On 13 Apr 2006 03:27:03 -0000, oleg@pobox.com
Creighton Hogg wrote:
No instance for (MatrixProduct a (Vec b) c) arising from use of `<*>' at <interactive>:1:3-5 Probable fix: add an instance declaration for (MatrixProduct a (Vec b) c) In the definition of `it': it = 10 <*> (vector 10 ([0 .. 9]))
Let us look at the instance
class MatrixProduct a b c | a b -> c where (<*>) :: a -> b -> c instance (Num a) => MatrixProduct a (Vec a) (Vec a) where
it defines what happens when multiplying a vector of some numeric type 'a' by a value _of the same_ type. Let us now look at the error message:
(MatrixProduct a (Vec b) c)
That is, when trying to compile your expression 10 <*> (vector 10 ([0 .. 9])) the typechecker went looking for (MatrixProduct a (Vec b) c) where the value and the vector have different numeric types. There is no instance for such a general case, hence the error. It is important to remember that the typechecker first infers the most general type for an expression, and then tries to resolve the constraints. In your expression, 10 <*> (vector 10 ([0 .. 9])) we see constants 10, 10, 0, 9. Each constant has the type Num a => a. Within the expression 0 .. 9, both 0 and 9 must be of the same type (because [n .. m] is an abbreviation for enumFromThen n m, and according to the type of the latter enumFromThen :: a -> a -> [a] both arguments must be of the same type).
But there is nothing that says that the first occurrence of 10 must be of the same numeric type as the occurrence of 9. So, the most general type assignment will be (Num a => a) for 10, and (Num b => b) for 9.
Thank you very much for the explanation: it makes alot of sense. So, if one does not want to for alot of type declarations into the code, which would be fairly awkward, is there a way to do this with fundeps or other type extensions that will be alot prettier or is any way of defining type classes going to run into the same problems?