We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of the shape A : B, our systems just have judgments of the ...
Herman Geuvers, Robbert Krebbers, James McKinna, F...
—There are two usual ways to describe equality in a dependent typing system, one that uses an external notion of computation like beta-reduction, and one that introduces a typed ...
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-calcu...
We introduce Erasure Pure Type Systems, an extension to Pure Type Systems with an erasure semantics centered around a type constructor indicating parametric polymorphism. The eras...
Pure Pattern Type Systems (P2 TS) combine in a unified setting the capabilities of rewriting and λ-calculus. Their type systems, adapted from Barendregt’s λ-cube, are especial...