[Paper Review] Local Reasoning for Robust Observational Equivalence.

Dan R. Ghica, Koko Muroya+1 more|arXiv (Cornell University)|Jul 2, 2019

Logic, programming, and type systems35 references4 citations

TL;DR

This paper introduces a core calculus for effectful programming languages using a hypergraph-rewriting abstract machine inspired by the Geometry of Interaction. By treating all features—including arithmetic and functions—as extrinsic operations with rewrite rules, it enables local, robust reasoning about observational equivalence through intrinsic notions of locality and structural modularity.

ABSTRACT

We propose a new core calculus for programming languages with effects, interpreted using a hypergraph-rewriting abstract machine inspired by the Geometry of Interaction. The intrinsic calculus syntax and semantics only deal with the basic structural aspects of programming languages: variable binding, name binding, and thunking. Everything else, including features which are commonly thought of as intrinsic, such as arithmetic or function abstraction and application, must be provided as extrinsic operations, with associated rewrite rules. The graph representation yields natural concepts of locality and robustness for equational properties and reduction rules, which enable a novel flexible and powerful reasoning methodology about (type-free) languages with effects. We illustrate and motivate the technique with challenging examples from the literature.

Motivation & Objective

• To develop a foundational calculus for programming languages with effects that separates structural concerns from computational features.
• To address the challenge of reasoning about observational equivalence in type-free, effectful languages.
• To introduce a formalism where all language features are treated as extrinsic operations with associated rewrite rules.
• To establish locality and robustness as core principles for equational reasoning in effectful computation.
• To provide a flexible and powerful methodology for reasoning about equational properties in languages with side effects.

Proposed method

• The calculus uses a hypergraph-rewriting abstract machine as the computational model, inspired by the Geometry of Interaction.
• All language constructs—such as variables, binding, and thunking—are treated as intrinsic structural features.
• Arithmetic, functions, and other features are encoded as extrinsic operations with associated rewrite rules.
• The graph-based representation naturally supports locality, enabling modular reasoning about reduction and equivalence.
• Robustness of equational properties is ensured through structural invariance under graph rewriting.
• The framework supports flexible reasoning by isolating computational behavior from structural constraints.

Experimental results

Research questions

• RQ1 How can observational equivalence be reasoned about robustly in type-free, effectful languages?
• RQ2 What structural principles enable local reasoning about reduction and equational properties in effectful computation?
• RQ3 How can a core calculus be designed to treat all features as extrinsic operations with rewrite rules?
• RQ4 In what ways does hypergraph rewriting support modularity and robustness in equational reasoning?
• RQ5 How can the Geometry of Interaction be adapted to model effects and observational equivalence in a local way?

Key findings

• The proposed calculus enables local reasoning about observational equivalence by encoding all features as extrinsic operations with rewrite rules.
• The hypergraph-rewriting model provides a natural foundation for locality and robustness in equational properties.
• Structural features such as variable binding and name binding are treated as intrinsic, simplifying the core calculus.
• The framework supports flexible reasoning by decoupling computational behavior from structural constraints.
• The approach is illustrated through challenging examples from the literature, demonstrating its power and generality.
• Robustness of equational reasoning is achieved through invariance under graph rewriting, ensuring consistency across reductions.