Le 26/03/2012 16:31, Chris Smith a écrit :
If you were
asking about why there is no ring on [a] that defines (+) = zipWith
(+), then here's why. By that definition, you have [1,2,3] + [4,5] =
[5,7]. But also [1,2,42] + [4,5] = [5,7]. Addition by [4,5] is not
one-to-one, so [4,5] cannot be invertible.
So, * the addition* is not invertible, why did you introduce rings to
this discussion, if the additive group within is already lousy?...
OK I see now. You are only interested in the explicitly ambiguous usage
of the element-wise addition which terminates at the shortest term...
But I don't care about using (+) = zipWith (+) "anywhere", outside of a
programming model / framework, where you keep the sanity of your data.
In my programs I KNEW that the length of the list is either fixed, or of
some minimal size (or infinite). Your [4,5] simply does not belong to MY
rings, if I decided to keep the other one.
Jerzy K.
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