Rewriting for Monoidal Closed Categories

This paper develops a formal string diagram language for monoidal closed categories. Previous work has shown that string diagrams for freely generated symmetric monoidal categories can be viewed as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams for monoidal closed categories. We then show double pushout rewriting captures the axioms of these closed categories

Pushdown Normal-Form Bisimulation: A Nominal Context-Free Approach to Program Equivalence

We propose Pushdown Normal Form (PDNF) Bisimulation to verify contextual equivalence in higher-order functional programming languages with local state. Similar to previous work on Normal Form (NF) bisimulation, PDNF Bisimulation is sound and complete with respect to contextual equivalence. However, unlike traditional NF Bisimulation, PDNF Bisimulation is also decidable for a class of program terms that reach bounded configurations but can potentially have unbounded call stacks and input an unbounded number of unknown functions from their context. Our approach relies on the principle that, in model-checking for reachability, pushdown systems can be simulated by finite-state automata designed to accept their initial/final stack content. We embody this in a stackless Labelled Transition System (LTS), together with an on-the-fly saturation procedure for call stacks, upon which bisimulation is defined. To enhance the effectiveness of our bisimulation, we develop up-to techniques and confirm their soundness for PDNF Bisimulation. We develop a prototype implementation of our technique which is able to verify equivalence in examples from practice and the literature that were out of reach for previous work

Introduction to the Literature On Programming Language Design

This is an introduction to the literature on programming language design and related topics. It is intended to cite the most important work, and to provide a place for students to start a literature search

A Completeness Theorem for Probabilistic Regular Expressions

We introduce Probabilistic Regular Expressions (PRE), a probabilistic analogue of regular expressions denoting probabilistic languages in which every word is assigned a probability of being generated. We present and prove the completeness of an inference system for reasoning about probabilistic language equivalence of PRE based on Salomaa's axiomatisation of Kleene Algebra

Bisimulations for Delimited-Control Operators

We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We consider different styles of bisimilarities (namely applicative, normal-form, and environmental) within a unifying framework, and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to extend this work to other delimited-control operators

A coalgebraic treatment of conditional transition systems with upgrades

We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these coalgebras live: Kleisli categories based on the reader and on the so-called lattice monad over Poset. We study two different functors describing the branching type of the coalgebra and investigate the resulting behavioural equivalence. Furthermore we show how an existing algorithm for coalgebra minimisation can be instantiated to derive behavioural equivalences in this setting

Revisiting sequential composition in process calculi

International audienceThe article reviews the various ways sequential composition is defined in traditional process calculi, and shows that such definitions are not optimal, thus limiting the dissemination of concurrency theory ideas among computer scientists. An alternative approach is proposed, based on a symmetric binary operator and write-many variables. This approach, which generalizes traditional process calculi, has been used to define the new LNT language implemented in the CADP toolbox. Feedback gained from university lectures and real-life case studies shows a high acceptance by computer-science students and industry engineers