Formalising mathematics in dependent type theory often requires to represent sets as
setoids, ie types with an explicit equality relation. This paper surveys some possible …

A fertile field of research in theoretical computer science investigates the representation of
general recursive functions in intensional type theories. Among the most successful …

We show how to write generic programs and proofs in Martin-Löf type theory. To this end we
consider several extensions of Martin-Löf's logical framework for dependent types. Each …

Constructive type theory is an expressive programming language in which both algorithms
and proofs can be represented. A limitation of constructive type theory as a programming …

Computer programs are ubiquitous. As we rely on computers more and more in all aspects
of daily life, it becomes more important to minimise errors in computer software; it is …

It is well known that mathematical proofs often contain (abstract) algorithms, but although
these algorithms can be understood by a human, it still takes a lot of time and effort to …

In the philosophy of mathematics one speaks about Formalism, Logicism, Platonism and
Intuitionism. Actually one should add also Calculism. These foundational views can be given …

In this thesis we examine a specific perspective to the issue of computation We arc
interested in certified computation; this is a computation process together with a certificate of …

Partial functions and choice principles present difficulties from constructive points of view,
but these difficulties can be dealt with in natural ways. That is the thesis to be defended in …

We develop a general tool to formalize and reason about languages expressed using higher—
order abstract syntax in a proof—tool based on type theory (Coq). A language is specified by …