Incremental functions category draft (PS)

incremental.purs

type Jet a = { position :: a, velocity :: Change a }

destination :: forall a da. Patch a da => Jet a -> a
destination {position, velocity} = patch position (fromChange velocity)

newtype Incremental a b = Incremental (Jet a -> Jet b)

-- | Construct an incremental function from a function on Jets. The user must
-- | verify that these laws hold:
-- |
-- | - `∀fxy. destination x = destination y ⇒ destination (f x) = destination (f y)`
-- | - `∀fxy. x.position = y.position ⇒ (f x).position = (f y).position`
incremental :: forall a b. (Jet a -> Jet b) -> Incremental a b
incremental = Incremental

instance semigroupoidIncremental :: Semigroupoid Incremental where
  compose (Incremental f) (Incremental g) = Incremental (compose f g)

instance categoryIncremental :: Category Incremental where
  identity = Incremental identity