Hello,
In my experience, defining monads in terms of "fmap" and "join" leads to
code duplication. The examples we have seen in this thread---so far---are a
bit misleading because they compare a partial implementation of a monad
(join without fmap) with a complete implementation (bind). Here is an
example of what I mean:
data SP a = PutChar Char (SP a)
| GetChar (Char -> SP a)
| Return a
fmapSP :: (a -> b) -> (SP a -> SP b)
fmapSP f (PutChar c sp) = PutChar c (fmapSP f sp)
fmapSP f (GetChar k) = GetChar (\c -> fmapSP f (k c))
fmapSP f (Return a) = Return (f a)
joinSP :: SP (SP a) -> SP a
joinSP (PutChar c sp) = PutChar c (joinSP sp)
joinSP (GetChar k) = GetChar (\c -> joinSP (k c))
joinSP (Return sp) = sp
bindSP :: (a -> SP b) -> (SP a -> SP b)
bindSP f (PutChar c sp) = PutChar c (bindSP f sp)
bindSP f (GetChar k) = GetChar (\c -> bindSP f (k c))
bindSP f (Return a) = f a
I chose this example because I think that it illustrates nicely how the
three operators work, I hope that other readers find it useful.
2011/1/9 Conal Elliott
* The familiarity advantage of (>>=) is a historical accident. I like to see the language improve over time, rather than accumulate accidents.
I would be surprised if choosing ">>=" was an accident: it seems more likely that it was chosen because it matches a commonly occurring pattern in functional programs, and abstraction is all about giving names to common patterns. I completely agree with the sentiment of your second sentence but I think that adding "join" to the Monad class would be an example of "accumulating an accident" rather then simplifying things. -Iavor