On the enumeration of closures and environments with an application to random generation

Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures

Bounded Verification of Message-Passing Concurrency in Go

Go is a programming language that has gained increased popularity due to its good support for system programming and its channel-based message passing concurrency mechanism. These features rendered Go the language of choice of many platform software developers. Go offers a wide range of primitives to coordinate lightweight threads, e.g., channels, waitgroups, and mutexes. Although, these concurrency primitives help mitigate data races, they introduce additional complications due to the complexity of reasoning about concurrency. In this thesis, we first perform an empirical analysis on concurrent Go programs which analyses 125 Go projects from GitHub in order to understand how concurrency is used in publicly available code. Our results include the following findings: (1) concurrency primitives are used frequently and intensively, (2) most projects use synchronous communication channels over asynchronous ones, and (3) most Go projects use simple concurrent thread topologies, which are however currently not fully supported by existing static verification frameworks. To address these limitations, we propose a novel static checker for Go programs that relies on performing bounded model checking of their concurrent behaviours. In contrast to previous works, our approach deals with large codebases, supports programs that have statically unknown parameters and is extensible to additional concurrency primitives. Our work includes an empirical analysis that studies the usage of concurrency in Go projects, a detailed presentation of the extraction algorithm from Go programs to Promela models, an algorithm to automatically check programs with statically unknown parameters, and a large scale evaluation of our approach. The latter shows that our approach outperforms the state-of-the-art

Pseudo-contractions as Gentle Repairs

Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas