-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Gregg Reynolds wrote: | As I understand it, a monad is a kind of programming trick the uses data dependency to force evaluation order. Actually, a monad does nothing more than supply some combinators. These combinators (and some trivial laws) are all you really need to know to understand monads. Specific monads are really just a case-by-case issue. Using some function names that are not used in the standard Haskell libraries, here are the important functions you have access to when you have a monad, all of which return monadic values: ~ point :: a -> f a ~ map :: (a -> b) -> f a -> f b ~ apply :: f (a -> b) -> f a -> f b ~ bind :: (a -> f b) -> f a -> f b I aligned the type signatures the way I did so you could see their similarities and differences more easily. point is the same as the return and pure functions. It lifts a pure value. map is the same as the (<$>), fmap, liftA, and liftM functions. It applies a pure function to a lifted value. apply is the same as the (<*>) and ap functions. It applies a lifted function to a lifted value. The type signature for bind is reversed from that of (>>=). It's the same as (=<<). I think it is more clear and better parallels the other functions I've already shown. It applies a "lifting" function to a lifted value. | since the value of f x depends on the value of x, the evaluator must evaluate x before f x This is actually not true. Remember, Haskell is a lazy language. x need not be evaluated before applying f to it. | However, consider: | | getChar >>= \x -> getChar | | An optimizer can see that the result of the first getChar is discarded and replace the entire expression with one getChar without changing the formal semantics. Consider how this expression would actually look in a Haskell program: ~ main :: IO () ~ main = getChar >>= \x -> getChar Remember, a type coincides with a value. That is, the entire main function is a _value_ of type IO (). The value, as it so happens, is an imperative program which the Haskell runtime performs. That is, the reduction semantics of IO expressions _produce_, rather than perform, actions. The actions are only performed by the runtime. Every monad has a "run" function. The IO monad's run function is the Haskell runtime. If you think of the IO monad as some sort of Writer monad, it is easy to see that Haskell's reduction semantics actually guarantee correct order of operations, and a semantics-preserving optimizer will not change it. In GHC, the IO monad is actually more like a State monad (over RealWorld). It is also easy to see that this preserves correct ordering of side-effects as well. I just wanted to present a different point of view. - - Jake -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org iEYEARECAAYFAkmLDpMACgkQye5hVyvIUKnUpwCfdAycTBv29wVt+J5VHZbNEQ3H 80kAnj7u7HS+5S1qxgzB90I7v+ftuazo =poXT -----END PGP SIGNATURE-----