Data.MFunctor

Documentation

data Variance

Variance kind used in MFunctor

Constructors

CoV

Variance for covariant parameters

ContraV

Variance for contravariant parameters

Instances

MFunctor * Bool ([] *) ([] Variance)

MFunctor * Ordering ([] *) ([] Variance)

MFunctor * () ([] *) ([] Variance)

AdaptFieldFunction ([] (Field *)) ([] Variance) ps vs

GFPMFunctor [Variance] n as vs => GFPMFunctor [Variance] (NS n) ((:) * (a -> b) as) ((:) Variance ContraV vs)

GFPMFunctor [Variance] n as vs => GFPMFunctor [Variance] (NS n) ((:) * (a -> b) as) ((:) Variance CoV vs)

MFunctor (* -> * -> * -> * -> * -> * -> * -> * -> * -> *) (,,,,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ((:) * (g -> g') ((:) * (h -> h') ((:) * (i -> i') ([] *)))))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))))))))

MFunctor (* -> * -> * -> * -> * -> * -> * -> * -> *) (,,,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ((:) * (g -> g') ((:) * (h -> h') ([] *))))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance)))))))))

MFunctor (* -> * -> * -> * -> * -> * -> * -> *) (,,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ((:) * (g -> g') ([] *)))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))))))

MFunctor (* -> * -> * -> * -> * -> * -> *) (,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ([] *))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance)))))))

MFunctor (* -> * -> * -> * -> * -> *) (,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ([] *)))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))))

MFunctor (* -> * -> * -> * -> *) (,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ([] *))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance)))))

MFunctor (* -> * -> * -> *) (,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ([] *)))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))

MFunctor (* -> * -> *) (->) ((:) * (a' -> a) ((:) * (b -> b') ([] *))) ((:) Variance ContraV ((:) Variance CoV ([] Variance)))

MFunctor (* -> * -> *) Either ((:) * (a -> a') ((:) * (b -> b') ([] *))) ((:) Variance CoV ((:) Variance CoV ([] Variance)))

MFunctor (* -> * -> *) (,) ((:) * (a -> a') ((:) * (b -> b') ([] *))) ((:) Variance CoV ((:) Variance CoV ([] Variance)))

MFunctor (* -> *) [] ((:) * (a -> a') ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Sum ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Product ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) First ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Last ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Maybe ((:) * (a -> a') ([] *)) ((:) Variance CoV ([] Variance))

(MFunctor k f (ExpandFieldFunction bs (FlipVariance vs') ps vs) vs', (~) [*] (ExpandFields bs (Domains ps vs)) (Codomains (ExpandFieldFunction bs (FlipVariance vs') ps vs) vs'), (~) [*] (ExpandFields bs (Codomains ps vs)) (Domains (ExpandFieldFunction bs (FlipVariance vs') ps vs) vs'), AdaptFieldFunction bs (FlipVariance vs') ps vs, AdaptFieldFunction as vfs ps vs) => AdaptFieldFunction ((:) (Field *) ((:@:) * k f bs) as) ((:) Variance ContraV vfs) ps vs

(MFunctor k f (ExpandFieldFunction bs vs' ps vs) vs', (~) [*] (ExpandFields bs (Codomains ps vs)) (Codomains (ExpandFieldFunction bs vs' ps vs) vs'), (~) [*] (ExpandFields bs (Domains ps vs)) (Domains (ExpandFieldFunction bs vs' ps vs) vs'), AdaptFieldFunction bs vs' ps vs, AdaptFieldFunction as vfs ps vs) => AdaptFieldFunction ((:) (Field *) ((:@:) * k f bs) as) ((:) Variance CoV vfs) ps vs

(GFPMFunctor [Variance] n ps vs, AdaptFieldFunction as vfs ps vs, (~) * (Flip ((:!:) * ps n)) ((:!:) * (Domains ps vs) n -> (:!:) * (Codomains ps vs) n)) => AdaptFieldFunction ((:) (Field *) (FP * n) as) ((:) Variance ContraV vfs) ps vs

(GFPMFunctor [Variance] n ps vs, AdaptFieldFunction as vfs ps vs, (~) * ((:!:) * ps n) ((:!:) * (Domains ps vs) n -> (:!:) * (Codomains ps vs) n)) => AdaptFieldFunction ((:) (Field *) (FP * n) as) ((:) Variance CoV vfs) ps vs

AdaptFieldFunction as vfs ps vs => AdaptFieldFunction ((:) (Field *) (FK * a) as) ((:) Variance v vfs) ps vs

type family Domains fs vs

Domain (a -> b) CoV ~ a
Domain (a -> b) ContraV ~ b
Domains fs vs ~ Map (Uncurry Domain) (Zip fs vs)

Equations

Domains [] [] = []

Domains ((a -> b) : as) (CoV : vs) = a : Domains as vs

Domains ((a -> b) : as) (ContraV : vs) = b : Domains as vs

type family Codomains fs vs

Codomain (a -> b) CoV ~ b
Codomain (a -> b) ContraV ~ a
Codomains fs vs ~ Map (Uncurry Codomain) (Zip fs vs)

Equations

Codomains [] [] = []

Codomains ((a -> b) : as) (CoV : vs) = b : Codomains as vs

Codomains ((a -> b) : as) (ContraV : vs) = a : Codomains as vs

class MFunctor f fs vs | f -> vs, fs -> k, vs -> k where

MFunctor type class, generalisation of Functor, Bifunctor, Contravariant, Profunctor, etc.

If f has a MGeneric instance, and types that appear in f have a MFunctor instance, it is possible to derive a MFunctor instance for f.

>>> instance MFunctor [] '[a -> a'] '[CoV]
>>> instance MFunctor (->) '[a' -> a, b -> b'] '[ContraV, CoV]

Minimal complete definition

Nothing

Methods

mmapP :: Proxy f -> Proxy vs -> HList fs -> (f :$: Domains fs vs) -> f :$: Codomains fs vs

see mmap

Instances

MFunctor * Bool ([] *) ([] Variance)

MFunctor * Ordering ([] *) ([] Variance)

MFunctor * () ([] *) ([] Variance)

MFunctor (* -> * -> * -> * -> * -> * -> * -> * -> * -> *) (,,,,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ((:) * (g -> g') ((:) * (h -> h') ((:) * (i -> i') ([] *)))))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))))))))

MFunctor (* -> * -> * -> * -> * -> * -> * -> * -> *) (,,,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ((:) * (g -> g') ((:) * (h -> h') ([] *))))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance)))))))))

MFunctor (* -> * -> * -> * -> * -> * -> * -> *) (,,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ((:) * (g -> g') ([] *)))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))))))

MFunctor (* -> * -> * -> * -> * -> * -> *) (,,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ((:) * (f -> f') ([] *))))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance)))))))

MFunctor (* -> * -> * -> * -> * -> *) (,,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ((:) * (e -> e') ([] *)))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))))

MFunctor (* -> * -> * -> * -> *) (,,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ((:) * (d -> d') ([] *))))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance)))))

MFunctor (* -> * -> * -> *) (,,) ((:) * (a -> a') ((:) * (b -> b') ((:) * (c -> c') ([] *)))) ((:) Variance CoV ((:) Variance CoV ((:) Variance CoV ([] Variance))))

MFunctor (* -> * -> *) (->) ((:) * (a' -> a) ((:) * (b -> b') ([] *))) ((:) Variance ContraV ((:) Variance CoV ([] Variance)))

MFunctor (* -> * -> *) Either ((:) * (a -> a') ((:) * (b -> b') ([] *))) ((:) Variance CoV ((:) Variance CoV ([] Variance)))

MFunctor (* -> * -> *) (,) ((:) * (a -> a') ((:) * (b -> b') ([] *))) ((:) Variance CoV ((:) Variance CoV ([] Variance)))

MFunctor (* -> *) [] ((:) * (a -> a') ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Sum ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Product ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) First ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Last ((:) * (a -> b) ([] *)) ((:) Variance CoV ([] Variance))

MFunctor (* -> *) Maybe ((:) * (a -> a') ([] *)) ((:) Variance CoV ([] Variance))

mmap :: forall a b f fs vs. (Unapply a f (Domains fs vs), Unapply b f (Codomains fs vs), MFunctor f fs vs) => HList fs -> a -> b

Proxy-less mmapP, generalisation of fmap, bimap, contramap, dimap, etc.

If f is covariant in all its parameters (its variances are '[CoV, CoV, ..., CoV]) :

mmap :: HList '[a1 -> b1, ..., an -> bn] -> f a1 ... an -> f b1 ... bn

e.g. when f is contravariant in some parameters (variances of (->) are '[ContraV, CoV])

mmap :: HList '[b1 -> a1, a2 -> b2] -> (a1 -> a2) -> (b1 -> b2)