The dynamic frames theory

The theory of Dynamic Frames has been invented to deal with the frame problem in the presence of encapsulation and pointers. It has proved more flexible and conceptually simpler than previous approaches that tackled the problem. It is now being actively used both for theoretical and for practical purposes related to the formal verification of program correctness. This paper presents the full theory of Dynamic Frames, together with its reasoning laws and exemplifies the use of these laws in proving correct several common design patterns. It also discusses the ongoing research on the topi

Heterogeneous Semantics and Unifying Theories

Model-driven development is being used increasingly in the development of modern computer-based systems. In the case of cyber-physical systems (including robotics and autonomous systems) no single modelling solution is adequate to cover all aspects of a system, such as discrete control, continuous dynamics, and communication networking. Instead, a heterogeneous modelling solution must be adopted. We propose a theory engineering technique involving Isabelle/HOL and Hoare & He’s Unifying Theories of Programming. We illustrate this approach with mechanised theories for building a contractual theory of sequential programming, a theory of pointer-based programs, and the reactive theory underpinning CSP’s process algebra. Galois connections provide the mechanism for linking these theories

Better than $1/Mflops sustained: a scalable PC-based parallel computer for lattice QCD

We study the feasibility of a PC-based parallel computer for medium to large scale lattice QCD simulations. The E\"otv\"os Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes with 512 MB RDRAM. The 32-bit, single precision sustained performance for dynamical QCD without communication is 1510 Mflops/node with Wilson and 970 Mflops/node with staggered fermions. This gives a total performance of 208 Gflops for Wilson and 133 Gflops for staggered QCD, respectively (for 64-bit applications the performance is approximately halved). The novel feature of our system is its communication architecture. In order to have a scalable, cost-effective machine we use Gigabit Ethernet cards for nearest-neighbor communications in a two-dimensional mesh. This type of communication is cost effective (only 30% of the hardware costs is spent on the communication). According to our benchmark measurements this type of communication results in around 40% communication time fraction for lattices upto 48^3\cdot96 in full QCD simulations. The price/sustained-performance ratio for full QCD is better than $1/Mflops for Wilson (and around$1.5/Mflops for staggered) quarks for practically any lattice size, which can fit in our parallel computer. The communication software is freely available upon request for non-profit organizations.Comment: 14 pages, 3 figures, final version to appear in Comp.Phys.Com

Automated Algebraic Reasoning for Collections and Local Variables with Lenses

Lenses are a useful algebraic structure for giving a unifying semantics to program variables in a variety of store models. They support efficient automated proof in the Isabelle/UTP verification framework. In this paper, we expand our lens library with (1) dynamic lenses, that support mutable indexed collections, such as arrays, and (2) symmetric lenses, that allow partitioning of a state space into disjoint local and global regions to support variable scopes. From this basis, we provide an enriched program model in Isabelle/UTP for collection variables and variable blocks. For the latter, we adopt an approach first used by Back and von Wright, and derive weakest precondition and Hoare calculi. We demonstrate several examples, including verification of insertion sor

Towards a UTP semantics for modelica

We describe our work on a UTP semantics for the dynamic systems modelling language Modelica. This is a language for modelling a system’s continuous behaviour using a combination of differential algebraic equations and an event-handling system. We develop a novel UTP theory of hybrid relations, inspired by Hybrid CSP and Duration Calculus, that is purely relational and provides uniform handling of continuous and discrete variables. This theory is mechanised in our Isabelle implementation of the UTP, Isabelle/UTP, with which we verify some algebraic properties. Finally, we show how a subset of Modelica models can be given semantics using our theory. When combined with the wealth of existing UTP theories for discrete system modelling, our work enables a sound approach to heterogeneous semantics for Cyber-Physical systems by leveraging the theory linking facilities of the UTP