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Reduction and unification in lambda calculi with a general notion of subtype

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Abstract

Reduction, equality, and unification are studied for a family of simply typed λ-calculi with subtypes. The subtype relation is required to relate base types only to base types and to satisfy some order-theoretic conditions. Constants are required to have a least type, that is, ‘no overloading’. We define the usual β and a subtype-dependent η-reduction. These are related to a typed equality relation and shown to be confluent in a certain sense. We present a generic algorithm for preunification modulo βη-conversion and an arbitrary subtype relation. Furthermore it is shown that unification with respect to any subtype relation is universal.

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Authors and Affiliations

  1. FB3 Informatik, Universität Bremen, Bibliothekstr., 28359, Bremen, Germany

    Zhenyu Qian

  2. Institut für Informatik, Technische Universität München, Arcisstr. 21, 80290, Munich, Germany

    Tobias Nipkow

Authors
  1. Zhenyu Qian
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Qian, Z., Nipkow, T. Reduction and unification in lambda calculi with a general notion of subtype. J Autom Reasoning 12, 389–406 (1994). https://doi.org/10.1007/BF00885767

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  • DOI: https://doi.org/10.1007/BF00885767

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