Data.Church.Pair

The church encoded pair type and associated operations.

Documentation

newtype Pair a b

The church encoded pair

Constructors

Pair (forall r. (a -> b -> r) -> r)

Instances

Eq2 Pair

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Pair a c -> Pair b d -> Bool

Ord2 Pair

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Pair a c -> Pair b d -> Ordering

Bifunctor Pair

Methods

bimap :: (a -> b) -> (c -> d) -> Pair a c -> Pair b d

first :: (a -> b) -> Pair a c -> Pair b c

second :: (b -> c) -> Pair a b -> Pair a c

Monoid a => Monad (Pair a)

Methods

(>>=) :: Pair a a -> (a -> Pair a b) -> Pair a b

(>>) :: Pair a a -> Pair a b -> Pair a b

return :: a -> Pair a a

fail :: String -> Pair a a

Functor (Pair a)

Methods

fmap :: (a -> b) -> Pair a a -> Pair a b

(<$) :: a -> Pair a b -> Pair a a

Monoid a => Applicative (Pair a)

Methods

pure :: a -> Pair a a

(<*>) :: Pair a (a -> b) -> Pair a a -> Pair a b

(*>) :: Pair a a -> Pair a b -> Pair a b

(<*) :: Pair a a -> Pair a b -> Pair a a

Foldable (Pair a)

Methods

fold :: Monoid m => Pair a m -> m

foldMap :: Monoid m => (a -> m) -> Pair a a -> m

foldr :: (a -> b -> b) -> b -> Pair a a -> b

foldr' :: (a -> b -> b) -> b -> Pair a a -> b

foldl :: (b -> a -> b) -> b -> Pair a a -> b

foldl' :: (b -> a -> b) -> b -> Pair a a -> b

foldr1 :: (a -> a -> a) -> Pair a a -> a

foldl1 :: (a -> a -> a) -> Pair a a -> a

toList :: Pair a a -> [a]

null :: Pair a a -> Bool

length :: Pair a a -> Int

elem :: Eq a => a -> Pair a a -> Bool

maximum :: Ord a => Pair a a -> a

minimum :: Ord a => Pair a a -> a

sum :: Num a => Pair a a -> a

product :: Num a => Pair a a -> a

Traversable (Pair a)

Methods

traverse :: Applicative f => (a -> f b) -> Pair a a -> f (Pair a b)

sequenceA :: Applicative f => Pair a (f a) -> f (Pair a a)

mapM :: Monad m => (a -> m b) -> Pair a a -> m (Pair a b)

sequence :: Monad m => Pair a (m a) -> m (Pair a a)

Eq a => Eq1 (Pair a)

Methods

liftEq :: (a -> b -> Bool) -> Pair a a -> Pair a b -> Bool

Ord a => Ord1 (Pair a)

Methods

liftCompare :: (a -> b -> Ordering) -> Pair a a -> Pair a b -> Ordering

(Eq a, Eq b) => Eq (Pair a b)

Methods

(==) :: Pair a b -> Pair a b -> Bool

(/=) :: Pair a b -> Pair a b -> Bool

(Ord a, Ord b) => Ord (Pair a b)

Methods

compare :: Pair a b -> Pair a b -> Ordering

(<) :: Pair a b -> Pair a b -> Bool

(<=) :: Pair a b -> Pair a b -> Bool

(>) :: Pair a b -> Pair a b -> Bool

(>=) :: Pair a b -> Pair a b -> Bool

max :: Pair a b -> Pair a b -> Pair a b

min :: Pair a b -> Pair a b -> Pair a b

(Semigroup a, Semigroup b) => Semigroup (Pair a b)

Methods

(<>) :: Pair a b -> Pair a b -> Pair a b

sconcat :: NonEmpty (Pair a b) -> Pair a b

stimes :: Integral b => b -> Pair a b -> Pair a b

(Monoid a, Monoid b) => Monoid (Pair a b)

Methods

mempty :: Pair a b

mappend :: Pair a b -> Pair a b -> Pair a b

mconcat :: [Pair a b] -> Pair a b

mkPair :: a -> b -> Pair a b

Construct a Pair from two values

pair :: (a -> b -> r) -> Pair a b -> r

Case analysis on Pair