> 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…
> 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…
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…
Thank you for clarifying. I see how your construction works now.
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…
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)…
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,…
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…
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!…
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…
> 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…
> 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…
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…
Thank you for clarifying. I see how your construction works now.
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…
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)…
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,…
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…
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!…
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…