Down and Dirty with Semantic Set-theoretic Types (a tutorial) v0.4

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2022-07-05 19:30:05

This is a “living” document: please submit bug reports and pull requests if you spot a problem!

Most of the "pseudo code" in this tutorial was generated directly from a functioning redex model  (Klein et al. 2012) to greatly reduce the chance for typos or other subtle bugs in their presentation.

We would like to thank Giuseppe Castagna for the time he spent writing the wonderful, detailed manuscript Covariance and Contravariance: a fresh look at an old issue (a primer in advanced type systems for learning functional programmers)  (Castagna 2013) which we used to initially understand the implementation details we will discuss, as well as Alain Frisch, Giuseppe Castagna, and Véronique Benzaken for their detailed journal article Semantic subtyping: Dealing set-theoretically with function, union, intersection, and negation types  (Frisch et al. 2008) which contains thorough mathematical and technical descriptions of semantic subtyping. Without those works this tutorial would simply not be possible! We highly recommend perusing those works as well for readers who are interested in this material.

We assume the reader has some mathematical maturity and is familiar with terminology commonly used by computer scientists for describing programming languages and types. In particular, we assume basic familiarity with:

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