A Concurrent Constraint Programming Interpretation of Access Permissions

TL;DR

This paper introduces a declarative interpretation of Access Permissions in object-oriented programming as Linear Concurrent Constraint Programs, enabling formal verification of properties like deadlock detection and correctness using linear logic.

Contribution

It presents a novel formal model for Access Permissions as linear concurrent constraints, facilitating verification through logic-based methods and implementing a tool for practical analysis.

Findings

Effective verification of AP properties using linear logic

Implementation of the Alcove tool for simulation and proof

Demonstrated deadlock detection and correctness verification

Abstract

A recent trend in object oriented (OO) programming languages is the use of Access Permissions (APs) as an abstraction for controlling concurrent executions of programs. The use of AP source code annotations defines a protocol specifying how object references can access the mutable state of objects. Although the use of APs simplifies the task of writing concurrent code, an unsystematic use of them can lead to subtle problems. This paper presents a declarative interpretation of APs as Linear Concurrent Constraint Programs (lcc). We represent APs as constraints (i.e., formulas in logic) in an underlying constraint system whose entailment relation models the transformation rules of APs. Moreover, we use processes in lcc to model the dependencies imposed by APs, thus allowing the faithful representation of their flow in the program. We verify relevant properties about AP programs by taking advantage of the interpretation of lcc processes as formulas in Girard's intuitionistic linear logic (ILL). Properties include deadlock detection, program correctness (whether programs adhere to their AP specifications or not), and the ability of methods to run concurrently. By relying on a focusing discipline for ILL, we provide a complexity measure for proofs of the above mentioned properties. The effectiveness of our verification techniques is demonstrated by implementing the Alcove tool that includes an animator and a verifier. The former executes the lcc model, observing the flow of APs and quickly finding inconsistencies of the APs vis-a-vis the implementation. The latter is an automatic theorem prover based on ILL. This paper is under consideration for publication in Theory and Practice of Logic Programming (TPLP).