free-vector-spaces: Instantiate the classes from the vector-space package with types from linear

[ bsd3, library, math ] [ Propose Tags ]

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.

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Versions [RSS] 0.1.0.0, 0.1.1.0, 0.1.2.0, 0.1.4.0, 0.1.5.0, 0.1.5.1, 0.1.5.2
Dependencies base (>=4.6 && <5.1), lens (>=4 && <6), linear (>=1.18 && <1.23), MemoTrie, pragmatic-show (>=0.1.2 && <0.2), template-haskell, vector, vector-space (>=0.11 && <0.18) [details]
License BSD-3-Clause
Author Justus Sagemüller
Maintainer (@) jsag $ hvl.no
Category Math
Home page https://github.com/leftaroundabout/free-vector-spaces
Source repo head: git clone git://github.com/leftaroundabout/free-vector-spaces.git
Uploaded by leftaroundabout at 2022-06-01T14:56:06Z
Distributions NixOS:0.1.5.2
Downloads 3637 total (13 in the last 30 days)
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Status Docs available [build log]
Last success reported on 2022-06-01 [all 1 reports]