Functor module:Data package:linear-base

Linear Data Functors should be thought of as containers holding values of type a over which you are able to apply a linear function of type a %1-> b on each value of type a in the functor and consume a given functor of type f a.

The Bifunctor class

Laws

If bimap is supplied, then bimap id id = id

• If first and second are supplied, then first id ≡ id second id ≡ id
• If all are supplied, then @bimap f g = first f . second g

A Profunctor can be thought of as a computation that involves taking a(s) as input and returning b(s). These computations compose with (linear) functions. Profunctors generalize the function arrow ->. Hence, think of a value of type x arr y for profunctor arr to be something like a function from x to y. Laws:

lmap id = id
lmap (f . g) = lmap f . lmap g
rmap id = id
rmap (f . g) = rmap f . rmap g