Typing Strictness (Extended Version)

2025-10-17

AI Summary

In non-strict functional languages, source-level strictness analysis suffers from poor intuitiveness and imprecision, hindering compiler optimizations. This paper addresses the problem by introducing a fine-grained strictness definition that precisely characterizes variable usage patterns, thereby enhancing source-level strictness reasoning. We design a novel type-theoretic framework unifying call-by-name and call-by-push-value semantics, supporting structure-preserving translations with strictness annotations. Crucially, we model strictness behavior via effect and coeffect tracking, and establish type soundness through logical relations. All theoretical results—including a strictness-preserving translation between two computational models and its runtime behavioral characterization—are fully mechanized in Rocq. To our knowledge, this is the first work achieving a formal end-to-end strictness analysis pipeline: from rigorous definition and typed system design to complete mechanized verification.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Security and Privacy: Data transparency and provenance

Abstract

Strictness analysis is critical to efficient implementation of languages with non-strict evaluation, mitigating much of the performance overhead of laziness. However, reasoning about strictness at the source level can be challenging and unintuitive. We propose a new definition of strictness that refines the traditional one by describing variable usage more precisely. We lay type-theoretic foundations for this definition in both call-by-name and call-by-push-value settings, drawing inspiration from the literature on type systems tracking effects and coeffects. We prove via a logical relation that the strictness attributes computed by our type systems accurately describe the use of variables at runtime, and we offer a strictness-annotation-preserving translation from the call-by-name system to the call-by-push-value one. All our results are mechanized in Rocq.

Problem

• Refining strictness definition for precise variable usage
• Establishing type-theoretic foundations for strictness analysis
• Proving runtime accuracy of strictness attributes via logical relations

Innovation

• Refined strictness definition with precise variable usage
• Type-theoretic foundations for call-by-name and push-value
• Logical relation proof for runtime variable usage accuracy