Abstract

Constructor subtyping is a form of subtyping in which an inductive type is viewed as a subtype of another inductive type τ if τ has more constructors than. As suggested in [5, 12], its (potential) uses include proof assistants and functional programming languages. In this paper, we introduce and study the properties of a simply typed λ-calculus with record types and datatypes, and which supports record subtyping and constructor subtyping. In the first part of the paper, we show that the calculus is confluent and strongly normalizing. In the second part of the paper, we show that the calculus admits a well-behaved theory of canonical inhabitants, provided one adopts expansive extensionality rules, including-expansion, surjective pairing, and a suitable expansion rule for datatypes. Finally, in the third part of the paper, we extend our calculus with unbounded recursion and show that confluence is preserved.

Citations