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.

Recycling workflows and services through discovery and reuse

Scientific workflows are becoming a valuable tool for scientists to capture and automate e-Science procedures. Their success brings the opportunity to publish, share, reuse and repurpose this explicitly captured knowledge. Within the myGrid project, we have identified key resources that can be shared including complete workflows, fragments of workflows and constituent services. We have examined the alternative ways these can be described by their authors (and subsequent users), and developed a unified descriptive model to support their later discovery. By basing this model on existing standards, we have been able to extend existing Web Service and Semantic Web Service infrastructure whilst still supporting the specific needs of the e-Scientist. myGrid components enable a workflow life-cycle that extends beyond execution, to include discovery of previous relevant designs, reuse of those designs, and subsequent publication. Experience with example groups of scientists indicates that this cycle is valuable. The growing number of workflows and services mean more work is needed to support the user in effective ranking of search results, and to support the repurposing process.