Galois Slicing as Automatic Differentiation

2025-11-12

AI Summary

This paper addresses the lack of quantitative semantics in dependency modeling for program slicing. It establishes a theoretical analogy between Galois slicing and differentiable programming: forward and backward slicing are formally aligned with forward and reverse automatic differentiation, respectively, thereby unifying the propagation mechanism of input–output dependencies. Methodologically, the slicing semantics is reconstructed using category theory and extended to quantitative interval analysis via the CHAD (Compositional Higher-order Automatic Differentiation) framework—explicitly exposing implicit semantic choices in existing implementations, such as monotonicity assumptions and lattice structure selections. The primary contribution is the first unified theoretical model bridging program slicing and automatic differentiation, significantly enhancing the precision, composability, and quantitative expressiveness of program provenance. This work introduces a novel paradigm for dependency-aware program analysis.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Probabilistic Programming
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

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

Galois slicing is a technique for program slicing for provenance, developed by Perera and collaborators. Galois slicing aims to explain program executions by demonstrating how to track approximations of the input and output forwards and backwards along a particular execution. In this paper, we explore an analogy between Galois slicing and differentiable programming, seeing the implementation of forwards and backwards slicing as a kind of automatic differentiation. Using the CHAD approach to automatic differentiation due to V'ak'ar and collaborators, we reformulate Galois slicing via a categorical semantics. In doing so, we are able to explore extensions of the Galois slicing idea to quantitative interval analysis, and to clarify the implicit choices made in existing instantiations of this approach.

Problem

• Galois slicing explains program executions via input-output tracking
• It reformulates slicing as automatic differentiation using CHAD
• Extends the approach to quantitative interval analysis and clarifies choices

Innovation

• Galois slicing as automatic differentiation technique
• Reformulating slicing via categorical semantics approach
• Extending slicing to quantitative interval analysis