Safe Haskell	Safe
Language	Haskell2010

Generics.MRSOP.Base.NS

Contents

Description

Standard representation of n-ary sums.

Synopsis

data NS :: (k -> *) -> [k] -> * where
- There :: NS p xs -> NS p (x ': xs)
- Here :: p x -> NS p (x ': xs)
mapNS :: (f :-> g) -> NS f ks -> NS g ks
mapNSM :: Monad m => (forall x. f x -> m (g x)) -> NS f ks -> m (NS g ks)
elimNS :: (forall x. f x -> a) -> NS f ks -> a
zipNS :: MonadPlus m => NS ki xs -> NS kj xs -> m (NS (ki :*: kj) xs)
cataNS :: (forall x xs. f x -> r (x ': xs)) -> (forall x xs. r xs -> r (x ': xs)) -> NS f xs -> r xs
eqNS :: (forall x. p x -> p x -> Bool) -> NS p xs -> NS p xs -> Bool

Documentation

data NS :: (k -> *) -> [k] -> * where Source #

Indexed n-ary sums. This is analogous to the Any datatype in Agda. Combinations of Here and Theres are also called injections.

Constructors

There :: NS p xs -> NS p (x ': xs)
Here :: p x -> NS p (x ': xs)

Instances

ShowHO phi => ShowHO (NS phi :: [k] -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.NS Methods showHO :: NS phi k0 -> String Source #
EqHO phi => EqHO (NS phi :: [k] -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.NS Methods eqHO :: NS phi k0 -> NS phi k0 -> Bool Source #
EqHO phi => Eq (NS phi xs) Source #
Instance details Defined in Generics.MRSOP.Base.NS Methods (==) :: NS phi xs -> NS phi xs -> Bool # (/=) :: NS phi xs -> NS phi xs -> Bool #
ShowHO phi => Show (NS phi xs) Source #
Instance details Defined in Generics.MRSOP.Base.NS Methods showsPrec :: Int -> NS phi xs -> ShowS # show :: NS phi xs -> String # showList :: [NS phi xs] -> ShowS #

Map, Zip and Elim

mapNS :: (f :-> g) -> NS f ks -> NS g ks Source #

Maps over a sum

mapNSM :: Monad m => (forall x. f x -> m (g x)) -> NS f ks -> m (NS g ks) Source #

Maps a monadic function over a sum

elimNS :: (forall x. f x -> a) -> NS f ks -> a Source #

Eliminates a sum

zipNS :: MonadPlus m => NS ki xs -> NS kj xs -> m (NS (ki :*: kj) xs) Source #

Combines two sums. Note that we have to fail if they are constructed from different injections.

cataNS :: (forall x xs. f x -> r (x ': xs)) -> (forall x xs. r xs -> r (x ': xs)) -> NS f xs -> r xs Source #

Consumes a value of type NS

eqNS :: (forall x. p x -> p x -> Bool) -> NS p xs -> NS p xs -> Bool Source #

Compares two values of type NS using the provided function in case they are made of the same injection.