Lambda Calculus in Core Aldwych

Core Aldwych is a simple model for concurrent computation, involving the concept of agents which communicate through shared variables. Each variable will have exactly one agent that can write to it, and its value can never be changed once written, but a value can contain further variables which are written to later. A key aspect is that the reader of a value may become the writer of variables in it. In this paper we show how this model can be used to encode lambda calculus. Individual function applications can be explicitly encoded as lazy or not, as required. We then show how this encoding can be extended to cover functions which manipulate mutable variables, but with the underlying Core Aldwych implementation still using only immutable variables. The ordering of function applications then becomes an issue, with Core Aldwych able to model either the enforcement of an ordering or the retention of indeterminate ordering, which allows parallel execution

Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

PrologPF: Parallel Logic and Functions on the Delphi Machine

PrologPF is a parallelising compiler targeting a distributed system of general purpose workstations connected by a relatively low performance network. The source language extends standard Prolog with the integration of higher-order functions. The execution of a compiled PrologPF program proceeds in a similar manner to standard Prolog, but uses oracles in one of two modes. An oracle represents the sequence of clauses used to reach a given point in the problem search tree, and the same PrologPF executable can be used to build oracles, or follow oracles previously generated. The parallelisation strategy used by PrologPF proceeds in two phases, which this research shows can be interleaved. An initial phase searches the problem tree to a limited depth, recording the discovered incomplete paths. In the second phase these paths are allocated to the available processors in the network. Each processor follows its assigned paths and fully searches the referenced subtree, sending solutions back to a control processor. This research investigates the use of the technique with a one-time partitioning of the problem and no further scheduling communication, and with the recursive application of the partitioning technique to effect dynamic work reassignment. For a problem requiring all solutions to be found, execution completes when all the distributed processors have completed the search of their assigned subtrees. If one solution is required, the execution of all the path processors is terminated when the control processor receives the first solution. The presence of the extra-logical Prolog predicate cut in the user program conflicts with the use of oracles to represent valid open subtrees. PrologPF promotes the use of higher-order functional programming as an alternative to the use of cut. The combined language shows that functional support can be added as a consistent extension to standard Prolog