A Unified View of Program Schemas and Proof Methods

Both proof planning and schema-guided program synthesis can be seen as a recursive problem decomposition process followed by a recursive solution composition process, with problems being either conjectures or specifications, and solutions being either tactics or programs. We thus develop a unified view of these two activities. This approach reveals an opportunity for identifying and integrating useful heuristics of when and how to apply what program schema, which dimension had hitherto been much neglected for program schemas, but not for proof methods, and allows us to encode program schemas as proof planning methods, so as to be able to use a proof planner (in particular Clam) as an implementation platform for developing the first schema-guided synthesiser of (standard or constraint) logic programs. This approach has the pleasant side-effect that any proof obligations — such as verification conditions, matchings, or simplifications — that arise during schema-guided program synthesis can also be handled within Clam.