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

Formal verification of higher-order probabilistic programs

Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru, derive their expressiveness from a powerful combination of continuous distributions, conditioning, and higher-order functions. Although very important for practical applications, these combined features raise fundamental challenges for program semantics and verification. Several recent works offer promising answers to these challenges, but their primary focus is on semantical issues. In this paper, we take a step further and we develop a set of program logics, named PPV, for proving properties of programs written in an expressive probabilistic higher-order language with continuous distributions and operators for conditioning distributions by real-valued functions. Pleasingly, our program logics retain the comfortable reasoning style of informal proofs thanks to carefully selected axiomatizations of key results from probability theory. The versatility of our logics is illustrated through the formal verification of several intricate examples from statistics, probabilistic inference, and machine learning. We further show the expressiveness of our logics by giving sound embeddings of existing logics. In particular, we do this in a parametric way by showing how the semantics idea of (unary and relational) TT-lifting can be internalized in our logics. The soundness of PPV follows by interpreting programs and assertions in quasi-Borel spaces (QBS), a recently proposed variant of Borel spaces with a good structure for interpreting higher order probabilistic programs

A Constrained Object Model for Configuration Based Workflow Composition

Automatic or assisted workflow composition is a field of intense research for applications to the world wide web or to business process modeling. Workflow composition is traditionally addressed in various ways, generally via theorem proving techniques. Recent research observed that building a composite workflow bears strong relationships with finite model search, and that some workflow languages can be defined as constrained object metamodels . This lead to consider the viability of applying configuration techniques to this problem, which was proven feasible. Constrained based configuration expects a constrained object model as input. The purpose of this document is to formally specify the constrained object model involved in ongoing experiments and research using the Z specification language.Comment: This is an extended version of the article published at BPM'05, Third International Conference on Business Process Management, Nancy Franc

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin