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| -rw-r--r-- | users/Profpatsch/lens.nix | 131 |
1 files changed, 131 insertions, 0 deletions
diff --git a/users/Profpatsch/lens.nix b/users/Profpatsch/lens.nix new file mode 100644 index 000000000000..3c429bbdb14e --- /dev/null +++ b/users/Profpatsch/lens.nix @@ -0,0 +1,131 @@ +{ ... }: +let + id = x: x; + + const = x: y: x; + + comp = f: g: x: f (g x); + + # 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 + + # 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 + ; +} |