From Traces to Program Incorrectness: A Type-Theoretic Approach

2025-09-02

AI Summary

This paper addresses the challenge of systematically detecting incorrect behaviors when functional programs interact with effectful library APIs. Methodologically, it introduces a trace-based type-theoretic framework that models API call sequences using symbolic regular expressions and performs compositional trace analysis via symbolic finite automata; it further designs a type inference algorithm for under-approximating erroneous behaviors of abstract data types (ADTs). Key contributions include: (i) the first trace-directed, systematic under-approximation technique for specifying incorrectness, (ii) support for modeling error propagation across function boundaries, and (iii) effective inference—within effectful library interaction contexts—of subsets of erroneous behaviors potentially triggered by ADT implementations. Empirical evaluation validates the feasibility and practicality of this compositional incorrectness analysis approach.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Data transparency and provenance

Abstract

We present a type-theoretic framework for reasoning about incorrectness in functional programs that interact with effectful, opaque library APIs. Our approach centers on traces -- temporally-ordered sequences of library API invocations -- which naturally characterize both the preconditions of individual APIs and their composite behavior. We represent these traces using symbolic regular expressions (SREs), enabling formal specification of incorrect abstract data type (ADT) behaviors across function boundaries. The core contribution is a novel type inference algorithm that operates modulo specified incorrectness properties and leverages the symbolic finite automata (SFAs) representations of regexes for compositional reasoning of traces. When the algorithm succeeds, the inferred types witness that an ADT implementation can exhibit some subset of the specified incorrect behaviors. This represents the first systematic approach to underapproximate reasoning against trace-based incorrectness specifications, enabling a new form of trace-guided compositional analysis.

Problem

• Reasoning about incorrectness in functional programs with opaque APIs
• Formal specification of incorrect abstract data type behaviors
• Underapproximate reasoning against trace-based incorrectness specifications

Innovation

• Type-theoretic framework for incorrectness reasoning
• Symbolic regular expressions for trace specification
• Type inference algorithm with SFA representations