Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

Prototype Generation from Ontology Charts

Semantic Analysis is a business analysis method designed to capture system requirements. While these requirements may be represented as text, the method also advocates the use of Ontology Charts to formally denote the system's required roles, relationships and forms of communication. Following model driven engineering techniques, Ontology Charts can be transformed to temporal Database schemas, class diagrams and component diagrams, which can then be used to produce software systems. A nice property of these transformations is that resulting system design models lend themselves to complicated extensions that do not require changes to the design models. For example, resulting databases can be extended with new types of data without the need to modify the database schema of the legacy system. Semantic Analysis is not widely used in software engineering, so there is a lack of experts in the field and no design patterns are available. This make it difficult for the analysts to pass organizational knowledge to the engineers. This study describes an implementation that is readily usable by engineers, which includes an automated technique that can produce a prototype from an Ontology Chart. The use of such tools should enable developers to make use of Semantic Analysis with minimal expertise of ontologies and MDA.

Modelling the Provenance of Data in Autonomous Systems

Determining the provenance of data, i.e. the process that led to that data, is vital in many disciplines. For example, in science, the process that produced a given result must be demonstrably rigorous for the result to be deemed reliable. A provenance system supports applications in recording adequate documentation about process executions to answer queries regarding provenance, and provides functionality to perform those queries. Several provenance systems are being developed, but all focus on systems in which the components are textitreactive, for example Web Services that act on the basis of a request, job submission system, etc. This limitation means that questions regarding the motives of autonomous actors, or textitagents, in such systems remain unanswerable in the general case. Such questions include: who was ultimately responsible for a given effect, what was their reason for initiating the process and does the effect of a process match what was intended to occur by those initiating the process? In this paper, we address this limitation by integrating two solutions: a generic, re-usable framework for representing the provenance of data in service-oriented architectures and a model for describing the goal-oriented delegation and engagement of agents in multi-agent systems. Using these solutions, we present algorithms to answer common questions regarding responsibility and success of a process and evaluate the approach with a simulated healthcare example.