Reduction and unification in Lambda calculi with subtypes

  • Tobias NipkowEmail author
  • Zhenyu QianEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 607)


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, i.e. “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.

A generic algorithm for pre-unification modulo βη-conversion and an arbitrary subtype relation is presented. Furthermore it is shown that unification w.r.t. any subtype relation is universal.


Normal Form Base Type Unification Algorithm Critical Pair Type Inference 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  1. 1.Institut für InformatikTU MünchenMünchen 2Germany
  2. 2.FB InformatikUniversität BremenBremen 33Germany

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