Seminars

Speaker: Pierre Pradic — perso.ens-lyon.fr/pierre.pradic/

Title: Synthesizing Nested Relational Queries from Implicit Specifications

Abstract:
Derived datasets can be defined implicitly or explicitly. An implicit
definition (of dataset O in terms of datasets I⃗ ) is a logical specification
involving the source data I⃗ and the interface data O. It is a valid definition
of O in terms of I⃗ , if any two models of the specification agreeing on I⃗
agree on O. In contrast, an explicit definition is a query that produces O from
I⃗ . Variants of Beth's theorem state that one can convert implicit definitions
to explicit ones. Further, this conversion can be done effectively given a
proof witnessing implicit definability in a suitable proof system. In this
talk, I will discuss an analogous effective implicit-to-explicit result for
nested relations: implicit definitions, given in the natural logic for nested
relations, can be effectively converted to explicit definitions in the nested
relational calculus NRC.

I will first spend some time explaining what NRC is and what logic we use to
describe implicit definitions of nested queries. Then I will present the
results obtained in our papers, attempt to give some intuitions on the proof of
the main theorem and say a few words on in particular the proof-theoretic
techniques and concerns that come up (namely, cut-elimination and focussing)
and how this can impact the complexity of extracting explicit definitions from
proofs of implicit definability. Then if time allows I will discuss a more
general model-theoretic result that we first used to give a non-constructive
proof of our theorem, and some ideas that we have towards making it
constructive and bounding the complexity of extracting explicit definitions.

This is Joint work with Michael Benedikt and Christoph Wenhard. The main
results I will be discussing were written up in
arxiv.org/abs/2005.06503 and arxiv.org/abs/2209.08299.