Add Group specification

[evilsoft]

A little Group therapy for the masses

This PR addresses this issue by adding a specification for Group. In addition to the new spec, I did the following to get the tests to work using "mocks" already in place:

• Moved the internal/string_sum to internal/sum and modified it to work with Number instead of String.
• Had to modify the monoid and traverable.composition specs to accommodate the newly Number dependentSum.
• Fixed up the semigroupoid spec to run. The spec was not included in the specs, it is now.

[rjmk]

There's more than one way to get to group, but we definitely shouldn't let that get in the way of this PR

(We could eventually have

class Magma m where
  concat :: m -> m -> m

class Magma m => Quasigroup m where
  latin :: (m, m) -> (m, m)

class Magma m => Unital m where
  empty :: () -> m

class Magma m => Semigroup m

class (Semigroup m, Unital m) => Monoid m
class (Quasigroup m, Unital m) => Loop m
class (Semigroup, Quasigroup, Unital m) => Group m

All (non-empty) associative quasigroups are groups, so there's no 8th member)

[evilsoft]

Oh snap. I see some possible opportunities here for another couple PRs!
Good call!

[evilsoft]

@gabejohnson 🏫 me on how to get dat png updated.
Will get that in there today and take the WIP of of this.

[evilsoft]

Also, I am not satisfied with the names rightInverse and leftInverse any suggestions for better/established names for those?

EDIT:
okay, never mind, I found it! will be changing these to right cancellation and left cancellation

ANOTHER EDIT:
Cancel (hehe) that, cancellation properties are not the droids I am looking for, looks like I am still open for names for these properties. Any suggestions?

[evilsoft]

Okay. Removed WIP, this is GTG and 🔴 👁 for review.

[joneshf]

Please move this to a separate line, alphabetically please.

Functor -> Traversable;
Monoid -> Group;
Plus -> Alternative;
Semigroup -> Monoid;

[evilsoft]

@joneshf addressed

[joneshf]

👍 Thanks!

[evilsoft]

Any other feedback or anything I should address that is keeping this from being merged in?

[xaviervia]

What's the status of this one? It looks good :D

[joneshf]

Agreed. We can follow up if something is missing/wrong.

[gabejohnson]

A little late to the party. I think there's a small mistake

1. g.concat(g.invert()) is equivalent to g.empty() (right inverse)
2. g.invert().concat(g) is equivalent to g.empty() (left inverse)

I think it should be either g.constructor.empty() or G.empty().

See https://github.com/fantasyland/fantasy-land#plus

[davidchambers]

Good catch, @gabejohnson. See #275.