The continuation-passing style transform (cps) and closure conversion (cc) are two techniques widely employed by compilers for functional languages, and have been studied extensively in the compiler correctness literature. Interestingly, typed versions of each can be proven to be equivalence preserving using polymorphic types and parametric reasoning, as shown by my advisor Amal Ahmed and Matthias Blume (cps,cc).
In fact, there is something like a duality between the two proofs, cps uses a universal type, closure-conversion uses an existential type and the isomorphism proofs use analogous reasoning. It turns out that both are instances of general theorems in category theory: the polymorphic cps isomorphism can be proven using the Yoneda lemma, and the polymorphic closure-conversion isomorphism can be proven using a less well known theorem often called the *co*Yoneda lemma.
The connection between cps and the Yoneda embedding/lemma is detailed elsewhere in the literature and blogosphere (ncafe, Bartosz), so I’ll focus on closure conversion here. Also, I’ll try to go into some detail in showing how the “usual” version of Yoneda/coYoneda (using the category of sets) relates to the appropriate version for compilers.
I’ll assume some background knowledge on closure conversion and parametricity below. Fortunately, Matt Might has a nice blog post explaining untyped closure conversion.
Last week, Northeastern hosted a PI meeting for the Gradual Typing Across the Spectrum NSF grant. The meeting was made of 20+ researchers from four institutions, and 12 technical talks. Schedule:
A common thread among the talks was the question: how to convert a research idea into a tool for software developers?
This year I reviewed many ICFP submissions, and got to be on the receiving end of equally many author responses (also sometimes called, somewhat combatively, rebuttals). I found that there was a large difference between the official written advice on author responses and what I, as a reviewer reading the responses, found effective. In particular, I now believe that limiting yourself to 500 words should strongly be avoided — we should even stop giving that advice.
From the PRL archives:
I think that I shall never see a matrix lovely as a tree. — Trees, by Guy L. Steele Jr., MIT, 1973
From the PRL archives:
It was also a concept that grabbed my mind, ran off with it, and only returned it after substantial renovation and expansion. — Continuations by Alan Nall, Indiana University, 1983
The ACM recently hosted a celebration of 50 years of the A.M. Turing award. These are some notes and thoughts from the event, including how Fred Brooks once rented a bus, Don Knuth’s outrageous implementation of batch processing, and Judea Pearl’s theory of homo sapiens.
The PL Junior Seminar is for beginning PhD and interested undergrad and masters students to understand the foundations of programming languages research. It serves to fill in background knowledge and get up to speed with different areas of PL research.
For the spring 2017 instance of PL Junior we chose program synthesis, the sequent calculus, and logic programming as topics we wanted to learn more about. We also did two group paper readings for Luca Cardelli’s Typeful Programming and Alan Kay’s Early History of Smalltalk. At the same time, we changed up the format from the previous semester.
Two weeks ago, I attended the first Programming Language Implementation Summer School, held in beautiful Bertinoro, Italy.
The goal of PLISS was “to prepare early graduate students and advanced undergraduates for research in the field,” and I think it successfully accomplished that. There were many talks in a variety of areas, such as just-in-time compilers, garbage collection, static analysis, and distributed systems. But PLISS was more than just a series of talks: PLISS provided an environment for interacting with other students as well as senior researchers.
In this blog post, reporting on a collaboration with Li-Yao Xia, I will show an example of how some results that we traditionally think of as arising from free theorems / parametricity can be established in a purely “syntactic” way, by looking at the structure of canonical derivations. More precisely, I prove that
is isomorphic to
is the type of integers smaller than
, corresponding to the set