Deokjae Lee cites:
The tutorial "All About Monads" says that "It is up to the programmer to ensure that any Monad instance he creates satisfies the monad laws".
The following is one of the laws.
(x >>= f) >>= g == x >>= (\v -> f v >>= g)
However, this seems to me a kind of mathematical identity. If it is mathematical identity, a programmer need not care about this law to implement a monad. Can anyone give me an example implementation of monad that violate this law ?
After three or five reactions to this posting, I think it it is time to generalize. Haskell is not math. Or rather, there is no way to be sure that the *implementation* of some mathematical domains and operations thereupon are fool-proof. Sometimes you break "en passant" some sacred laws. For example the transitivity of ordering. 5>2, right? and 8>5 as well. But, imagine a - little esoteric example of cyclic arithmetic modulo 10, where the shortest distance gives you the order, so 2>8. A mathematician will shrug, saying that calling +that+ an order relation is nonsense, and he/she will be absolutely right. But people do that... There is a small obscure religious sect of people who want to implement several mathematical entities as functional operators, where multiplication is f. composition. You do it too generically, too optimistically, and then some octonions come and break your teeth. So, people *should care*. Jerzy Karczmarczuk