Refining specifications to logic programs

The refinement calculus provides a framework for the stepwise development of imperative programs from specifications. In this paper we study a refinement calculus for deriving logic programs. Dealing with logic programs rather than imperative programs has the dual advantages that, due to the expressive power of logic programs, the final program is closer to the original specification, and each refinement step can achieve more. Together these reduce the overall number of derivation steps. We present a logic programming language extended with specification constructs (including general predicates, assertions, and types and invariants) to form a wide-spectrum language. General predicates allow non-executable properties to be included in specifications. Assertions, types and invariants make assumptions about the intended inputs of a procedure explicit, and can be used during refinement to optimize the constructed logic program. We provide a semantics for the extended logic programming language and derive a set of refinement laws. Finally we apply these to an example derivation.

Separation and hedging results with state-contingent production

A state-contingent model of production under uncertainty is developed and compared with more traditional models of production under uncertainty. Producer behaviour with both production and price risk, in the presence and in the absence of futures and forward markets, is analysed in this state-contingent framework. Conditions for the optimal hedge to be positive or negative are derived. We also show that, under plausible conditions, a risk-averse producer facing price uncertainty and the ability to hedge price risk will never willingly adopt a nonstochastic technology. New separation results, which hold in the presence of both price and production risk, are then developed. These separation results generalize Townsend's spanning results by reducing the number of necessary forward markets by one.

Developing logic programs from specifications using stepwise refinement

In this paper we demonstrate a refinement calculus for logic programs, which is a framework for developing logic programs from specifications. The paper is written in a tutorial-style, using a running example to illustrate how the refinement calculus is used to develop logic programs. The paper also presents an overview of some of the advanced features of the calculus, including the introduction of higher-order procedures and the refinement of abstract data types.

Separation of mercury (II), lead (II), and silver (I) from aqueous solution using an aminopolycarboxylate silica

A quartz crystal microbalance modified by the attachment of silica particles derivatized with the aminopolycarboxylate ligand N-[(3-trimethoxysilyl)propyl]ethylenediamine-N,N',N'-triacetic acid has been employed to assess conditions under which mercury (II), lead (II), and silver (I) nitrates may be separated in aqueous solution. The separation protocol, which involved removal of Hg(II), as [HgI4](2-), and Pb(II) with H+ was successfully applied to a batchwise separation of the 3 metal ions.

A refinement calculus for logic programs

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.

Nondeterministic gates for photonic single-rail quantum logic

We discuss techniques for producing, manipulating, and measuring qubits encoded optically as vacuum- and single-photon states. We show that a universal set of nondeterministic gates can be constructed using linear optics and photon counting. We investigate the efficacy of a test gate given realistic detector efficiencies.