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PODeclaring a type class for multiplication of an N-by-N-element matrix and an N-element column vector
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copied!<p>In Haskell, if you have a "family" of types (say, N-by-N-element matrices, for some values of N), and a parallel family of "related" types (say, N-element vectors, for the same values of N), and an operation that requires one specific type from each family (say, multiplying an N-by-N-element matrix and an N-element column vector), is it then possible to declare a type class for that operation?</p> <p>For this specific example, I imagine it would look something like this:</p> <pre><code>class MatrixNxN m where --| Multiplication of two N-by-N-element matrices mmul :: Num a => m a -> m a -> m a --| Multiplication of an N-by-N-element matrix and an N-element column vector vmul :: Num a => m a -> v a -> v a </code></pre> <p>I don't know how to constrain the type <code>v</code>, however. Is it possible to do something like this?</p> <p>Please note that I welcome both answers to the general question of declaring a type class of multiple, related types, as well as answers to the specific question of declaring a type class for matrix-vector multiplication. In my specific case, there is only a small, known set of values of N (2, 3, and 4), but I'm generally interested in understanding what is possible to encode in Haskell's type system.</p> <p><strong>EDIT:</strong> I implemented this using <a href="http://www.haskell.org/haskellwiki/Multi-parameter_type_class" rel="nofollow"><code>MultiParamTypeClasses</code></a> and <a href="http://www.haskell.org/haskellwiki/Functional_dependencies" rel="nofollow"><code>FunctionalDependencies</code></a> as suggested by Gabriel Gonzalez and MFlamer below. This is what the relevant bits of my implementation ended up looking like:</p> <pre><code>class MatrixVectorMultiplication m v | m -> v, v -> m where vmul :: Num a => m a -> v a -> v a data Matrix3x3 a = ... data Vector3 a = ... instance MatrixVectorMultiplication Matrix3x3 Vector3 where vmul = ... </code></pre> <p>This is the type signature of <code>vmul</code>, on its own and partially applied:</p> <pre><code>vmul :: (Num a, MatrixVectorMultiplication m v) => m a -> v a -> v a (`vmul` v) :: Matrix3x3 Integer -> Vector3 Integer (m `vmul`) :: Vector3 Integer -> Vector3 Integer </code></pre> <p>I find this all very elegant. Thanks for the answers! :)</p>

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