Exponentiation?

[chadbrewbaker]

Exponentiation?

[snowleopard]

Hey @chadbrewbaker! Sorry, just noticed the issue -- I didn't expect so much interest to this repo, so I wasn't even watching it :)

One simple way to define exponentiation is via the connect that is similar to multiplication:

(^) :: Graph g => g -> Int -> g
g^0 = empty
g^n = g^(n-1) `connect` g

Although this seems natural, the result is a bit boring:

g^0 = empty
g^1 = g
g^2 = g `connect` g -- This is a clique on vertices in g
g^3 = g `connect` g `connect` g = g^2 -- via the decomposition axiom
...
g^n = g^2

So, we only have three different values g^0, g^1 and g^2 = g^3 = g^4 ....

At this point I don't know of any other definition of the exponent that makes sense algebraically.

[snowleopard]

By the way, (^) from Prelude almost works as desired. The only problem with it is that it returns 1 for g^0 which is not what we want, we want it to return the multiplicative identity, which is empty in our case.

P.S.: Interestingly, the foundation library does this right! So, if you use it, (^) will work as I described above out of the box.