Ahem On 17 Jan 2011, at 17:22, Tyson Whitehead wrote:
On January 15, 2011 22:43:32 Jan-Willem Maessen wrote:
For example, I find it relatively easy to understand >>= in the continuation monad, but have to spend a long time puzzling my way through join.
It's not that bad once you get used to thinking of it. Join simply merges an inner computation into an outer one.
[..]
Something a lot more friendly to the notation would be if A, B, and C were independent computations whose combined results were to determine another computation via a function g. This result, along with D and E, where then to be fed into yet another function f. This is simply expressed as
f <$> join (g <$> A <*> B <*> C) <*> D <*> E
Funnily enough, SHE lets you write (| f (| g A B C @ |) D E |) where the postfixed @ denotes a join: g's effects happen "after" those of A, B and C, but "before" those of D and E. [..] I'm tempted to support if <- b then t else f for (b >>= \ z -> if z then t else f) and case <- s of {p1 -> e1; ..} similarly.
The unfortunate pain you pay for this additional power is manually having to specify the application (<$> and <*>) and merging (join). If the compiler could figure this all out for you based on the underlying types, wow!
To achieve such a thing, one would need to ensure a slightly more deliberate separation of "value" and "computation" in the presentation of types. In Haskell, we use, e.g., [Int], for * pure computations of lists of integers * nondeterministic computations of integers and we spend syntax (do-notation, lifting operators) to distinguish the two modes of usage. If every type was clearly decomposable into its computation and value components, the above possibilities would be distinct (but isomorphic) and we could spend less syntax on plumbing in programs. I fear it's too late to reorganize Haskell along these lines, but it's bound to happen in some language (Disciple? Eff?) sometime. As any ML programmer will tell you, functional programming is really cool, even when it isn't purely functional programming. All the best Conor