Row-Polymorphic Types for Strategic Rewriting

Abstract

We present a type system for strategy languages that express program transformations as compositions of rewrite rules. Our row-polymorphic type system assists compiler engineers to write correct strategies by statically rejecting non meaningful compositions of rewrites that otherwise would fail during rewriting at runtime. Furthermore, our type system enables reasoning about how rewriting transforms the shape of the computational program. We present a formalization of our language at its type system and demonstrate its practical use for expressing compiler optimization strategies.Our type system builds the foundation for many interesting future applications, including verifying the correctness of program transformations and synthesizing program transformations from specifications encoded as types.

P3 problem and Magnolia language: Specializing array computations for emerging architectures

“…Hagedorn et al (2020) introduce a functional approach to high-performance code generation based on rewriting strategies: computations are expressed in the RISE programming language, and rewrite rules and strategies in the ELEVATE strategy language. Fu et al (2021) later added a type system to ELEVATE to ensure statically that rewrites are composed correctly. As shown throughout the paper, our rewriting system today only provides the ability to apply sets of rewrite rules a certain number of times, in sequence.…”