An Interactive Approach to Control in Proof Search: Preliminary Results

Logic programming, as well as functional programming, benefitted from a strong connection with logic and proof theory which allowed to provide formal tools to analyze programs through logical tools. However, this logical analysis fails when control operators are concerned. A informal way to understand this is that the role of those operators is mostly to prune the search space while the search space does not admit a good logical representation in proof-theoretical frameworks. Indeed, proof-search is concerned with partial proofs, proofs being constructed as well as failed searches whereas proo-theory (and in particular sequent calculus) is deals with completed proofs. Considering the strong relations between proof theory and programming languages theory, one may expect that when making progress in the understanding of the essence of proofs one shall also get better tools to understand computation. Ludics has been introduced about a decade ago by Girard as an interactive approach to logic. In a previous work, we used this framework to introduce a paradigm of interactive proof-search, where proof search in not specified by a sequent to be proved, but rather by a set of tests that shall be passed. In this short abstract, we discuss how interactive proof-search allow for an interactive analysis of control (or pruning) mechanisms in logic programming.