> int foo(int, int);
Doesn't tell you anything. Ok, you are right! But that code translated to Haskell would be:
> foo :: Int -> Int -> Int
How does that give you more information about foo than the C code above?
Now if you say you use type synonyms in Haskell, I would agree, but you can use typedefs in C as well.
You get much stronger statements by using type variables (not type synonyms). This is actually laid out rather clearly in Theorems for Free by Wadler[1]. The essence is that the more generic a type signature gets, the more you can reason about it's behavior. Since if you want to perform (+) (-) (*) (/) for example you'll need to include a (Num) constraint.
[1] http://ttic.uchicago.edu/~dreyer/course/papers/wadler.pdf
That's so vague it's almost meaningless, and doesn't support the original assertion, which was "But with HASKELL, with just the type signature you can write a program that does what you want even though you don't know what the components you used do!"
Even given a simple thing like foo:: int -> int -> int, there's really no way to tell what it's doing. It could be multiplying the arguments together, dividing, adding, computing psuedo-random numbers using two seed values, ...
Not only that, but I'm not sure it's true that it's limited to the Int type because there are things like System.IO.Unsafe.
Ahh, this is an important point. The reason you can't tell what it's doing is because it is quite concrete. One really cool thing about this kind of type system is that the more generic your functions, the more you can tell about what it's doing. Consider this function:
foo :: (a, b) -> a
b.) Functions that are non-trivial will have additional constraints often hinting exactly at what the function does.
Most important is not the fact that you can write poor Haskell code which does not exibit this self-documenting behavior, but rather that if you choose to exploit the type system it has the expressiveness to allow you to do so! (and enforce it)
If you are working with a Haskell library and see a function with the signature (IO Int) you may start to question your choice of library :)
The only problem is, once you get a taste of this power it is easy to yearn for even more such as dependent types (i.e. Agda, Idris...)
> There's only one possible thing this function can do!
Ah, so it scales a vector by a scalar returning a new vector, right?
The parent you are responding to is quoting a proven result of computer science.
And all its brothers :)
That's not at all true... it can do all sorts of transformations on the first value of the tuple. I suppose without type restrictions on the parameters it can't do too much because there are relatively few functions defined on all types, but then, how often are you going to see a function signature that vague?
More likely, you'd see
`foo :: MyClass a => (a, b) -> a`
or
`foo :: (MyType, b) -> MyType`
which opens up the possibilities considerably, because you don't know which of MyType's behaviors is being invoked.
That's not an accident. Factoring out little helper functions like this is considered a virtue in Haskell (and acording to Paul Graham, also in Lisp).
Even if you only use them once---because they make reasoning easier.