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typelevel / algebra

Experimental project to lay out basic algebra type classes
https://typelevel.org/algebra/
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Topic/basic property tables #16

Closed non closed 9 years ago

non commented 9 years ago

From the main commit:

This commit tries to start writing some documentation around
how the algebraic structures work and their relationship to
each other. It is very rough but hopefully moves us in the
right direction.

I'm not sure this is 100% good in terms of pedagogy but hopefully it is better than nothing. Maybe using the infix notation is a bad idea but I tried it with function syntax and found the laws very difficult to read and reason about.

non commented 9 years ago

I haven't looked into the proofs for commutativity yet, I just tried to use the "canonical definitions" I'll take a crack at them tonight and see what I can do. Do you think this PR should wait on that, or would it be OK to merge now and then amend those properties later if necessary (since we would also have to change actual code in that case)?

tixxit commented 9 years ago

I provided a proof of commutativity for Rng, but I can't find one for Rig, but also can't think of any counterexamples immediately. Nonetheless, the proof for commutativity in Rng really hinges on an additive inverse, which doesn't exist in Rig.

tixxit commented 9 years ago

:+1: BTW

non commented 9 years ago

I think the bug @johnynek found is fixed, and at this point everything should be good-to-go.

non commented 9 years ago

Just fixed the other issues @johnynek raised. At this point my assurances don't count for much :mouse: but I think it should be good to go.

johnynek commented 9 years ago

LGTM