International Workshop on
Proof-Search in Type Theories

Monday 3rd August 2009

Joint event with LFMTP, Sunday 2nd August 2009

affiliated to CADE 2009
Montreal, Canada

Tutorial (Monday 3rd August): Wilmer Ricciotti, University of Bologna
Proof-search in Matita
Invited talk (Sunday 2nd August): Gilles Dowek, Ecole Polytechnique
How Can We Prove That a Proof Method is not an Instance of Another?

Workshop organisers:
St├ęphane LENGRAND,CNRS
Dale MILLER,INRIA

The PSTT workshop resumes a series of workshops on Proof Search in Type Theoretic Languages, in light of the progress that has been made over the last decade in e.g. the development of proof assistants or our understanding of proof theory.

The declarative approach to programming has evolved two paradigms that are based on different aspects of the theories of proofs and types: Proof normalisation provides a foundation for functional programming and type systems --on which numerous proof assistants are based, while proof search provides a foundation for logic programming and other areas of automated deduction. On the one hand, proof search mechanisms and their automation are decisive features of proof assitants that have much to gain from a proper understanding and formalisation. On the other hand, the framework of logic programming has also extended to more expressive logics and more complex data structures, e.g. with bindings.

Better specifying the proof search mechanisms in type theories is thus a key concern that brings both approaches forward, and closer together. This concern involves a wide range of issues and techniques (some of which directly arising from implementation) that both approaches share --or could share, and that form the scope of this workshop.

TOPICS:
Papers are solicited on topics including, but not limited to:
- proof search strategies and tactics, complexity & completeness,
- tactics specification language,
- properties of inference systems, invertibility, polarity of connectives,
- focusing, normal forms for proofs,
- proof-term representation,
- meta-variables, representation of partial proofs,
- searching for proofs by induction, search for invariants,
- unification,
- variable binding, scoping management and freshness
- logic programming and other paradigms based on proof search, termination & computational expressivity,
- deduction-modulo, deduction vs. computation during search,
- using failure in proof search,
- model checking as deduction,
- user interaction and interfaces,
- systems implementing any of the above.