Weak normalization for the simply-typed Î»-calculus is proven in Twelf, an implementation of the Edinburgh Logical Framework. Since due to proof-theoretical restrictions Twelf Taitâ€™s computabilityâ€¦ (More)

We present a new strong normalisation proof for a Î»-calculus with interleaving strictly positive inductive types Î» which avoids the use of impredicative reasoning, i.e., the theorem ofâ€¦ (More)

We present a normalization-by-evaluation (NbE) algorithm for System F with Î²Î·-equality, the simplest impredicative type theory with computation on the type level. Values are kept abstract andâ€¦ (More)

A type theoretic programming language is introduced that is based on lambda calculus with coproducts, products and inductive types, and additionally allows the deenition of recursive functions in theâ€¦ (More)

Andreas Abel Andreas Bauer Kristina Kelber Wolfgang Schwarz Technical University Dresden Faculty of Electrical Engineering / IEE Mommsenstra e 13, 01062 Dresden, Germany fabel,â€¦ (More)

Higher-order logical frameworks provide a powerful technology to reason about object languages with binders. This will be demonstrated for the case of the Î»Î¼-calculus with two different binders whichâ€¦ (More)

We consider the Calculus of Constructions with typed beta-eta equality and an algorithm which computes long normal forms. The normalization algorithm evaluates terms into a semantic domain, andâ€¦ (More)

A general version of the fundamental theorem for System F is presented which can be instantiated to obtain proofs of weak Î²and Î²Î·-normalization and normalization by evaluation.

In this paper, we study strong normalization of a core language based on System F-omega which supports programming with finite and infinite structures. Building on our prior work, finite data such asâ€¦ (More)

We investigate the intersection type system of Coquand and Spiwack with rewrite rules and natural numbers and give an elementary proof of strong normalization which can be formalized in a weakâ€¦ (More)