The Curry-Howard isomorphism states an amazing correspondence between systems of
formal logic as encountered in proof theory and computational calculi as found in type …

We introduce a new framework of algebraic pure type systems in which we consider rewrite
rules as lambda terms with patterns and rewrite rule application as abstraction application …

A typed model of strategic term rewriting is developed. The key innovation is that generic
traversal is covered. To this end, we define a typed rewriting calculus S′ γ. The calculus …

In this paper, we present Λ∧ t, a fully typed λ-calculus based on the intersection-type system
discipline, which is a counterpart àla Church of the type assignment system as invented by …

Dependent types are a key feature of the proof assistants based on the Curry-Howard
isomorphism. It is well known that this correspondence can be extended to classical logic by …

This thesis focused on the computational content of classical proofs, and specifically on
proofs with side-effects and Krivine classical realizability. The manuscript is divided in three …

These notes comprise the lecture “Introduction to Type Theory” that I gave at the Alpha
Lernet Summer School in Piriapolis, Uruguay in February 2008. The lecture was meant as …

For nested or heterogeneous datatypes, terminating recursion schemes considered so far
have been instances of iteration, excluding efficient definitions of fixed-point unfolding. Two …

Positive recursive (fixpoint) types can be added to the polymorphic (Church-style) lambda
calculus λ2 (System F) in several different ways, depending on the choice of the elimination …

Functional programming languages often feature mechanisms that involve complex
computations at the level of types. These mechanisms can be analyzed uniformly in the …