6 ms·
> Propagating "Nothing" is not inherent to the Maybe data type, it's just a convenient behavior to have. nitpick about this particular example: is there anothe
by uryga 6y ago
> Propagating "Nothing" is not inherent to the Maybe data type, it's just a convenient behavior to have.
nitpick about this particular example: is there another lawful implementation of Monad for Maybe? i can't think of any, apart from the trivial
pure _ = Nothing
_ >>= _ = Nothing
(eyeballing the lawfulness, but it'll all be `Nothing` so all the equalities should hold, trivially :D)
- mjhoy 6y agoI don't think that holds for left identity: pure a >>= f ≡ f a
- klodolph 6y agoExactly, and the right identity is also violated: m >>= pure ≡ m
- uryga 6y agoahh right! serves me right, i should've spent more than 10 secs checking
- klodolph 6y agoEveryone experiences this in Haskell, where you make some statement online and then someone tells you some way in which it’s incorrect. I’m sure most real-world Haskell programs are “incorrect” in some way.
- deleted 6y ago[deleted]
- tel 6y agoThe trivial implementation isn't law abiding. This law doesn't hold (written in Kleisli form for simplicity) pure >=> f == f (left identity) There are no other monads for Maybe. First, any definition of pure must be Just as Nothing doesn't work because of left identity and parametricity prevents any other funny business. Now, by law we know pure a >>= f == f a Thus, we must define Just a >>= f = f a So the only variable is what (Nothing >>= f) does. For (f: A -> B) we must end up with a Maybe B. We don't have one to start and we can produce Maybe values only via Nothing and Just. So, either >>= is the standard definition or we have to do Nothing >>= f = Just (_: B) -- we can achieve a B only via use of f, so Nothing >>= f = Just (f (_: A)) -- now we are stuck, there are no values of A Thus, we must define pure a = Just a Just a >>= f = f a Nothing >>= f = Nothing
- uryga 6y agoyeah, and as others pointed out it fails right-identity as well. had a brain fart recapping the laws, though i think i got associativity right at least!