k a ([] k))) Source #
type WitnessC p q (Sum k f ((:) k a ([] k))) = Witness p q (f a)

nilSum :: Sum f Ø -> Void Source #

There are no possible values of the type Sum f Ø.

decomp :: Sum f (a :< as) -> Either (f a) (Sum f as) Source #

injectSum :: Index as a -> f a -> Sum f as Source #

inj :: a ∈ as => f a -> Sum f as Source #

prj :: a ∈ as => Sum f as -> Maybe (f a) Source #

index :: Index as a -> Sum f as -> Maybe (f a) Source #

elimSum :: (forall x xs. f x -> p (x :< xs)) -> (forall x xs. Index as x -> p xs -> p (x :< xs)) -> Sum f as -> p as Source #