Re: [Haskell-cafe] References for topological arguments of programs?

I've not been following this, but (a -> Bool) -> a is essentially a choice function, which figured in Ernst Zermelo's proof of the well-ordering theorem.

On Dec 10, 2018, at 6:38 AM, Siddharth Bhat wrote:

Hello,

I was recently intrigued by this style of argument on haskell cafe:

One can write a function Eq a => ((a -> Bool) -> a) -> [a] that enumerates the elements of the set. Because we have universal quantification, this list can not be infinite. Which makes sense, topologically: These so-called searchable sets are topologically compact, and the Eq constraint means the space is discrete. Compact subsets of a discrete space are finite. -------

I've seen arguments like these "in the wild" during Scott topology construction and in some other weird places (hyperfunctions), but I've never seen a systematic treatment of this.

I'd love to have a reference (papers / textbook preferred) to self learn this stuff!

Thanks Siddharth -- Sending this from my phone, please excuse any typos! _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.