A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Compositional Event Structure Semantics of the Internal pi-Calculus

Accepté à CONCUR 2007International audienceWe propose the first compositional event structure semantics for a fully expressive pi-calculus, generalising Winskel's event structures for CCS. The pi-calculus we model is the piI-calculus with recursive definitions and summations. First we model the synchronous calculus, introducing a notion of dynamic renaming to the standard operators on event structures. Then we model the asynchronous calculus, for which a new additional operator, called rooting, is necessary for representing causality due to new name binding. The semantics are shown to be operationally adequate and sound with respect to bisimulation

Typed event structures and the p-calculus

We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of con uence to systems that allow nondeterminism. Ours is the rst typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the p-calculi with internal mobility. The semantics we provide is the rst event structure semantics of the p-calculus and generalises Winskel's original event structure semantics of CCS

Construction of Continuous Abstractions for Discrete-Time Time-Delay Systems

In this paper we construct continuous abstraction for discrete-time time-delay systems via the notion of so-called Razumikhin simulation functions. We show that the existence of such a function guarantees that the mismatch between the output trajectory of the concrete system and that of its abstraction lies within an appropriate bound. By transforming a system with time delay into an interconnected system without time delay, we show that the Razumikhin method is a small-gain type approach for time-delay systems and enables us to effectively manage computational complexity of constructing abstractions. We further extend our approach to compositional construction of large-scale systems containing interconnection and/or local time delays. For linear systems, we provide an algorithmic procedure for compositional construction of abstractions, which is expressed in terms of linear matrix inequalities.</p

Substructural Simple Type Theories for Separation and In-place Update

This thesis studies two substructural simple type theories, extending the "separation" and "number-of-uses" readings of the basic substructural simply typed lambda-calculus with exchange. The first calculus, lambda_sep, extends the alpha lambda-calculus of O'Hearn and Pym by directly considering the representation of separation in a type system. We define type contexts with separation relations and introduce new type constructors of separated products and separated functions. We describe the basic metatheory of the calculus, including a sound and complete type-checking algorithm. We then give new categorical structure for interpreting the type judgements, and prove that it coherently, soundly and completely interprets the type theory. To show how the structure models separation we extend Day's construction of closed symmetric monoidal structure on functor categories to our categorical structure, and describe two instances dealing with the global and local separation. The second system, lambda_inplc, is a re-presentation of substructural calculus for in-place update with linear and non-linear values, based on Wadler's Linear typed system with non-linear types and Hofmann's LFPL. We identify some problems with the metatheory of the calculus, in particular the failure of the substitution rule to hold due to the call-by-value interpretation inherent in the type rules. To resolve this issue, we turn to categorical models of call-by-value computation, namely Moggi's Computational Monads and Power and Robinson's Freyd-Categories. We extend both of these to include additional information about the current state of the computation, defining Parameterised Freyd-categories and Parameterised Strong Monads. These definitions are equivalent in the closed case. We prove that by adding a commutativity condition they are a sound class of models for lambda_inplc. To obtain a complete class of models for lambda_inplc we refine the structure to better match the syntax. We also give a direct syntactic presentation of Parameterised Freyd-categories and prove that it is soundly and completely modelled by the syntax. We give a concrete model based on Day's construction, demonstrating how the categorical structure can be used to model call-by-value computation with in-place update and bounded heaps