Here is one way to do it. First, you have to interpret operations on matrices as being elementwise applied. E.g, (*) is interpreted as zipWith (zipWith (*)) rather than matrix multiply, and similar for (+) etc. You then obtain a lazy semantics for the operations, where the extent of the resulting matrix is the intersection of the extents of the argument matrices. Second, you lift constants into infinite matrices containing the constant, that is: fromInteger n = repeat (repeat n). Now your examples will work as intended. Björn Lisper Atila Romero:
Good point.
And there is another problem: one could expect 10 * [[1,2],[3,4]] to be equal to [[10,20],[30,40]] and in this case 10 should be equal to [[10,0],[0,10]], instead of [[10,10],[10,10]] or [[10]].
I dont see how to fix this. Could be better to forget about fromInteger...
Atila
Jared Updike wrote:
fromInteger x = [[fromInteger x]]
Wouldn't you want the expression
[[1,0],[0,2]] + 10
to yield
[[11,10],[10,12]]
instead of [[11]] ? I guess you would need some complicated machinery so this is one thing you have to ignore to keep your otherwise nifty instance nice and simple.
Jared.
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