Type Stability in Julia: Avoiding Performance Pathologies in JIT Compilation (Extended Version)

TL;DR

This paper formalizes the concept of type stability in Julia, demonstrating its importance for performance, introducing the notion of type groundedness, and analyzing real-world code to promote better programming practices.

Contribution

It provides a formal definition of type stability and groundedness, proves compiler correctness, and analyzes how these properties appear in practice.

Findings

Type groundedness enables compiler optimizations.

Formal proof of compiler correctness for type stability.

Corpus analysis reveals practical manifestation of type properties.

Abstract

As a scientific programming language, Julia strives for performance but also provides high-level productivity features. To avoid performance pathologies, Julia users are expected to adhere to a coding discipline that enables so-called type stability. Informally, a function is type stable if the type of the output depends only on the types of the inputs, not their values. This paper provides a formal definition of type stability as well as a stronger property of type groundedness, shows that groundedness enables compiler optimizations, and proves the compiler correct. We also perform a corpus analysis to uncover how these type-related properties manifest in practice.