Colloquium Details
A Proof Pearl with the Fan Theorem and Bar Induction:
Walking through infinite trees with mixed induction and coinduction
| Author: | Keiko Nakata Tallinn University of Technology, Estonia |
|---|---|
| Date: | November 03, 2011 |
| Time: | 15:30 |
| Location: | 220 Deschutes |
| Host: | Zena Ariola |
Abstract
We study temporal properties over infinite binary red-blue trees in the setting of constructive type theory. We consider several familiar path-based properties, typical to linear-time and branching-time temporal logics like LTL and CTL*, and the corresponding tree-based properties, in the spirit of the modal mu-calculus. We conduct a systematic study of the relationships of the path-based and tree-based versions of "eventually always blueness" and mixed inductive-coinductive "almost always blueness" and arrive at a diagram relating these properties to each other in terms of implications that hold either unconditionally or under specific assumptions (Weak Continuity for Numbers, the Fan Theorem, Lesser Principle of Omniscience, Bar Induction).
We have fully formalized our development with the Coq proof assistant. The work will appear at APLAS 2011.
(Joint work with Marc Bezem and Tarmo Uustalu)
Biography
Dr. Nakata is a senior researcher at Institute of Cybernetics, Tallinn University of Technology, Estonia. Her work is concerned around programming language semantics and constructive mathematics. She received the PhD degree in 2007 from the Research Institute for Mathematical Sciences, Kyoto University, Japan.