Added property tests for Algebra.Graph.Label

[adithyaov]

The initial draft for Algebra.Graph.Test.Label.

[adithyaov]

Minimum unfortunately fails the right distributive property. It cannot be a Semiring.
Consider String as the underlying monoid.
With,

<+> ~ min
<.> ~ mappend
0 ~ inf
1 ~ ""

Consider,

a = Minimum (Finite "a")
b = Minimum (Finite "") ~ 1
c = Minimum (Finite "c")

x = (a <+> b) <.> c = Minimum (Finite "c")
y = (a <.> c) <+> (b <.> c) = Minimum (Finite "ac")

Clearly x is not equal to y.
This property fails if the monoid is String.
Similarly, this property will fail if the monoid is Path a as well.

Minimum String and Minimum (Path a) can be described as a Left Near Ring but not a Semiring.
In general, I think Minimum a can be described as a left near ring (intuition). I'm still working out the formal proof though.

[snowleopard]

Many thanks @adithyaov! This looks very nice. I've left a couple of minor comments.

[snowleopard]

@adithyaov This doesn't currently pass CI. Could you push a fix please?

[snowleopard]

Just restarted CI, perhaps we need to increase/remove Travis time limit for long-running commands?

[snowleopard]

@adithyaov Very nice PR, many thanks!

Just managed to find time for review and left a few minor comments.

P.S.: CI has passed after restarting.

[adithyaov]

@snowleopard Although semigroup and rightNearRing are unused I'm leaving them there, gives a sense of completion of properties.
Ideally, I'd want to replace liftA2 with coerce but using liftA2 seems cleaner. Since the correctness isn't violated, I don't think it's a problem.

[adithyaov]

@snowleopard Could you please restart Travis CI. I don't understand why it fails. As you suggested, increasing the time limit might work.

[snowleopard]

@adithyaov I've restarted the CI.

If you can find a way to make CI more reliable, please let me know how.

[adithyaov]

@snowleopard I think this PR is ready for merge. Profiling might take a little more time. Can we safely ignore timeouts for the time being?

[snowleopard]

@adithyaov Having reliable CI is very important since it helps a lot with reviews.

This particular PR seems to push the testsuite too far, making CI unreliable, so I don't think we should merge it until we either get rid of slow tests in general, or slow tests in this particular PR that are responsible for slowing down the testsuite.

[adithyaov]

@snowleopard Agreed. I'll try to complete profiling the tests as soon as possible.

[snowleopard]

You are actually testing Minimum (Path Int) below, not Minimum.

I think we should add tests for all types of labels we define in Algebra.Graph.Label, perhaps, also adding some combinations like Minimum (Path Int).

[adithyaov]

perhaps, also adding some combinations like Minimum (Path Int).

Perhaps you meant something else? Minimum (Path Int) already exists.

[snowleopard]

I meant similar to Minimum Path that you are already testing.

[adithyaov]

I will do it in another PR. Some types (Optimum) need not satisfy Semiring yet can be used. I need to come up with a proper/better reasoning.

[snowleopard]

@adithyaov Thanks a lot for fixing the testsuite! I've added some comments.

[snowleopard]

@adithyaov Great work, thank you. Merged!