On a New Notion of Partial Refinement

Formal specification techniques allow expressing idealized specifications, which abstract from restrictions that may arise in implementations. However, partial implementations are universal in software development due to practical limitations. Our goal is to contribute to a method of program refinement that allows for partial implementations. For programs with a normal and an exceptional exit, we propose a new notion of partial refinement which allows an implementation to terminate exceptionally if the desired results cannot be achieved, provided the initial state is maintained. Partial refinement leads to a systematic method of developing programs with exception handling.Comment: In Proceedings Refine 2013, arXiv:1305.563

Modal logics for reasoning about object-based component composition

Component-oriented development of software supports the adaptability and maintainability of large systems, in particular if requirements change over time and parts of a system have to be modified or replaced. The software architecture in such systems can be described by components and their composition. In order to describe larger architectures, the composition concept becomes crucial. We will present a formal framework for component composition for object-based software development. The deployment of modal logics for defining components and component composition will allow us to reason about and prove properties of components and compositions

Reasoning about the garden of forking paths

Lazy evaluation is a powerful tool for functional programmers. It enables the concise expression of on-demand computation and a form of compositionality not available under other evaluation strategies. However, the stateful nature of lazy evaluation makes it hard to analyze a program's computational cost, either informally or formally. In this work, we present a novel and simple framework for formally reasoning about lazy computation costs based on a recent model of lazy evaluation: clairvoyant call-by-value. The key feature of our framework is its simplicity, as expressed by our definition of the clairvoyance monad. This monad is both simple to define (around 20 lines of Coq) and simple to reason about. We show that this monad can be effectively used to mechanically reason about the computational cost of lazy functional programs written in Coq.Comment: 28 pages, accepted by ICFP'2

Program Calculation Properties of Continuous Algebras

Defining data types as initial algebras, or dually as final co-algebras, is beneficial, if not indispensible, for an algebraic calculus for program construction, in view of the nice equational properties that then become available. It is not hard to render finite lists as an initial algebra and, dually, infinite lists as a final co-algebra. However, this would mean that there are two distinct data types for lists, and then a program that is applicable to both finite and infinite lists is not possible, and arbitrary recursive definitions are not allowed. We prove the existence of algebras that are both initial in one category of algebras and final in the closely related category of co-algebras, and for which arbitrary (continuous) fixed point definitions ("recursion") do have a solution. Thus there is a single data type that comprises both the finite and the infinite lists. The price to be paid, however, is that partiality (of functions and values) is unavoidable. \ud We derive, for any such data type, various laws that are useful for an algebraic calculus of programs

Unifying parsing and reflective printing for fully disambiguated grammars

Language designers usually need to implement parsers and printers. Despite being two closely related programs, in practice they are often designed separately, and then need to be revised and kept consistent as the language evolves. It will be more convenient if the parser and printer can be unified and developed in a single program, with their consistency guaranteed automatically. Furthermore, in certain scenarios (like showing compiler optimisation results to the programmer), it is desirable to have a more powerful reflective printer that, when an abstract syntax tree corresponding to a piece of program text is modified, can propagate the modification to the program text while preserving layouts, comments, and syntactic sugar. To address these needs, we propose a domain-specific language BiYacc, whose programs denote both a parser and a reflective printer for a fully disambiguated context-free grammar. BiYacc is based on the theory of bidirectional transformations, which helps to guarantee by construction that the generated pairs of parsers and reflective printers are consistent. Handling grammatical ambiguity is particularly challenging: we propose an approach based on generalised parsing and disambiguation filters, which produce all the parse results and (try to) select the only correct one in the parsing direction; the filters are carefully bidirectionalised so that they also work in the printing direction and do not break the consistency between the parsers and reflective printers. We show that BiYacc is capable of facilitating many tasks such as Pombrio and Krishnamurthi's 'resugaring', simple refactoring, and language evolution.We thank the reviewers and the editor for their selflessness and effort spent on reviewing our paper, a quite long one. With their help, the readability of the paper is much improved, especially regarding how several case studies are structured, how theorems for the basic BiYacc and theorems for the extended version handling ambiguous grammars are related, and how look-alike notions are `disambiguated'. This work is partially supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (S) No. 17H06099; in particular, most of the second author's contributions were made when he worked at the National Institute of Informatics and funded by the Grant

Weighted programming: A programming paradigm for specifying mathematical models

We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces. Weights can be numbers but also other objects like words from an alphabet, polynomials, formal power series, or cardinal numbers. We argue that weighted programming as a paradigm can be used to specify mathematical models beyond probability distributions (as is done in probabilistic programming). We develop weakest-precondition- and weakest-liberal-precondition-style calculi à la Dijkstra for reasoning about mathematical models specified by weighted programs. We present several case studies. For instance, we use weighted programming to model the ski rental problem - an optimization problem. We model not only the optimization problem itself, but also the best deterministic online algorithm for solving this problem as weighted programs. By means of weakest-precondition-style reasoning, we can determine the competitive ratio of the online algorithm on source code level