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...
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 applicatio...
Gilles Barthe, Horatiu Cirstea, Claude Kirchner, L...
Abstract. The logical and operational aspects of rewriting logic as a logical framework are tested and illustrated in detail by representing pure type systems as object logics. Mor...
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 ...