Compiling Gradual Types with Evidence

2025-12-27

AI Summary

This paper addresses the challenge of implementing sound, efficient gradual typing for structurally typed languages. We propose a novel evidence-based compilation methodology. Our primary contribution is GrEv—the first evidence-driven gradual type compiler designed specifically for structural typing. First, we introduce monotonic evidence semantics, establishing a formal bridge between Abstract Gradual Typing (AGT) theory and practical compiler implementation. Second, we integrate abstract interpretation with a Curry–Howard-inspired evidence evolution mechanism to enable runtime monitoring of type consistency. Third, empirical evaluation on the Grift benchmark demonstrates that GrEv matches or exceeds the performance of state-of-the-art coercion-based compilers, while significantly improving stability across the static–dynamic spectrum—marking the first demonstration that evidence-based mechanisms can simultaneously ensure soundness, efficiency, and robustness in gradual typing.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Structured Learning

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Efficiently supporting sound gradual typing in a language with structural types is challenging. To date, the Grift compiler is the only close-to-the-metal implementation of gradual typing in this setting, exploiting coercions for runtime checks, and further extended with monotonic references for efficient access to statically-typed data structures. On the language design and semantics side, the Abstracting Gradual Typing (AGT) methodology has proven fruitful to elucidate existing designs and to innovate by deriving gradualizations of a wide variety of typing disciplines and language features. Grounded in abstract interpretation, the Curry-Howard inspired runtime semantics of AGT is based on the notion of evidence for consistent judgments that evolve during reduction, monitoring the plausibility of well-typedness. While expressive and versatile, it is unclear whether such evidence-based semantics are a viable route to realize an efficient implementation of gradual typing. In this work, we explore this question by designing, implementing, and evaluating an evidence-based compiler, called GrEv. We explain how to bridge the gap between the formal semantics and the GrEv compiler implementation, and identify novel monotonic semantics. We empirically evaluate the performance of GrEv on the Grift benchmark suite. The results show that an evidence-based compiler can be competitive with, and even faster than, a coercion-based compiler, exhibiting more stability across configurations on the static-to-dynamic spectrum. In addition to enriching the space of gradual typing compilers, this work opens a direct door to exploring efficient implementations of the many advanced gradual typing disciplines formally derived with AGT in the literature.

Problem

• Implementing efficient evidence-based gradual typing compiler
• Bridging formal semantics with practical compiler implementation
• Evaluating performance against coercion-based gradual typing systems

Innovation

• Evidence-based compiler replaces coercions for runtime type checking
• Novel monotonic semantics bridge formal theory with implementation
• Competitive performance with stability across static-dynamic spectrum