Ian Stark

Bio: Ian Stark is an academic researcher from University of Edinburgh. The author has contributed to research in topics: Operational semantics & Bisimulation. The author has an hindex of 21, co-authored 51 publications receiving 2817 citations. Previous affiliations of Ian Stark include Aarhus University & University of Cambridge.

Free-algebra models for the π-calculus

Abstract: The finite π-calculus has an explicit set-theoretic functor-category model that is known to be fully abstract for strong late bisimulation congruence. We characterize this as the initial free algebra for an appropriate set of operations and equations in the enriched Lawvere theories of Plotkin and Power. Thus we obtain a novel algebraic description for models of the π-calculus, and validate an existing construction as the universal such model. The algebraic operations are intuitive, covering name creation, communication of names over channels, and nondeterminism; the equations then combine these features in a modular fashion. We work in an enriched setting, over a “possible worlds” category of sets indexed by available names. This expands significantly on the classical notion of algebraic theories, and in particular allows us to use nonstandard arities that vary as processes evolve. Based on our algebraic theory we describe a category of models for the π-calculus, and show that they all preserve bisimulation congruence. We develop a direct construction of free models in this category; and generalise previous results to prove that all free-algebra models are fully abstract.

The Continuous π-Calculus: A Process Algebra for Biochemical Modelling

Abstract: We introduce the continuous π-calculus, a process algebra for modelling behaviour and variation in molecular systems. Key features of the language are: its expressive succinctness; support for diverse interaction between agents via a flexible network of molecular affinities; and operational semantics for a continuous space of processes. This compositional semantics also gives a modular way to generate conventional differential equations for system behaviour over time. We illustrate these features with a model of an existing biological system, a simple oscillatory pathway in cyanobacteria. We then discuss future research directions, in particular routes to applying the calculus in the study of evolutionary properties of biochemical pathways.

Mobile Resource Guarantees for smart devices

Abstract: We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from run-time violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certificates of code origin, these are independent of trust networks. A novel programming language with resource constraints encoded in function types is used to streamline the generation of proofs of resource usage.

Operational reasoning for functions with local state

Abstract: Languages such as ML or Lisp permit the use of recursively defined function expressions with locally declared storage locations. Although this can be very convenient from a programming point of view it severely complicates the properties of program equivalence even for relatively simple fragments of such languages—such as the simply typed fragment of Standard ML with integer-valued references considered here. This paper presents a method for reasoning about contextual equivalence of programs involving this combination of functional and procedural features. The method is based upon the use of a certain kind of logical relation parameterised by relations between program states. The form of this logical relation is novel, in as much as it involves relations not only between program expressions, but also between program continuations (also known as evaluation contexts). The authors found this approach necessary in order to establish the ‘Fundamental Property of logical relations’ in the presence of both dynamically allocated local state and recursion. The logical relation characterises contextual equivalence and yields a proof of the best known context lemma for this kind of language— the Mason-Talcott ‘ciu’ theorem. Moreover, it is shown that the method can prove examples where such a context lemma is not much help and which involve representation independence, higher order memoising functions, and profiling functions.

Mobile resource guarantees for smart devices

Abstract: We present the Mobile Resource Guarantees framework: a system for ensuring that downloaded programs are free from run-time violations of resource bounds. Certificates are attached to code in the form of efficiently checkable proofs of resource bounds; in contrast to cryptographic certificates of code origin, these are independent of trust networks. A novel programming language with resource constraints encoded in function types is used to streamline the generation of proofs of resource usage.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Z3: an efficient SMT solver

Abstract: Satisfiability Modulo Theories (SMT) problem is a decision problem for logical first order formulas with respect to combinations of background theories such as: arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is a new and efficient SMT Solver freely available from Microsoft Research. It is used in various software verification and analysis applications.

Amortised Memory Analysis Using the Depth of Data Structures

Abstract: Hofmann and Jost have presented a heap space analysis [1] that finds linear space bounds for many functional programs. It uses an amortised analysis: assigning hypothetical amounts of free space (called potential) to data structures in proportion to their sizes using type annotations. Constraints on these annotations in the type system ensure that the total potential assigned to the input is an upper bound on the total memory required to satisfy all allocations. We describe a related system for bounding the stack space requirements which uses the depth of data structures, by expressing potential in terms of maxima as well as sums. This is achieved by adding extra structure to typing contexts (inspired by O'Hearn's bunched typing [2]) to describe the form of the bounds. We will also present the extra steps that must be taken to construct a typing during the analysis.

Dafny: an automatic program verifier for functional correctness

Abstract: Traditionally, the full verification of a program's functional correctness has been obtained with pen and paper or with interactive proof assistants, whereas only reduced verification tasks, such as extended static checking, have enjoyed the automation offered by satisfiability-modulo-theories (SMT) solvers. More recently, powerful SMT solvers and well-designed program verifiers are starting to break that tradition, thus reducing the effort involved in doing full verification. This paper gives a tour of the language and verifier Dafny, which has been used to verify the functional correctness of a number of challenging pointer-based programs. The paper describes the features incorporated in Dafny, illustrating their use by small examples and giving a taste of how they are coded for an SMT solver. As a larger case study, the paper shows the full functional specification of the Schorr-Waite algorithm in Dafny.

Robust satisfaction of temporal logic over real-valued signals

Abstract: We consider temporal logic formulae specifying constraints in continuous time and space on the behaviors of continuous and hybrid dynamical system admitting uncertain parameters. We present several variants of robustness measures that indicate how far a given trajectory stands, in space and time, from satisfying or violating a property. We present a method to compute these robustness measures as well as their sensitivity to the parameters of the system or parameters appearing in the formula. Combined with an appropriate strategy for exploring the parameter space, this technique can be used to guide simulation-based verification of complex nonlinear and hybrid systems against temporal properties. Our methodology can be used for other non-traditional applications of temporal logic such as characterizing subsets of the parameter space for which a system is guaranteed to satisfy a formula with a desired robustness degree.