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Coinductive axiomatization of recursive type equality and subtyping

Brandt M., Henglein F.

Fundamenta Informaticae

1998

Vol. 33, nr 4

309-338

We present new sound and complete axiomatizations of type equality and subtype inequality for a first-order type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle). It states that from A,Pý P one may deduce Aý P, where P is either a type equality t = t1 or type containment t