(Bi)Simulations Up-to Characterise Process Semantics

We define (bi)simulations up-to a preorder and show how we can use them to provide a coinductive, (bi)simulation-like, characterisation of semantic (equivalences) preorders for processes. In particular, we can apply our results to all the semantics in the linear time-branching time spectrum that are defined by preorders coarser than the ready simulation preorder. The relation between bisimulations up-to and simulations up-to allows us to find some new relations between the equivalences that define the semantics and the corresponding preorders. In particular, we have shown that the simulation up-to an equivalence relation is a canonical preorder whose kernel is the given equivalence relation. Since all of these canonical preorders are defined in an homogeneous way, we can prove properties for them in a generic way. As an illustrative example of this technique, we generate an axiomatic characterisation of each of these canonical preorders, that is obtained simply by adding a single axiom to the axiomatization of the original equivalence relation. Thus we provide an alternative axiomatization for any axiomatizable preorder in the linear time-branching time spectrum, whose correctness and completeness can be proved once and for all. Although we first prove, by induction, our results for finite processes, then we see, by using continuity arguments, that they are also valid for infinite (finitary) processes

Contexts, refinement and determinism

In this paper we have been influenced by those who take an “engineering view” of the problem of designing systems, i.e. a view that is motivated by what someone designing a real system will be concerned with, and what questions will arise as they work on their design. Specifically, we have borrowed from the testing work of Hennessy, de Nicola and van Glabbeek, e.g. [13, 5, 21, 40, 39]. Here we concentrate on one fundamental part of the engineering view and where consideration of it leads. The aspects we are concerned with are computational entities in contexts, observed by users. This leads to formalising design steps that are often left informal, and that in turn gives insights into non-determinism and ultimately leads to being able to use refinement in situations where existing techniques fail

Code mobility and Java RMI

Imperial Users onl

Formal Modeling and Analysis of Mobile Ad hoc Networks

Fokkink, W.J. [Promotor]Luttik, S.P. [Copromotor

Relational reasoning for effects and handlers

This thesis studies relational reasoning techniques for FRANK, a strict functional language supporting algebraic effects and their handlers, within a general, formalised approach for completely characterising observational equivalence. Algebraic effects and handlers are an emerging paradigm for representing computational effects where primitive operations, which give rise to an effect, are primary, and given semantics through their interpretation by effect handlers. FRANK is a novel point in the design space because it recasts effect handling as part of a generalisation of call-by-value function application. Furthermore, FRANK generalises unary effect handlers to the n-ary notion of multihandlers, supporting more elegant expression of certain handlers. There have been recent efforts to develop sound reasoning principles, with respect to observational equivalence, for languages supporting effects and handlers. Such techniques support powerful equational reasoning about code, such as substitution of equivalent sub-terms (‘equals for equals’) in larger programs. However, few studies have considered a complete characterisation of observational equivalence, and its implications for reasoning techniques. Furthermore, there has been no account of reasoning principles for FRANK programs. Our first contribution is a formal reconstruction of a general proof technique, triangulation, for proving completeness results for observational equivalence. The technique brackets observational equivalence between two structural relations, a logical and an applicative notion. We demonstrate the triangulation proof method for a pure simply-typed λ-calculus. We show that such results are readily formalisable in an implementation of type theory, specifically AGDA, using state-of-the-art technology for dealing with syntaxes with binding. Our second contribution is a calculus, ELLA, capturing the essence of FRANK’s novel design. In particular, ELLA supports binary handlers and generalises function application to incorporate effect handling. We extend our triangulation proof technique to this new setting, completely characterising observational equivalence for this calculus. We report on our partial progress in formalising our extension to ELLA in AGDA. Our final contribution is the application of sound reasoning principles, inspired by existing literature, to a variety of ELLA programs, including a proof of associativity for a canonical pipe multihandler. Moreover, we show how leveraging completeness leads, in certain instances, to simpler proofs of observational equivalence