Towards Cumulative Abstract Semantics via Handlers

2025-12-11

AI Summary

Modular control-flow handling in abstract interpretation and supporting multiple analysis strategies—such as path- vs. flow-sensitivity, forward vs. backward directionality, and upper vs. lower approximations—traditionally relies on complex monad transformers, leading to implementation brittleness and poor composability. Method: This paper introduces the *cumulative abstract semantics* framework, the first to incorporate *scoped effects* into abstract interpretation. It decouples syntactic structure from semantic behavior via two classes of effect handlers: *syntax-resolving* and *domain-semantics-introducing*. A single syntax-driven interpreter suffices to generate diverse dynamic evaluators and static analyzers. Contribution/Results: The framework eliminates heavyweight data structures, preserving expressiveness while drastically reducing implementation complexity for multi-strategy analyses. It enhances maintainability, composability, and modularity—providing a concise, unified, and extensible theoretical and practical foundation for modular program analysis.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We consider the problem of modularizing control flow in a generic abstract interpretation framework. A generic abstract interpretation framework is not truly flexible if it does not allow interpreting with different path- and flow-sensitivities, by going forwards or backwards, and over- or under-approximately. Most interpreters inherently intertwine syntax and semantics, making the implementation antagonistic to modularity. Current approaches to modular designs require the use of complex data structures (e.g., monad transformers), providing modularity but often proving unwieldy (e.g., lifts). We observe that leveraging scoped effects within an interpreter facilitates the accumulation of semantic fragments against a fixed syntax. In this paper, we define cumulative abstract semantics, illustrating the potential for creating multiple dynamic evaluators and static analyses from one interpreter. This modularity is achieved by grouping effects into two categories: syntax elimination and domain-semantic introduction handlers. Our contribution shows the benefits of using effects as an instrument for designing a clean, elegant, and modular abstract interpretation framework.

Problem

• Modularizing control flow in abstract interpretation frameworks.
• Separating syntax and semantics for flexible path and flow sensitivities.
• Using effects to design clean, modular interpreters and analyses.

Innovation

• Using scoped effects for semantic accumulation
• Grouping effects into syntax elimination handlers
• Creating multiple evaluators from one interpreter