[Haskell-beginners] Question about constraints, signatures

[Philippe Sismondi]

On 2011-05-06, at 12:12 PM, Brent Yorgey wrote:

> On Fri, May 06, 2011 at 11:34:47AM -0400, Philippe Sismondi wrote:
>> I am trying to understand the Typeclassopedia article by Brent Yorgey in Monad.Reader. I am simultaneously working my way through Real World Haskell, so I may be doing things a bit out of order.
>> 
>> Here is my question (which may itself be unclear, as I am a true *noob* at this):
>> 
>> Why are there two different kinds of "constraints" in a signature, viz. those that specify types and those that specify typeclasses?  For instance, we could write this:
>> 
>> f :: (Num d) => d -> String -> Int
>> 
>> In my example above there are two kinds of things that constrain f: 
>> 
>> (a) d must be an instance of Num; and
>> (b) the second argument to f must be of type String, and f must return an Int.
>> 
>> I (more or less) understand that types and typeclasses are not the same. But it seems to me that they do conflate in a way, if we think of types as defined by functions on them. So why should we not be able to write:
>> 
>> f ::  Num d -> String -> Int
> 
> Your intuition is good: in fact, this is the way type classes are
> implemented under the hood!  A constraint (Num d => ...) is translated
> into a parameter (Num d -> ...) where an argument of type 'Num d' is a
> *dictionary* (i.e. record) containing implementations of the Num
> methods for the type d.
> 
> The reason for the special syntax is that for you, the programmer,
> there is a fundamental difference: arguments (dictionaries) coming
> before => are *implicit*, that is, you do not provide them yourself,
> the compiler figures out what they should be and supplies them
> automatically.  Arguments coming after => are explicit arguments which
> you must provide when calling a function.
> 
> One might ask why it is not possible to explicitly provide
> dictionaries if you want: this is a good question and an interesting
> area of research, and very related to the notion of "functors"
> (i.e. parameterized modules, not the same thing as Haskell Functors)
> in ML.
> 
> -Brent

Thanks for the quick reply, Brent. It will take me a day or so to digest your answer.

- Phil -