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.

Connecting Scientific Data to Scientific Experiments with Provenance

As scientific workflows and the data they operate on, grow in size and complexity, the task of defining how those workflows should execute (which resources to use, where the resources must be in readiness for processing etc.) becomes proportionally more difficult. While "workflow compilers", such as Pegasus, reduce this burden, a further problem arises: since specifying details of execution is now automatic, a workflow's results are harder to interpret, as they are partly due to specifics of execution. By automating steps between the experiment design and its results, we lose the connection between them, hindering interpretation of results. To reconnect the scientific data with the original experiment, we argue that scientists should have access to the full provenance of their data, including not only parameters, inputs and intermediary data, but also the abstract experiment, refined into a concrete execution by the "workflow compiler". In this paper, we describe preliminary work on adapting Pegasus to capture the process of workflow refinement in the PASOA provenance system.