I'm a complete newcomer to Haskell, having learned about only recently. I'm intrigued by the possibility of in using it for numerical applications, specifically linear algebra. I understand that (at least in its present state) Haskell 98 isn't competitive with imperative languages when it comes to primitive matrix-vector operations, which often rely on destructive updating. It strikes me that one approach that takes advantage of the strengths of both paradigms would be create an imperative subsystem to handle primitive operations, then create a functional matrix algebra layer on top of it. Based on my very limited understanding of Haskell, I envision a linear algebra library which would work something like this: (1) Create a wrapper for the standard BLAS library. Since an optimized BLAS is available for various architectures with the same interface, this would provide a way of optimizing the library for a particular architecture. (2) Encapsulate this (using a monad?) in a way that provides safe access to the imperative routines from Haskell. (3) Using this as a foundation, define a matrix algebra in a "smart" way which avoids redundant evaluations. For instance, if A is an arbitrary invertible matrix, we know that A - A = 0 A + 0 = A A * Indentity = A A * inverse A = Identity so if we write an expression like "X = A * inverse A + B - B" we should expect our library to compute the correct result, "Identity" without actually performing any inversion, multiplication or elementwise matrix addition. (4) Create a Haskell module which exposes a pure functional interface, hiding the imperative subsystem from the user. My questions are: (a) Is this idea sound? (b) Has someone already done this? (c) Is there a better way of doing efficient linear algebra in Haskell? I would greatly appreciate any advice in this regard. --Jeff Austin