how do i define a monad for such a datatype in Haskell? It is basically a salsa interpreter. And I cant figure out what should the return look like. It is making me crazy...
newtype Salsa a = Salsa { runSalsa :: Context -> Either String (a, Context, Animation)} instance Monad Salsa where return a = Salsa $ .......... instance Functor Salsa where fmap = liftM instance Applicative Salsa where pure = return (<*>) = ap http://ap-e2015.onlineta.org/assignments/assignment-1-salsa-interpreter.html
You need a function which takes a Context so use a lambda \con ->.
You don't have anything that has failed so far so you can always succeed. Right.
a is provided by the call to return. (a,.
Context is provided by the call to the lambda. con,.
Now you have to decide on the animations to include, I would guess none. []). (Note I don't remember offhand the exact syntax there but I think this is right).
Putting it all together you get:
return a = Salsa $ \con -> Right (a, con, []) Now comes the complicated case where you have to handle bind (>>=).
instance Monad Salsa where return a = Salsa $ \con -> (a, con, [] :: Animation) but it says that Couldn't match expected type Either String (a, Context, Animation)' with actual type (a, Context, Animation)' Relevant bindings include a :: a (bound at SalsaInterp.hs:33:12) return :: a -> Salsa a (bound at SalsaInterp.hs:33:5) In the expression: (a, con, [] :: Animation) In the second argument of ($)', namely \ con -> (a, con, [] :: Animation)' In the expression:.....Left case and what in Right?
return, at least) is wrapping the tuple in Right.Help yourself with typed holes: Write an underscore where you are stuck:
instance Monad Salsa where return a = Salsa $ _ and the compiler tells you it needs a function here
Found hole ‘_’ with type: Context -> Either String (a, Context, Animation) Now you can work your way with
instance Monad Salsa where return a = Salsa $ \x -> _ For >>=, do almost the same:
(Salsa s) >>= f = Salsa $ \x -> _ and the compiler outputs
Found hole ‘_’ with type: Either String (b, Context, Animation) Relevant bindings include con :: Context f :: a -> Salsa b s :: Context -> Either String (a, Context, Animation) So, s is function that requires a Context, but our con supplies one, put it together:
(Salsa s) >>= f = Salsa $ \con -> let s' = s con in _ ... s' :: Either String (a, Context, Animation) (bound at Review.hs:12:43) f :: a -> Salsa b (bound at Review.hs:12:19) So we need that a thing out of s' to supply it to f. Pattern match on s' (while renaming):
(Salsa salsaFunction1) >>= f = Salsa $ \context1 -> let salsaResult1 = salsaFunction1 context1 in case salsaResult1 of Left errorMsg -> Left errorMsg Right (a, context2, animation1) -> let Salsa salsaFunction2 = f a salsaResult2 = salsaFunction2 context2 in _ salsaFunction2 :: Context -> Either String (b, Context, Animation) animation1 :: Animation context2 :: Context a :: a salsaResult1 :: Either String (a, Context, Animation) context1 :: Context f :: a -> Salsa b salsaFunction1 :: Context -> Either String (a, Context, Animation) So, we have another salsaFunction2, and an unused context2. You already saw how to put this together: do another case analysis, in the Right case supply context3, the monadic result b and combine both animations to provide the final Either String (b, Context, Animation) that was seen again and again:
Found hole ‘_’ with type: Either String (b, Context, Animation) 
instance Monad Salsa where return a = Salsa $ \con -> Right (a, con, [] :: Animation) (Salsa function) >>= f = Salsa $ \con1 -> let result = function con1 in case result of Left errorMsg -> Left errorMsg Right (a, con2, anim) -> let Salsa function2 = f a result2 = function2 con2 in case result2 of Left errorMsg -> Left errorMsg anim3 = anim ++ anim2 Right (b, con3, anim2) -> Right (b,con3, anim3)instance Monad Salsa where return a = Salsa $ \con -> Right (a, con, [] :: Animation) (Salsa function) >>= f = Salsa $ \con1 -> let result = function con1 in case result of Left errorMsg -> Left errorMsg Right (a, con2, anim) -> let Salsa function2 = f a result2 = function2 con2 in case result2 of Left errorMsg -> Left errorMsg Right (b, con3, anim2) -> Right (b,con3, mappend anim anim2)
Well, I don't know anything about Salsa, but after reading Guvante's answer foreshadowing the difficulty of implementing >>=, I thought it would be an interesting exercise. And since I don't know what Salsa's Context or Animation types are, I decided to just parameterize over them, which I think worked out fairly well: the type of Context can be totally opaque to us as implementors of >>=, and we just need Animation to be a monoid:
newtype Salsa ctx error anim a = Salsa { runSalsa :: ctx -> Either error (a, ctx, anim) } instance Monoid anim => Monad (Salsa ctx error anim) where return x = Salsa $ \ctx -> return (x, ctx, mempty) (Salsa m) >>= f = Salsa m' where m' ctx = m ctx >>= handle handle (x, ctx, anims) = let (Salsa f') = f x merge (a, b, c) = (a, b, mappend anims c) in merge <$> f' ctx instance Monoid anim => Functor (Salsa ctx error anim) where fmap = liftM instance Monoid anim => Applicative (Salsa ctx error anim) where pure = return (<*>) = ap This as general as I could figure how to make it, and I'm still not totally happy with the implementation of handle: it seems like there must be a better way to get the animation results combined than letting a function and then fmapping it, but I couldn't find anything prettier.
Incidentally I think it would be nicer to have a real data type for this (a, Context, Animation) group rather than just a tuple. Then you could, for example, give it a Functor instance and simplify the implementation of handle, removing the merge function and just writing
mappend anims <$> f' ctx 
>>= they were omitting the >>= part on purpose, so not to hand out the full solution to the assignment and make the OP work on it on their own.