Andrew Coppin wrote:
Janis Voigtlaender wrote:
"It is well-known that trees with substitution form a monad."
...OK, I just learned something new. Hanging around Haskell Cafe can be so illuminating! :-)
Now, if only I could actually comprehend the rest of the paper... o_O
I'll probably regret this for the rest of my life, but... As best as I can tell, a monad is essentially a container of some kind, together with a function that puts stuff into a container, and another function that maps over the container and combines the results in some way. That would rather suggest that *any* container type is potentially a monad of some kind. [Although possibly not a *useful* one...] Since a tree is a kind of container, yes, it should be a monad. [I'm still not really sure whether it's "useful".] Presumably a set monad would work something like the list monad. One could imagine an array monad [although counting the size of the result set before allocating the array would seem rather expensive]. Perhaps a dictionary could be a monad? I'm not precisely sure how that would work. Hmm, what other kinds of random containers could you make a monad out of? [And would you bother?] On the other hand, Maybe is a rather odd kind of container, but a very useful monad...