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    <p>This is entirely possible in Haskell.</p> <p><strong>Statically checked dimensions</strong></p> <p>Haskell has arrays with <strong><a href="http://hackage.haskell.org/packages/archive/repa/2.0.0.3/doc/html/Data-Array-Repa-Shape.html" rel="noreferrer">statically checked dimensions</a></strong>, where the dimensions can be manipulated and checked statically, preventing indexing into the wrong dimension. Some examples:</p> <p>This will only work <a href="http://hackage.haskell.org/packages/archive/repa-algorithms/2.0.0.3/doc/html/Data-Array-Repa-Algorithms-Matrix.html" rel="noreferrer">on 2-D arrays</a>:</p> <pre><code>multiplyMM :: Array DIM2 Double -&gt; Array DIM2 Double -&gt; Array DIM2 Double </code></pre> <p>An example from <code>repa</code> should give you a sense. Here, taking a diagonal requires a 2D array, returns a 1D array of the same type.</p> <pre><code>diagonal :: Array DIM2 e -&gt; Array DIM1 e </code></pre> <p>or, from <a href="http://syntacticsalt.com/2011/02/13/getting-started-with-repa/" rel="noreferrer">Matt sottile's repa tutorial</a>, statically checked dimensions on a 3D matrix transform:</p> <pre><code>f :: Array DIM3 Double -&gt; Array DIM2 Double f u = let slabX = (Z:.All:.All:.(0::Int)) slabY = (Z:.All:.All:.(1::Int)) u' = (slice u slabX) * (slice u slabX) + (slice u slabY) * (slice u slabY) in R.map sqrt u' </code></pre> <p><strong>Statically checked units</strong></p> <p>Another example from outside of matrix programming: statically checked <strong><a href="http://hackage.haskell.org/package/dimensional" rel="noreferrer">units of dimension</a></strong>, making it a type error to confuse e.g. feet and meters, without doing the conversion.</p> <pre><code> Prelude&gt; 3 *~ foot + 1 *~ metre 1.9144 m </code></pre> <p>or for a whole suite of <a href="http://hackage.haskell.org/packages/archive/dimensional/0.9/doc/html/Numeric-Units-Dimensional-Quantities.html" rel="noreferrer">SI units and quanities</a>. </p> <p>E.g. can't add things of different dimension, such as volumes and lengths:</p> <pre><code>&gt; 1 *~ centi litre + 2 *~ inch Error: Expected type: Unit DVolume a1 Actual type: Unit DLength a0 </code></pre> <p>So, following <a href="http://www.cse.unsw.edu.au/~chak/papers/repa.pdf" rel="noreferrer">the <code>repa</code>-style array dimension types</a>, I'd suggest adding a <code>Base</code> phantom type parameter to your array type, and using that to distinguish between bases. In Haskell, the index <code>Dim</code> type argument gives the rank of the array (i.e. its shape), and you could do similarly.</p> <p>Or, if by base you mean some dimension on the units, using dimensional types.</p> <p>So, yep, this is almost a commodity technique in Haskell now, and there's some examples of designing with types like this to help you get started.</p>
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    1. POCan good type systems distinguish between matrices in different bases?
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    1. USDon Stewart
    1. USDon Stewart
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    1. COStatically checked dimensions is no different to the template he's already using in C++.
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    2. COThe statically checked units of dimension is almost exactly what I want, except instead of meters and feet my "units" would themselves be matrices.
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    3. COGreat. An example `let v = Data.Vector.replicate 10 (1 *~ litre)` is a 1d vector of volume quanities, whose type is inferred as `Vector (Quantity DVolume Double)`
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