Section: New Results
A logic for reasoning about logic specifications
As described in Section 3.3 , there has been a decade-long effort to design a logical framework for reasoning about logic specifications. Finally in 2008 and 2009 team members have reached what appears to be a natural culmination of this development. In particular, David Baelde's PhD  and Andrew Gacek's PhD thesis  provided rich analysis of how the -quantification can be related to fixed point definitions and their associated induction and co-induction inference rules. Baelde has concentrated on proving focusing-style results that are critical for proof automation and on a minimal generic interpretation of the -quantifier. Gacek has concentrated on a nominal generic interpretation of the -quantifier. We now understand the difference between these logics: the nominal approach resembles much more closely the approach developed by Pitts  .
Full proofs of the important meta-theory results of the logic in Gacek's thesis have been submitted for publication  . Gacek has also provided an implementation of his logic within the Abella prover that he has worked on as part of his PhD thesis.
We have developed extensive examples of our this new logic: significant examples taken from the -calculus have been published in  and the Abella distribution contains a large number of examples.