In 1933 Gödel introduced a calculus of provability (also known as modal logic S4) and left
open the question of its exact intended semantics. In this paper we give a solution to this …

We present the linear type theory λΠ⊸ &⊤ as the formal basis for LLF, a conservative
extension of the logical framework LF. LLF combines the expressive power of dependent …

Starting from a denotational semantics of the eager untyped lambda-calculus with explicit
runtime errors, the standard collecting semantics is defined as specifying the strongest …

The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be
extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi …

While type soundness proofs are taught in every graduate PL class, the gap between
realistic languages and what is accessible to formal proofs is large. In the case of Scala, it …

Negative facts get a bad press. One reason for this is that it is not clear what negative facts
are. We provide a theory of negative facts on which they are no stranger than positive atomic …

This paper extends the termination proof techniques based on reduction orderings to a
higher-order setting, by adapting the recursive path ordering definition to terms of a typed …

For twenty years the Nuprl (“new pearl”) system has been used to develop software systems
and formal theories of computational mathematics. It has also been used to explore and …

We define a generic notion of cut that applies to many first-order theories. We prove a
generic cut elimination theorem showing that the cut elimination property holds for all …

We present an approach to enriching the type system of ML with a restricted form of
dependent types, where type index terms are required to be drawn from a given type index …