Journal of Automated Reasoning

, Volume 12, Issue 3, pp 389–406 | Cite as

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

  • Zhenyu Qian
  • Tobias Nipkow


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.

Key words

simply typed λ-calculi subtypes reduction higher-order unification 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Zhenyu Qian
    • 1
  • Tobias Nipkow
    • 2
  1. 1.FB3 InformatikUniversität Bremen, Bibliothekstr.BremenGermany
  2. 2.Institut für InformatikTechnische Universität MünchenMunichGermany

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