Re: [Haskell-cafe] Can I have a typeclass for topological spaces?
You may want to, instead, check out the methods of point-free topology (also known as pointless topology) where you, basically, study topological spaces in terms of their open-set lattices. This allows you to use a more algebraic language which probably fits better into Haskell (I think this is used, for example, when studying topology within type theories). A search for stone-duality should give you somewhere to start (I know there are a sequence of posts on http://topologicalmusings.wordpress.com/ on the subject). Somewhat less known is the theory of formal topology (see for example n-lab http://ncatlab.org/nlab/show/formal+topology). Which might also be an approach to doing some topology in Haskell. Hope that's of some help :) On 11/08/2011, Grigory Sarnitskiy sargrig...@ya.ru wrote: Hello! I just wonder whether it is possible to have a typeclass for topological spaces? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Can I have a typeclass for topological spaces?
It may not be exactly what you want, but I played with https://github.com/luqui/topology-extras/blob/master/TopologyExtras/Topology.hs a few months ago, it may be a good basis to start with. (no pun intended) On Thu, Aug 11, 2011 at 5:08 PM, Grigory Sarnitskiy sargrig...@ya.ruwrote: Oh, I guess the class would look something like that: class TopologicalSpace a where ifOpen :: (Subset a) - Bool and Subset x is a type corresponding to subsets of x. 11.08.2011, 17:52, Grigory Sarnitskiy sargrig...@ya.ru: Hello! I just wonder whether it is possible to have a typeclass for topological spaces? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe -- Alp Mestanogullari http://alpmestan.wordpress.com/ http://alp.developpez.com/ ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Can I have a typeclass for topological spaces?
Hello! I just wonder whether it is possible to have a typeclass for topological spaces? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Can I have a typeclass for topological spaces?
Oh, I guess the class would look something like that: class TopologicalSpace a where ifOpen :: (Subset a) - Bool and Subset x is a type corresponding to subsets of x. 11.08.2011, 17:52, Grigory Sarnitskiy sargrig...@ya.ru: Hello! I just wonder whether it is possible to have a typeclass for topological spaces? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
