Hi Tillmann and Richard, Thanks for your answers.

I have tried to analyze the code snippets you proposed. I've tried to transpose your examples to what I need, but it is not easy. The problem I see with putting the list of independent variables (*) at the type level is that at some time in my code I want for instance to perform formal mathematical operations, for example I want a function "deriv" that takes f(x(t),y(t),z(t)) as input, and returns df/dt = ∂f/∂x*dx/dt + ∂f/∂y*dy/dt + ∂f/∂z*dz/dt If the list of dependencies is encoded at the type level, I don't see how to produce the previous output from the knowledge of "f(x(t),y(t),z(t))". You understand that what I want to do is some type of basic Computer Algebra System library. Moreover, I want overloading for infix functions as '*', '/', '⋅' (scalar product), × (vector product) etc., that is why I have used typeclasses (see the code I showed in my previous post). For example, for the time being I will restrict myself to scalar product between vector and vector, vector and dyadic, dyadic and vector (a dyadic is a tensor of order 2, a matrix if you prefer). So I have three instances for scalar product '⋅'. I don't see how to combine this idea of overloading or derivation function with what you proposed. But I have perhaps missed something. Thanks, TP (*): That is to say the list of tensors of which one tensor depends, e.g. [t,r] for E(t,r), or simply [x,y,z] for f(x(t),y(t),z(t)) where x, y, and z themselves are scalars depending on a scalar t). In the test file of my library, my code currently looks like: ----------------- type Scalar = Tensor Zero type Vector = Tensor One [...] let s = (t "s" []) :: Scalar let v = (t "v" [i s]) :: Vector let c1 = v + v let c2 = s + v⋅v ----------------- t is a smart constructor taking a string str and a list of independent variables, and makes a (Tensor order) of name str. So in the example above, s is a scalar that depends on nothing (thus it is an independent variable), v is a vector that depends on s (i is a smart constructor that wraps s into a Box constructor, such that I can put all independent variables in an heterogeneous list). c1 is the sum of v and v, i.e. is equal to 2*v. c2 is the sum of s and v scalar v. If I try to write: let c3 = s + v I will obtain a compilation error, because adding a scalar and a vector has no meaning. Is there some way to avoid typeable in my case? Moreover, if I wanted to avoid the String in the first argument of my smart constructor "t", such that let s = (t []) :: Scalar constructs an independent Scalar of name "s", googling on the topic seems to indicated that I am compelled to use "Template Haskell" (I don't know it at all, and this is not my priority). Thus, in a general way, it seems to me that I am compelled to use some "meta" features as typeable or Template Haskell to obtain exactly the result I need while taking benefit from a maximum amount of static type checking. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe