Fred: An approach to generating real, correct, reusable programs from proofs

In this paper we describe our system for automatically extracting "correct" programs from proofs using a development of the Curry-Howard process. Although program extraction has been developed by many authors, our system has a number of novel features designed to make it very easy to use and as close as possible to ordinary mathematical terminology and practice. These features include 1. the use of Henkin's technique to reduce higher-order logic to many-sorted (first-order) logic; 2. the free use of new rules for induction subject to certain conditions; 3. the extensive use of previously programmed (total, recursive) functions; 4. the use of templates to make the reasoning much closer to normal mathematical proofs and 5. a conceptual distinction between the computational type theory (for representing programs)and the logical type theory (for reasoning about programs). As an example of our system we give a constructive proof of the well known theorem that every graph of even parity, which is non-trivial in the sense that it does not consist of isolated vertices, has a cycle. Given such a graph as input, the extracted program produces a cycle as promised.

Quantified Analysis of the Leakage of Confidential Data

Basic information theory is used to analyse the amount of confidential information which may be leaked by programs written in a very simple imperative language. In particular, a detailed analysis is given of the possible leakage due to equality tests and if statements. The analysis is presented as a set of syntax-directed inference rules and can readily be automated.

The Requirements of Using Provenance in e-Science Experiments

In e-Science experiments, it is vital to record the experimental process for later use such as in interpreting results, verifying that the correct process took place or tracing where data came from. The process that led to some data is called the provenance of that data, and a provenance architecture is the software architecture for a system that will provide the necessary functionality to record, store and use process documentation. However, there has been little principled analysis of what is actually required of a provenance architecture, so it is impossible to determine the functionality they would ideally support. In this paper, we present use cases for a provenance architecture from current experiments in biology, chemistry, physics and computer science, and analyse the use cases to determine the technical requirements of a generic, technology and application-independent architecture. We propose an architecture that meets these requirements and evaluate a preliminary implementation by attempting to realise two of the use cases.