Floating point operations are fast, but require continuous effort on the part of the user in
order to ensure that the results are correct. This burden can be shifted away from the user by …

The paper describes the refinement algorithm for the Calculus of (Co) Inductive
Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement …

In this article, we show how one can formalise in type theory mathematical objects, for which
dependent types are usually deemed unavoidable, using only simple types. We outline a …

This is the fourth in a series of papers extending Martin-L\" of's meaning explanation of
dependent type theory to higher-dimensional types. In this installment, we show how to …

Nakano's later modality can be used to specify and define recursive functions which are
causal or synchronous; in concert with a notion of clock variable, it is possible to also …

Floating point operations are fast, but require continuous effort on the part of the user in
order to ensure that the results are correct. This burden can be shifted away from the user by …

RedPRL is an experimental proof assistant based on Cartesian cubical computational type
theory, a new type theory for higher-dimensional constructions inspired by homotopy type …

We contribute a general apparatus for dependent tactic-based proof refinement in the LCF
tradition, in which the statements of subgoals may express a dependency on the proofs of …

This is the third in a series of papers extending Martin-L\" of's meaning explanations of
dependent type theory to a Cartesian cubical realizability framework that accounts for higher …

When implementing a logical system in a programming language, it is important to
understand and minimize the size of the portion of this system which must be “trusted”, ie on …