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, 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.

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