This papers extends the Nuprl proof assistant (a system representative of the class of extensional type theories a la Martin-Lof) with named exceptions and handlers, as well as a nominal fresh operator. Using these new features, we prove a version of Brouwer’s Continuity Principle for numbers. We also provide a simpler proof of a weaker version of this principle that only uses diverging terms. We prove these two principles in Nuprl’s meta-theory using our formalization of Nuprl in Coq and show how we can reflect these meta-theoretical results in the Nuprl theory as derivation rules. We also show that these additions preserve Nuprl’s key meta-theoretical properties, in particular consistency and the congruence of Howe’s computational equivalence relation. Using continuity and the fan theorem we prove important results of Intuitionistic Mathematics: Brouwer’s continuity theorem and bar induction on monotone bars.
Tue 19 Jan
|10:30 - 11:00|
|11:00 - 11:30|
Floris van DoornCarnegie Mellon University
|11:30 - 12:00|