Type theory should be able to handle its own meta-theory, both to justify its foundational
claims and to obtain a verified implementation. At the core of a type checker for intensional …

We present a graded modal type theory, a dependent type theory with grades that can be
used to enforce various properties of the code. The theory has Π-types, weak and strong Σ …

Proof checking consists of the automated verification of mathematical theories by first fully
formalizing the underlying primitive notions, the definitions, the axioms and the proofs. Then …

Graded type theories are an emerging paradigm for augmenting the reasoning power of
types with parameterizable, fine-grained analyses of program properties. There have been …

We propose a new language for writing programs with dependent types on top of the Coq
proof assistant. This language permits to establish a phase distinction between writing and …

Type theory is a fast-evolving field at the crossroads of logic, computer science and
mathematics. This gentle step-by-step introduction is ideal for graduate students and …

We propose a new collection of benchmark problems in mechanizing the metatheory of
programming languages, in order to compare and push the state of the art of proof …

Most dependently-typed programming languages either require that all expressions
terminate (eg Coq, Agda, and Epigram), or allow infinite loops but are inconsistent when …

This paper presents general syntactic conditions ensuring the strong normalisation and the
logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus …

The essential step of the formal verification of a proof-checker such as Coq is the verification
of its kernel: a type-checker for the Calculus of Inductive Constructions (CIC) which is its …