Many fields of study in compilers give rise to the concept of a join point—a place where different execution paths come together. Join points are often treated as functions or continuations, but we believe it is time to study them in their own right. We show that adding join points to a direct-style functional intermediate language is a simple but powerful change that allows new optimizations to be performed, including a significant improvement to list fusion. Finally, we report on recent work on adding join points to the intermediate language of the Glasgow Haskell Compiler.

The λ-calculus is popular as an intermediate language for practical compilers. But in the world of logic it has a lesser-known twin, born at the same time, called the sequent calculus. Perhaps that would make for a good intermediate language, too? To explore this question we designed Sequent Core, a practically-oriented core calculus based on the sequent calculus, and used it to re-implement a substantial chunk of the Glasgow Haskell Compiler.

Continuation-passing style (CPS) transforms have long been important tools in the study of programming. They have been shown to correspond to abstract machines and, when combined with a naming transform that expresses shared values, they enjoy a direct correspondence with encodings into process calculi such as the π-calculus. We present our notion of correctness and discuss the sufficient conditions that guarantee the correctness of transforms. We then consider the call-by-value, call-by-name and call-by-need evaluation strategies for the λ-calculus and present their CPS transforms, abstract machines, π-encodings, and proofs of correctness. Our analysis covers a uniform CPS transform, which differentiates the three evaluation strategies only by the treatment of function calls. This leads to a new CPS transform for call-by-need requiring a less expressive form of side effect, which we call constructive update.