Yes, in fact any functor gives rise to a unique comonad in this way, unless f==0. Let F be an endofunctor on Hask. Let W(a) = ∀r.F(a->r)->r W(f) = F(f∗)∗ where g∗(h) = h∘g The puzzle becomes geometric/combinatoric in nature once you realize the following isomorphism: Theorem 1. Suppose neither of the types (∀r.r->F(r)) (∀r.F(r)->r) … Read more
Let’s just recap the definition of the Cofree datatype. data Cofree f a = a :< f (Cofree f a) That’s at least enough to diagnose the problem with the example. When you wrote 1 :< [2, 3] you made a small error that’s reported rather more subtly than is helpful. Here, f = [] … Read more
Given the following definition of store, data Store s a = Store { peek :: s -> a, pos :: s } I like to think of a Store as a big warehouse filled with values of type a. Each value of type a is slotted into a position labeled by an index value of … Read more
A monad only supplies two functions: return :: Monad m => a -> m a (>>=) :: Monad m => m a -> (a -> m b) -> m b Both of these return something of type m a, so there is no way to combine these in any way to get a function of … Read more
Jagger/Richards: you can’t always get what you want, but if you try sometime you just might find that you get what you need. Cursors in Lists Let me rebuild the components of your structure using snoc- and cons-lists to keep the spatial properties clear. I define data Bwd x = B0 | Bwd x :< … Read more
Like the childcatcher in Chitty-Chitty-Bang-Bang luring kids into captivity with sweets and toys, recruiters to undergraduate Physics like to fool about with soap bubbles and boomerangs, but when the door clangs shut, it’s “Right, children, time to learn about partial differentiation!”. Me too. Don’t say I didn’t warn you. Here’s another warning: the following code … Read more
These links may be helpful: Evaluating cellular automata is comonadic. In particular, “whenever you see large datastructures pieced together from lots of small but similar computations there’s a good chance that we’re dealing with a comonad”. Sequences, streams, and segments Comonads in everyday life
As this question is popping up regularly in the top of the “unanswered” list, let me just copy my comment as an answer here – nothing considerably more constructive has appeared since a year ago anyway. A List can be viewed as a comonad just as well (in multiple ways), while a Zipper can be … Read more