Type-Level Lenses

gistfile1.txt

ghci> :kind! View FirstFieldSym0 '(1, True)
1
ghci> :kind! Over SecondFieldSym0 NotSym0 '(1, True)
'(1, False)

singleton_lenses.hs

-- singletons can promote these to the type level using template haskell
type Setter s t a b = (a -> Identity b) -> (s -> Identity t)
over :: Setter s t a b -> (a -> b) -> (s -> t)
over l f = (\(Identity x) -> x) . l (Identity . f)

type Getter s a = (a -> Const a a) -> (s -> Const a s)
view :: Getter s a -> s -> a
view l = (\(Const x) -> x) . l Const

firstField :: Functor f => (a -> f b) -> (a, c) -> f (b, c)
firstField f (x, y) = (\x' -> (x', y)) <$> f x

secondField :: Functor f => (b -> f c) -> (a, b) -> f (a, c)
secondField f (x, y) = (\y' -> (x, y')) <$> f y