## Section: Software

### Abella

Participants : Kaustuv Chaudhuri [correspondant] , Matteo Cimini, Dale Miller.

Abella is an interactive theorem prover based on the two-level logic logic approach. It consists of a sophisticated reasoning logic that supports induction, co-induction, and generic reasoning, and a specification logic that is based on logic programming. Abella was initially designed to reason about simple second-order Lambda Prolog programs, which is sufficient for the computational specifications.

During 2012, as part of the RAPT Associated Team, Chaudhuri and Yuting Wang (intern from Univ. Minnesota) have been working on extending the expressive power of both levels of the Abella system. The following modifications have been made.

We have extended the specification logic to support the full Lambda Prolog, which can be used to provide succinct higher-order specifications that tend to be unnatural and difficult to reason about with only second-order Lambda Prolog programs.

We have extended the type system of Abella from simple types to parametrically polymorphic types. This is a significant improvement in the user-friendliness of the system as a lot of code does not have to be manually monomorphised and duplicated any more.

We have experimented with extending the type system of Abella even further to higher-order predicate quantification. The theoretical basis of this work is a part of ongoing research, although we already have a number of examples of practical benefits of this extension.

Finally, several improvements have been made to Abella's proof language to make the proofs more robust and reusable. We intend to make a more drastic change to the proof language in the future that will make proofs more declarative and high level.

The core development of Abella has also been centralized, with a single canonical repository and a new web-page: http://abella-prover.org . These resources are managed jointly by members of Parsifal and our colleagues at the University of Minnesota.

The next version of Abella, version 2.0, is in beta testing with expected release early in 2013.