@hackage free-vector-spaces0.1.5.2

The linear package offers efficient vector types — where vector means element of a free vector space, i.e. fixed-length arrays of numbers. The entire interface of that library is based on this concept of free vectors with a canonical coordinate representation.

While this is practically speaking often useful, it is also

• Questionable in terms of conceptual elegance. The idea of a vector has originally not much to do with number-arrays; in physics a vector is just a quantity with magnitude and direction. Only by fixing a basis can a coordinate representation arise from that.

• Not as safe as we'd like. The typical linear-algebra languages like Matlab or Fortran are notorious for hard-to spot mistakes that often arise from the total reliance on coordinate representations (every vector/linear map is just a matrix of number). linear already avoids most of these problems because it can at least check dimensions at compile-time and usually doesn't need any indices, but some trouble still remains. E.g., two different 3-dimensional spaces are indistinguishable by the type system (unless you wrap one of them in a newtype, however that also needs to be parameterised on the coordinate type to work with the rest of the library).

The vector-space library has arguably a better (albeit less complete) interface. To gain access to that interface with the more efficient types from linear, we here provide the necessary orphan instances.