Computer-Assisted Program Reasoning Based on a Relational Semantics of Programs

We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its denotation from which subsequently the verification conditions are generated. However, even before (and independently of) any verification attempt, one may investigate the denotation itself to get insight into the "semantic essence" of the program, in particular to see whether the denotation indeed gives reason to believe that the program has the expected behavior. Errors in the program and in the meta-information may thus be detected and fixed prior to actually performing the formal verification. More concretely, following the relational approach to program semantics, we model the effect of a program as a binary relation on program states. A formal calculus is devised to derive from a program a logic formula that describes this relation and is subject for inspection and manipulation. We have implemented this idea in a comprehensive form in the RISC ProgramExplorer, a new program reasoning environment for educational purposes which encompasses the previously developed RISC ProofNavigator as an interactive proving assistant.Comment: In Proceedings THedu'11, arXiv:1202.453

Finite Countermodel Based Verification for Program Transformation (A Case Study)

Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction, specialization, supercompilation) for verification of unreachability properties of computing systems were introduced and demonstrated. On the other hand, the semantics based unfold-fold program transformation methods pose themselves diverse kinds of reachability tasks and try to solve them, aiming at improving the semantics tree of the program being transformed. That means some general-purpose verification methods may be used for strengthening program transformation techniques. This paper considers the question how finite countermodels for safety verification method might be used in Turchin's supercompilation method. We extract a number of supercompilation sub-algorithms trying to solve reachability problems and demonstrate use of an external countermodel finder for solving some of the problems.Comment: In Proceedings VPT 2015, arXiv:1512.0221

Koka: Programming with Row Polymorphic Effect Types

We propose a programming model where effects are treated in a disciplined way, and where the potential side-effects of a function are apparent in its type signature. The type and effect of expressions can also be inferred automatically, and we describe a polymorphic type inference system based on Hindley-Milner style inference. A novel feature is that we support polymorphic effects through row-polymorphism using duplicate labels. Moreover, we show that our effects are not just syntactic labels but have a deep semantic connection to the program. For example, if an expression can be typed without an exn effect, then it will never throw an unhandled exception. Similar to Haskell's `runST` we show how we can safely encapsulate stateful operations. Through the state effect, we can also safely combine state with let-polymorphism without needing either imperative type variables or a syntactic value restriction. Finally, our system is implemented fully in a new language called Koka and has been used successfully on various small to medium-sized sample programs ranging from a Markdown processor to a tier-splitted chat application. You can try out Koka live at www.rise4fun.com/koka/tutorial.Comment: In Proceedings MSFP 2014, arXiv:1406.153

Enhancing Semantic Bidirectionalization via Shape Bidirectionalizer Plug-ins

Matsuda et al. (2007) and Voigtlander (2009) have introduced two techniques that given a source-to-view function provide an update propagation function mapping an original source and an updated view back to an updated source, subject to standard consistency conditions. Previously, we developed a synthesis of the two techniques, based on a separation of shape and content aspects (Voigtlander et al. 2010). Here, we carry that idea further, reworking the technique of Voigtlander such that any shape bidirectionalizer (based on the work of Matsuda et al. or not) can be used as a plug-in, to good effect. We also provide a data-type-generic account, enabling wider reuse, including the use of pluggable bidirectionalization itself as a plug-in

A Case Study in Refactoring Functional Programs

Refactoring is the process of redesigning existing code without changing its functionality. Refactoring has recently come to prominence in the OO community. In this paper we explore the prospects for refactoring functional programs. Our paper centres on the case study of refactoring a 400 line Haskell program written by one of our students. The case study illustrates the type and variety of program manipulations involved in refactoring. Similarly to other program transformations, refactorings are based on program equivalences, and thus ultimately on language semantics. In the context of functional languages, refactorings can be based on existing theory and program analyses. However, the use of program transformations for program restructuring emphasises a different kind of transformation from the more traditional derivation or optimisation: characteristically, they often require wholesale changes to a collection of modules, and although they are best controlled by programmers, their application may require nontrivial semantic analyses. The paper also explores the background to refactoring, provides a taxonomy for describing refactorings and draws some conclusions about refactoring for functional programs

Refactoring Functional Programs

Refactoring is the process of redesigning existing code without changing its functionality. Refactoring has recently come to prominence in the OO community. In this paper we explore the prospects for refactoring functional programs. Our paper centres on the case study of refactoring a 400 line Haskell program written by one of our students. The case study illustrates the type and variety of program manipulations involved in refactoring. Similarly to other program transformations, refactorings are based on program equivalences, and thus ultimately on language semantics. In the context of functional languages, refactorings can be based on existing theory and program analyses. However, the use of program transformations for program restructuring emphasises a different kind of transformation from the more traditional derivation or optimisation: characteristically, they often require wholesale changes to a collection of modules, and although they are best controlled by programmers, their application may require nontrivial semantic analyses. The paper also explores the background to refactoring, provides a taxonomy for describing refactorings and draws some conclusions about refactoring for functional programs