I have implemented array coercions between
array[array[T,N],M] -- array[T,N*M]
i.e. from an array of arrays to a matrix.
however this is only one case, just rank 2 to rank 1 and back.
In general, there is an isomorphism between any arrays of the
same length, between
2 + 3 and 5
and between
((1,2),3) and (1,2,3) and (1,(2,3))
and so on. These generally isomorphic things are easy to write coercions for.
The problem is I'm not sure its desirable. For example a 2 x 3 matrix is
isomorphic
to a 3 x 2 matrix, but you'd never want to do that coercion -- it would really
jumble
things up .. we're not talking about transposing the values here, but casting!
But the problem is successive application of the 2 <--> 1 rank operation
does NOT yield 3 <--> 1. The index would become
(N * M) * P
instead of
N * M * P
They're isomorphic .. but not equal. But i can't write out all the possible
coercions, and i'm not even sure how to limit them to "what's desirable"
because I'm not actually sure what that is!
--
john skaller
[email protected]
http://felix-lang.org
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