Proving Correctness and Completeness of Normal Programs - a Declarative Approach

We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the operational semantics, in particular on the selection rule. We show how to deal with correctness and completeness in a declarative way, treating programs only from the logical point of view. Specifications used in this approach are interpretations (or theories). We point out that specifications for correctness may differ from those for completeness, as usually there are answers which are neither considered erroneous nor required to be computed. We present proof methods for correctness and completeness for definite programs and generalize them to normal programs. For normal programs we use the 3-valued completion semantics; this is a standard semantics corresponding to negation as finite failure. The proof methods employ solely the classical 2-valued logic. We use a 2-valued characterization of the 3-valued completion semantics which may be of separate interest. The presented methods are compared with an approach based on operational semantics. We also employ the ideas of this work to generalize a known method of proving termination of normal programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP). 44 page

Polynomial-Time Fence Insertion for Structured Programs

To enhance performance, common processors feature relaxed memory models that reorder instructions. However, the correctness of concurrent programs is often dependent on the preservation of the program order of certain instructions. Thus, the instruction set architectures offer memory fences. Using fences is a subtle task with performance and correctness implications: using too few can compromise correctness and using too many can hinder performance. Thus, fence insertion algorithms that given the required program orders can automatically find the optimum fencing can enhance the ease of programming, reliability, and performance of concurrent programs. In this paper, we consider the class of programs with structured branch and loop statements and present a greedy and polynomial-time optimum fence insertion algorithm. The algorithm incrementally reduces fence insertion for a control-flow graph to fence insertion for a set of paths. In addition, we show that the minimum fence insertion problem with multiple types of fence instructions is NP-hard even for straight-line programs

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Program Repair by Stepwise Correctness Enhancement

Relative correctness is the property of a program to be more-correct than another with respect to a given specification. Whereas the traditional definition of (absolute) correctness divides candidate program into two classes (correct, and incorrect), relative correctness arranges candidate programs on the richer structure of a partial ordering. In other venues we discuss the impact of relative correctness on program derivation, and on program verification. In this paper, we discuss the impact of relative correctness on program testing; specifically, we argue that when we remove a fault from a program, we ought to test the new program for relative correctness over the old program, rather than for absolute correctness. We present analytical arguments to support our position, as well as an empirical argument in the form of a small program whose faults are removed in a stepwise manner as its relative correctness rises with each fault removal until we obtain a correct program.Comment: In Proceedings PrePost 2016, arXiv:1605.0809

Correctness and completeness of logic programs

We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we show how to prove completeness and correctness in the presence of SLD-tree pruning, and point out that approximate specifications simplify specifications and proofs. We compare the proof methods to declarative diagnosis (algorithmic debugging), showing that approximate specifications eliminate a major drawback of the latter. We argue that our proof methods reflect natural declarative thinking about programs, and that they can be used, formally or informally, in every-day programming.Comment: 29 pages, 2 figures; with editorial modifications, small corrections and extensions. arXiv admin note: text overlap with arXiv:1411.3015. Overlaps explained in "Related Work" (p. 21

Future-based Static Analysis of Message Passing Programs

Message passing is widely used in industry to develop programs consisting of several distributed communicating components. Developing functionally correct message passing software is very challenging due to the concurrent nature of message exchanges. Nonetheless, many safety-critical applications rely on the message passing paradigm, including air traffic control systems and emergency services, which makes proving their correctness crucial. We focus on the modular verification of MPI programs by statically verifying concrete Java code. We use separation logic to reason about local correctness and define abstractions of the communication protocol in the process algebra used by mCRL2. We call these abstractions futures as they predict how components will interact during program execution. We establish a provable link between futures and program code and analyse the abstract futures via model checking to prove global correctness. Finally, we verify a leader election protocol to demonstrate our approach.Comment: In Proceedings PLACES 2016, arXiv:1606.0540

Generating Efficient, Terminating Logic Programs

The objective of control generation in logic programming is to automatically derive a computation rule for a program that is efficient and yet does not compromise program correctness. Progress in solving this important problem has been slow and, to date, only partial solutions have been proposed where the generated programs are either incorrect or inefficient. We show how the control generation problem can be tackled with a simple automatic transformation that relies on information about the depths of derivations. To prove correctness of our transform we introduce the notion of a semi delay recurrent program which generalises previous ideas in the termination literature for reasoning about logic programs with dynamic selection rules