Functors again

We’ve seen several different functors:

arrOf: C -> C
makeProduct: C* -> C
makeInterface: C* -> C
hom: Cᵒᵖ × C -> C
makeCoproduct: C* -> C

• The functor arrOf takes a contract and produces one contract that accepts an empty list, or a 1-item list, or a 2-item list, and so on up to a (2³¹ – 1)-item list. It can also take an arbitrary function and iterate over an array.
• The functor makeProduct takes an array of contracts and produces one that accepts tuples of values whose individual entries pass the corresponding contracts. It can also take an array of functions to apply in parallel.
• The functor makeInterface is the same as makeProduct, but with string indices instead of numeric indices.
• The functor hom takes two contracts and produces one contract that accepts functions whose input passes the first contract and whose output passes the second. It can also take two functions and apply them serially, doing one function before and one after.
• The functor makeCoproduct takes an array of contracts and produces one that accepts values that pass one of the contracts. It can also take an array of functions and apply one of them depending on the tag.

In each case, the functor takes some contracts and produces a single new contract, and each one encapsulates some control structure of the language in the way you take apart the values that pass the new contract.