A Denotational Semantics for Communicating Unstructured Code

An important property of programming language semantics is that they should be compositional. However, unstructured low-level code contains goto-like commands making it hard to define a semantics that is compositional. In this paper, we follow the ideas of Saabas and Uustalu to structure low-level code. This gives us the possibility to define a compositional denotational semantics based on least fixed points to allow for the use of inductive verification methods. We capture the semantics of communication using finite traces similar to the denotations of CSP. In addition, we examine properties of this semantics and give an example that demonstrates reasoning about communication and jumps. With this semantics, we lay the foundations for a proof calculus that captures both, the semantics of unstructured low-level code and communication.Comment: In Proceedings FESCA 2015, arXiv:1503.0437

Enriched Lawvere Theories for Operational Semantics

Enriched Lawvere theories are a generalization of Lawvere theories that allow us to describe the operational semantics of formal systems. For example, a graph enriched Lawvere theory describes structures that have a graph of operations of each arity, where the vertices are operations and the edges are rewrites between operations. Enriched theories can be used to equip systems with operational semantics, and maps between enriching categories can serve to translate between different forms of operational and denotational semantics. The Grothendieck construction lets us study all models of all enriched theories in all contexts in a single category. We illustrate these ideas with the SKI-combinator calculus, a variable-free version of the lambda calculus.Comment: In Proceedings ACT 2019, arXiv:2009.0633

Calculi for higher order communicating systems

This thesis develops two Calculi for Higher Order Communicating Systems. Both calculi consider sending and receiving processes to be as fundamental as nondeterminism and parallel composition. The first calculus called CHOCS is an extension of Milner's CCS in the sense that all the constructions of CCS are included or may be derived from more fundamental constructs. Most of the mathematical framework of CCS carries over almost unchanged. The operational semantics of CHOCS is given as a labelled transition system and it is a direct extension of the semantics of CCS with value passing. A set of algebraic laws satisfied by the calculus is presented. These are similar to the CCS laws only introducing obvious extra laws for sending and receiving processes. The power of process passing is underlined by a result showing that the recursion operator is unnecessary in the sense that recursion can be simulated by means of process passing and communication. The CHOCS language is also studied by means of a denotational semantics. A major result is the full abstractness of this semantics with respect to the operational semantics. The denotational semantics is used to provide an easy proof of the simulation of recursion. Introducing processes as first class objects yields a powerful metalanguage. It is shown that it is possible to simulate various reduction strategies of the untyped λ-Calculus in CHOCS. As pointed out by Milner, CCS has its limitations when one wants to describe unboundedly expanding systems, e.g. an unbounded number of procedure invocations in an imperative concurrent programming language P with recursive procedures. CHOCS may neatly describe both call-by-value and call-by-reference parameter mechanisms for P. We also consider call-by-name and lazy parameter mechanisms for P. The second calculus is called Plain CHOCS. Essential to the new calculus is the treatment of restriction as a static binding operator on port names. This calculus is given an operational semantics using labelled transition systems which combines ideas from the applicative transition systems described by Abramsky and the transition systems used for CHOCS. This calculus enjoys algebraic properties which are similar to those of CHOCS only needing obvious extra laws for the static nature of the restriction operator. Processes as first class objects enable description of networks with changing interconnection structure and there is a close connection between the Plain CHOCS calculus and the π-Calculus described by Milner, Parrow and Walker: the two calculi can simulate one another. Recently object oriented programming has grown into a major discipline in computational practice as well as in computer science. From a theoretical point of view object oriented programming presents a challenge to any metalanguage since most object oriented languages have no formal semantics. We show how Plain CHOCS may be used to give a semantics to a prototype object oriented language called 0.Open Acess

Extending and Relating Semantic Models of Compensating CSP

Business transactions involve multiple partners coordinating and interacting with each other. These transactions have hierarchies of activities which need to be orchestrated. Usual database approaches (e.g.,checkpoint, rollback) are not applicable to handle faults in a long running transaction due to interaction with multiple partners. The compensation mechanism handles faults that can arise in a long running transaction. Based on the framework of Hoare's CSP process algebra, Butler et al introduced Compensating CSP (cCSP), a language to model long-running transactions. The language introduces a method to declare a transaction as a process and it has constructs for orchestration of compensation. Butler et al also defines a trace semantics for cCSP. In this thesis, the semantic models of compensating CSP are extended by defining an operational semantics, describing how the state of a program changes during its execution. The semantics is encoded into Prolog to animate the specification. The semantic models are further extended to define the synchronisation of processes. The notion of partial behaviour is defined to model the behaviour of deadlock that arises during process synchronisation. A correspondence relationship is then defined between the semantic models and proved by using structural induction. Proving the correspondence means that any of the presentation can be accepted as a primary definition of the meaning of the language and each definition can be used correctly at different times, and for different purposes. The semantic models and their relationships are mechanised by using the theorem prover PVS. The semantic models are embedded in PVS by using Shallow embedding. The relationships between semantic models are proved by mutual structural induction. The mechanisation overcomes the problems in hand proofs and improves the scalability of the approach