Abstract
We present a general method for proving properties of typed lambda terms. This method is obtained by introducing a semantic notion of realizability which uses the notion of a cover algebra (as in abstract sheaf theory). For this, we introduce a new class of semantic structures equipped with preorders, called preapplicative structures. In this framework, a general realizability theorem can be shown. Applying this theorem to the special case of the term model, yields a general theorem for proving properties of typed lambda terms, in particular, strong normalization and confluence. This approach clarifies the reducibility method by showing that the closure conditions on candidates of reducibility can be viewed as sheaf conditions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gallier, J. (1993). Proving properties of typed lambda terms: Realizability, covers, and sheaves. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-662-21551-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56868-1
Online ISBN: 978-3-662-21551-7
eBook Packages: Springer Book Archive