Abstract. We study subtyping in first-order object calculi with respect to thelogical semantics obtained by identifying terms that satisfy the same set of predicates, as formalized through an assignment system. It is shown that equality inthe full first-order &-calculus is modeled by this notion, which is included in aMorris-style contextual equivalence. 1 Introduction Subtyping is a prominent feature of type-theoretic foundation of object oriented pro-gramming languages. The basic idea is expressed by subsumption: any piece of code of type A can masquerade as a code of type B whenever A is a subtype of B, written A<: B.In typed calculi, equations are stated amongst terms of the same type; when term
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