On Wed, Sep 29, 2010 at 11:08 AM, DavidA
Hi,
I have the following code:
{-# LANGUAGE TypeSynonymInstances #-}
data Vect k b = V [(k,b)] -- vector space over field k with basis b -- for example, V [(5, E 1), (7, E 2)] would represent the vector 5 e1 + 7 e2
data Monomial v = M [(v,Int)] -- monomials over variables v -- for example, M [(A,3), (B,5)] would represent the monomial a^3 b^5
type Poly k v = Vect k (Monomial v) -- multivariate polynomials over field k and variables v
instance Monad (Poly k) where return v = V [(1, M [(v,1)])] p >>= f = ... -- variable substitution
So my thinking is: 1. The Monad type class is for one parameter type constructors (eg [], IO) 2. Poly is a two-parameter type constructor 3. So Poly k is a one-parameter type constructor 4. What I'm trying to express, that polynomials over field k are a monad, is true.
However, GHC 6.12.2 complains:
Type synonym `Poly' should have 2 arguments, but has been given 1 In the instance declaration for `Monad (Poly k)'
What is going wrong?
Haskell doesn't have true type functions; what you are really saying is instance Monad (\v -> Vect k (Monomial v)) TypeSynonymInstances just lets you write stuff like this type Foo = [Int] instance C Foo where ... instead of type Foo = [Int] instance C [Int] where ... But it doesn't let you partially apply the type synonym. On the other hand, if you did this: newtype Compose f g a = O { unO :: f (g a) } type Poly k = Compose (Vect k) Monomial instance Monad (Poly k) where ... would work, but now you have to wrap/unwrap Compose in the instance definition. -- ryan