Lambda the Ultimate

A recent story over at Ars Mathematica reminded me that I have seen a lot of interesting work in applying topology to programming language semantics.

The paper linked-to on Ars Mathematica is more about applications to software engineering (precise notion of refinement, but since implementations are the ultimate refinement of a specification, this is quite relevant to PLs as well). But there is a lot more work in this area! For those with a theoretical bent, there are a series of articles by John Tucker and Jeffery (Jeff) Zucker, for example Abstract versus Concrete Computation on Metric Partial Algebras (many more available from their respective web pages). Another thread that I like is the work of Abbas Edalat; he has written many papers relating topology, domain theory and computations in analysis. I am particularly fond of the work of Martin Escardo; the lecture notes on Mathematical foundations of functional programming with real numbers might interest a few people here. But as far as I am concerned (and Haskell fans might agree), his Magnum Opus is Synthetic topology of data types and classical spaces.