An Intrinsically Typed Compiler for Algebraic Effect Handlers

A type-preserving compiler converts a well-typed input program into a well-typed output program. Previous studies have developed type-preserving compilers for various source languages, including the simply-typed lambda calculus and calculi with control constructs. Our goal is to realize type-preserving compilation of languages that have facilities for manipulating first-class continuations. In this paper, we focus on algebraic effects and handlers, a generalization of exceptions and their handlers with resumable continuations. Specifically, we choose an effect handler calculus and a typed stack-machine-based assembly language as the source and the target languages, respectively, and formalize the target language and a type preserving compiler. The main challenge posed by first-class continuation is how to ensure safety of continuation capture and resumption, which involves concatenation of unknown stacks. We solve this challenge by incorporating stack polymorphism, a technique that has been used for compilation from a language without first-class continuations to a stack-based assembly language. To prove that our compiler is type preserving, we implemented the compiler in Agda as a function between intrinsically typed ASTs. We believe that our contributions could lead to correct and efficient compilation of continuation-manipulating facilities in general.