sn0wleopard

4 ms·

1. 1.▲
   by sn0wleopard 10y ago

   > Indeed, I did say that it was a monad and not a `Monad`; math doesn't suffer from these implementation constraints. :-) Ah, I see :-) Indeed, from the mathematical standpoint we can both inject a vertex into the graph type with `v
2. 2.▲
   by sn0wleopard 10y ago

   > By the way, your code doesn't seem to give any way of producing inhabitants of `Vertex g`. In fully polymorphic code (like clique) you indeed can't produce new inhabitants, or do anything else with the values of type `Vertex
3. 3.▲
   by sn0wleopard 10y ago

   Thanks LolWolf! You mentioned a few interesting ideas about monotonicity/fixed-point theorems & computability/hardness and I'd very curious to know if you come up with anything on these fronts -- please drop me an email i
4. 4.▲
   by sn0wleopard 10y ago

   Thank you for clarifying. I see how your construction works now.
5. 5.▲
   by sn0wleopard 10y ago

   JadeNB: This works but I believe only in the case with undirected graphs and if the graphs being connected do not have common vertices. So, indeed there is a sort of de Morgan law: a -- b = !(!a + !b) where ! is the graph edge-complement, a
6. 6.▲
   by sn0wleopard 10y ago

   rjtobin, Sorry I don't understand what happens if the two graphs have common vertices? For example, in the algebra I described, you can do 1 -> (1 + 2) and this represents a graph with vertices {1,2} and two edges (1,1) and (1,2). H
7. 7.▲
   by sn0wleopard 10y ago

   solidangle: Indeed, there are a lot of graph algebras out there, and I looked at many of them, including the Kleene Algebras. So far I haven't found any algebra with the decomposition axiom, but if you come across one, please let me kn
8. 8.▲
   by sn0wleopard 10y ago

   LolWolf, thank you very much for 'defending' the algebra much better than I could possibly have defended it myself :-) Just to add: I don't understand why we should compare the algebra and the matrix encoding suggested above.
9. 9.▲
   by sn0wleopard 10y ago

   I'm sad that you found my blog post snobbish. If you point out specifically which part you can't stand I'll see if I can make it better. But I'm afraid I can't remove the algebra part, as there will be nothing left!
10. 10.▲
    by sn0wleopard 10y ago

    I'm the author of the blog post -- thank you for your comment! I was wondering whether anyone would be interested in a different version of the algebra that modells hypergraphs with k-edges. For example, you can change the decompositio