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|
{ ... }:
let
id = x: x;
const = x: y: x;
comp = f: g: x: f (g x);
_ = v: f: f v;
# Profunctor (p :: Type -> Type -> Type)
Profunctor = rec {
# dimap :: (a -> b) -> (c -> d) -> p b c -> p a d
dimap = f: g: x: lmap f (rmap g x);
# lmap :: (a -> b) -> p b c -> p a c
lmap = f: dimap f id;
# rmap :: (c -> d) -> p b c -> p b d
rmap = g: dimap id g;
};
# Profunctor (->)
profunctorFun = Profunctor // {
# dimap :: (a -> b) -> (c -> d) -> (b -> c) -> a -> d
dimap = ab: cd: bc: a: cd (bc (ab a));
# lmap :: (a -> b) -> (b -> c) -> (a -> c)
lmap = ab: bc: a: bc (ab a);
# rmap :: (c -> d) -> (b -> c) -> (b -> d)
rmap = cd: bc: b: cd (bc b);
};
tuple = fst: snd: {
inherit fst snd;
};
swap = {fst, snd}: {
fst = snd;
snd = fst;
};
# Profunctor p => Strong (p :: Type -> Type -> Type)
Strong = pro: pro // rec {
# firstP :: p a b -> p (a, c) (b, c)
firstP = pab: pro.dimap swap swap (pro.secondP pab);
# secondP :: p a b -> p (c, a) (c, b)
secondP = pab: pro.dimap swap swap (pro.firstP pab);
};
# Strong (->)
strongFun = Strong profunctorFun // {
# firstP :: (a -> b) -> (a, c) -> (b, c)
firstP = f: { fst, snd }: { fst = f fst; inherit snd; };
# secondP :: (a -> b) -> (c, a) -> (c, b)
secondP = f: { snd, fst }: { snd = f snd; inherit fst; };
};
# Iso s t a b :: forall p. Profunctor p -> p a b -> p s t
# iso :: (s -> a) -> (b -> t) -> Iso s t a b
iso = pro: pro.dimap;
# Lens s t a b :: forall p. Strong p -> p a b -> p s t
# lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b
lens = strong: get: set: pab:
lensP
strong
(s: tuple (get s) (b: set s b))
pab;
# lensP :: (s -> (a, b -> t)) -> Lens s t a b
lensP = strong: to: pab:
strong.dimap
to
({fst,snd}: snd fst)
(strong.firstP pab);
# first element of a tuple
# _1 :: Lens (a, c) (b, c) a b
_1 = strong: strong.firstP;
# second element of a tuple
# _2 :: Lens (c, a) (c, b) a b
_2 = strong: strong.secondP;
# a the given field in the record
# field :: (f :: String) -> Lens { f :: a; ... } { f :: b; ... } a b
field = name: strong:
lens
strong
(attrs: attrs.${name})
(attrs: a: attrs // { ${name} = a; });
# Setter :: (->) a b -> (->) s t
# Setter :: (a -> b) -> (s -> t)
# Subclasses of profunctor for (->).
# We only have Strong for now, but when we implement Choice we need to add it here.
profunctorSubclassesFun = strongFun;
# over :: Setter s t a b -> (a -> b) -> s -> t
over = setter:
# A setter needs to be instanced to the profunctor-subclass instances of (->).
(setter profunctorSubclassesFun);
# set :: Setter s t a b -> b -> s -> t
set = setter: b: over setter (const b);
# combine a bunch of optics, for the subclass instance of profunctor you give it.
optic = accessors: profunctorSubclass:
builtins.foldl' comp id
(map (accessor: accessor profunctorSubclass) accessors);
in {
inherit
id
_
const
comp
Profunctor
profunctorFun
Strong
strongFun
iso
lens
optic
_1
_2
field
tuple
swap
over
set
;
}
|
