A Unified View of Programming Schemas and Proof Methods

The objectives of this investigation are (a) to study the similarities between proof planning and schema-guided programming (i.e., between proof methods and programming schemas), and (b) to express the latter in terms of the former, so as to be able to use any proof planner as an existing implementation platform for developing the first schema-guided developer of (standard or constraint) logic programs. This approach has the pleasant side-effect that any proof obligations, such as verifications, matchings, or simplifications, arising during schema-guided programming can also be handled within the plan-guided automated theorem prover. At the same time, this approach reveals an opportunity for identifying and integrating useful heuristics of when and how to apply what programming schema, which dimension had hitherto been much neglected for programming schemas, but not for proof methods. We will first revisit plan-guided theorem proving [2] (in Section 2) and then introduce the notion of schema-guided programming, as a generalisation of schema-guided program synthesis (whether through specification decomposition [25, 10] or through pre-computation for a specification schema [26, 12]) and of schema-guided program transformation [27, 6, 23] (in Section 3). This provides us with a framework [22] for unifying plan-guided theorem proving and schema-guided programming, and allows us thus to encode programming schemas as proof methods (in Section 4). Finally, we outline some first heuristics of when and how to apply what programming schema (in Section 5), as such heuristics naturally fit within this encoding. In the conclusion (Section 6), we summarise and sketch how to continue this research.