Equational theories for inductive types Original Research Article

This paper provides characterisations of the equational theory of the PER model of a typed lambda calculus with inductive types. The characterisation may be cast as a full abstraction result; in other words, we show that the equations between terms valid in this model coincides with a certain syntactically defined equivalence relation. Along the way we give other characterisations of this equivalence; from below, from above, and from a domain model, a version of the Kreisel-Lacombe-Shoenfield theorem allows us to transfer the result from the domain model to the PER model.