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## Section: Research Program

### Inductive and co-inductive reasoning

The team has spent a number of years in designing a strong new logic that can be used to reason (inductively and co-inductively) on syntactic expressions containing bindings. This work is based on earlier work by McDowell, Miller, and Tiu [66] [65] [71] [77] , and on more recent work by Gacek, Miller, and Nadathur [3] [52] . The Parsifal team, along with our colleagues in Minneapolis, Canberra, Singapore, and Cachen, have been building two tools that exploit the novel features of this logic. These two systems are the following.

• Abella, which is an interactive theorem prover for the full logic.

• Bedwyr, which is a model checker for the “finite” part of the logic.

We have used these systems to provide formalize reasoning of a number of complex formal systems, ranging from programming languages to the $\lambda$-calculus and $\pi$-calculus.

During 2014, the Abella system has been extended with a number of new features. A number of new significant examples have been implemented in Abella and an extensive tutorial for it has been written [31] .