Explanation of Monad laws

Question

From a gentle introduction to Haskell, there are the following monad laws. Can anyone intuitively explain what they mean?

return a >>= k             = k a
         


        

Answer 1

The first three laws say that "return" only wraps a value and does nothing else. So you can eliminate "return" calls without changing the semantics.

The last law is associativity for bind. It means that you take something like:

do
   x <- foo
   bar x
   z <- baz

and turn it into

do
   do
      x <- foo
      bar x
   z <- baz

without changing the meaning. Of course you wouldn't do exactly this, but you might want to put the inner "do" clause in an "if" statement and want it to mean the same when the "if" is true.

Sometimes monads don't exactly follow these laws, particularly when some kind of bottom value occurs. That's OK as long as its documented and is "morally correct" (i.e. the laws are followed for non-bottom values, or the results are considered equivalent in some other way).