On Sun, May 12, 2002, Emre Tezel wrote:
Hi all,
I recently bought Simon Thompson's Haskell book. I have been doing the exercises while I read on. There are couple questions that I can not solve. Any help would be greatly appreciated.
I got stuck on this question in Chapter 10.
Define a function composeList which composes a list of functions into a single function. What is the type of composeList?
I naively tried the following but the hugs compiler complained about the inferred type not being generic enough.
composeList :: [(a -> b)] -> (c -> b) composeList [] = id composeList (x:xs) = x . (composeList xs)
The type signature is wrong. It indicates that for any a,b,c, and d, composeList takes a list of (a->b) and produces a (c->b). So for example, that would mean that if I gave it [(+3), (*4), (-5)] it would be able to produce something of type (Maybe String -> Int). This is of course totally wrong. You're going to have to restrict it some more . The first thing to note is that a=c: if you give it a list of functions that take Floats, it's going to give back a function that takes a float. So that restricts it to [a -> b] -> (a -> b). Now look at the function itself: composeList (x:xs) = x . (composeList xs) Now in order for f . g to make any sense, f must take values of the type that g returns! So if x has type p -> q, (composeList xs) must have type r -> p. But since x is in xs, xs must have type [p -> q], so (composeList xs) has type p -> q. So r -> p = p -> q. This implies immediately that p = q = r. So the type of composeList is restricted all the way down to [a -> a] -> (a -> a). This can also be written [a -> a] -> a -> a. This may seem disappointing, but it is made necessary by the type safety of Haskell, which requires that all the elements of a list have the same type. You can do a lot better in Glasgow Haskell: data Fun a b = forall c . Comp (c -> b) (Fun a c) | End (a -> b) compose :: Fun a b -> a -> b --GHC needs this type signature --to compile the program, but --I don't understand why. --Any tips? compose (End f) = f compose (Comp f l) = f . compose l f::Int -> Float f x = fromIntegral x g::String -> Int g = read h::Int -> String h x = take x "123456789" main = do putStrLn "hello!" print $ compose (End (\x -> "Foo!")) 3 print $ compose (Comp f (Comp g (End h))) 4 -- Night. An owl flies o'er rooftops. The moon sheds its soft light upon the trees. David Feuer