On 28/07/2009, at 12:59 PM, Richard O'Keefe wrote:
On Jul 28, 2009, at 2:25 PM, Peter Gammie wrote:
But Richard (or am I arguing with Kay?) - monads don't interact.
You're arguing with Alan Kay here: the reference to Leibniz was his. The key link here is (Wikipedia): " Leibniz allows just one type of element in the build of the universe" (sic.). In precisely the same way, Alan Kay allowed just one kind of 'thing' in his computational universe: object. Just as in the lambda calculus, everything is a function and in set theory everything is a set, so in Smalltalk _everything_ (including classes and the number 42 and anonymous functions) is an object.
Yea gods, that's the thinnest use of monads ever. The concept that lead to idealism, away from mind-body dualism is reduced to ... monism. Awesome. http://en.wikipedia.org/wiki/Monism He could've cited just about any of the major philosophies for that - and I'm not going to talk about religions.
How are you going to relate Leibniz's monads and Haskell's? I can't find my way, neatly or otherwise. :-P
Verbally.
Sure, but I was hoping you'd explain why Wadler uses the pineal gland allusions in his COMPREHENDING MONADS (capitals denoting paper title). That structure was *exactly* what Leibniz was doing his best to avoid in his monadology. I think Wadler was making a joke. cheers peter