A categorical foundation for structured reversible flowchart languages: Soundness and adequacy

Structured reversible flowchart languages is a class of imperative reversible programming languages allowing for a simple diagrammatic representation of control flow built from a limited set of control flow structures. This class includes the reversible programming language Janus (without recursion), as well as more recently developed reversible programming languages such as R-CORE and R-WHILE. In the present paper, we develop a categorical foundation for this class of languages based on inverse categories with joins. We generalize the notion of extensivity of restriction categories to one that may be accommodated by inverse categories, and use the resulting decisions to give a reversible representation of predicates and assertions. This leads to a categorical semantics for structured reversible flowcharts, which we show to be computationally sound and adequate, as well as equationally fully abstract with respect to the operational semantics under certain conditions

The agent programming language meta-APL

Abstract. We describe a novel agent programming language, Meta-APL, and give its operational semantics. Meta-APL allows both agent programs and their associated deliberation strategy to be encoded in the same programming language. We define a notion of equivalence between programs written in different agent programming languages based on the notion of weak bisimulation equivalence. We show how to simulate (up to this notion of equivalence) programs written in other agent programming languages by programs of Meta-APL. This involves translating both the agent program and the deliberation strategy under which it is executed into Meta-APL.

A Coalgebraic Semantics for Imperative Programming Languages

In the theory of programming languages, one often takes two complementary perspectives. In operational semantics, one defines and reasons about the behaviour of programs; and in denotational semantics, one abstracts away implementation details, and reasons about programs as mathematical objects or denotations. The denotational semantics should be compositional, meaning that denotations of programs are determined by the denotations of their parts. It should also be adequate with respect to operational equivalence: programs with the same denotation should be behaviourally indistinguishable. One often has to prove adequacy and compositionality independently for different languages, and the proofs are often laborious and repetitive. These proofs were provided systematically in the context of process algebras by the mathematical operational semantics framework of Turi and Plotkin – which represented transition systems as coalgebras, and program syntax by free algebras; operational specifications were given by distributive laws of syntax over behaviour. By framing the semantics on this abstract level, one derives denotational and operational semantics which are guaranteed to be adequate and compositional for a wide variety of examples. However, despite speculation on the possibility, it is hard to apply the framework to programming languages, because one obtains undesirably fine-grained behavioural equivalences, and unconventional notions of operational semantics. Moreover, the behaviour of these languages is often formalised in a different way – such as computational effects, which may be thought of as an interface between programs and external factors such as non-determinism or a variable store; and comodels, or transition systems which implement these effects. This thesis adapts the mathematical operational semantics framework to provide semantics for various classes of programming languages. After identifying the need for such an adaptation, we show how program behaviour may be characterised by final coalgebras in suitably order- enriched Kleisli categories. We define both operational and denotational semantics, first for languages with syntactic effects, and then for languages with effects and/or comodels given by a Lawvere theory. To ensure adequacy and compositionality, we define concrete and abstract operational rule-formats for these languages, based on the idea of evaluation-in-context; we give syntactic and then categorical proofs that those properties are guaranteed by operational specifications in these rule-formats.Open Acces

An operational approach to semantics and translation for concurrent programming languages

The problems of semantics and translation for concurrent programming languages are studied in this thesis. A structural operational approach is introduced to specify the semantics of parallelism and communication. Using this approach, semantics for the concurrent programming languages CSP (Hoare's Communicating Sequential Processes), multitasking and exception handling in Ada, Brinch-Hansen's Edison and CCS (Milner's Calculus of Communicating Systems) are defined and some of their properties are studied. An operational translation theory for concurrent programming languages is given. The concept of the correctness of a translation is formalised, the problem of composing transitions is studied and a composition theorem is proved. A set of sufficient conditions for proving the correctness of a translation is given. A syntax-directed translation from CSP to CCS is given and proved correct. Through this example the proof techniques of this approach is demonstrated. Finally, as an application of operational semantics and translation, a proposal for implementing multitasking in Ada is given via a two-step syntax-directed translation

A Certified Study of a Reversible Programming Language

We advance in the study of the semantics of Janus, a C-like reversible programming language. Our study makes utterly explicit some backward and forward evaluation symmetries. We want to deepen mathematical knowledge about the foundations and design principles of reversible computing and programming languages. We formalize a big-step operational semantics and a denotational semantics of Janus. We show a full abstraction result between the operational and denotational semantics. Last, we certify our results by means of the proof assistant Matita

An operational semantics for a fragment of PRS

The Procedural Reasoning System (PRS) is arguably the first implementation of the Belief–Desire–Intention (BDI) approach to agent programming. PRS remains extremely influential, directly or indirectly inspiring the development of subsequent BDI agent programming languages. However, perhaps surprisingly given its centrality in the BDI paradigm, PRS lacks a formal operational semantics, making it difficult to determine its expressive power relative to other agent programming languages. This paper takes a first step towards closing this gap, by giving a formal semantics for a significant fragment of PRS. We prove key properties of the semantics relating to PRS-specific programming constructs, and show that even the fragment of PRS we consider is strictly more expressive than the plan constructs found in typical BDI languages

Mechanized semantics

The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and over generic program transformations, as typically found in compilers. The topics covered include: operational semantics (small-step, big-step, definitional interpreters); a simple form of denotational semantics; axiomatic semantics and Hoare logic; generation of verification conditions, with application to program proof; compilation to virtual machine code and its proof of correctness; an example of an optimizing program transformation (dead code elimination) and its proof of correctness