Axioms and Decidability for Type Isomorphism in the Presence of Sums

Danko Ilik (1)

1 PARSIFAL - Proof search and reasoning with logic specifications

We consider the problem of characterizing isomorphisms of types, or, equivalently, constructive cardinality of sets, in the simultaneous presence of disjoint unions, Cartesian products, and exponentials. Mostly relying on results about polynomials with exponentiation that have not been used in our context, we derive: that the usual finite axiomatization known as High-School Identities (HSI) is complete for a significant subclass of types; that it is decidable for that subclass when two types are isomorphic; that, for the whole of the set of types, a recursive extension of the axioms of HSI exists that is complete; and that, for the whole of the set of types, the question as to whether two types are isomorphic is decidable when base types are to be interpreted as finite sets. We also point out certain related open problems.

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]; Logique [math.LO]

Danko Ilik. Axioms and Decidability for Type Isomorphism in the Presence of Sums. CSL-LICS '14 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), SIGLOG ACM Special Interest Group on Logic and Computation; EACSL European Association for Computer Science Logic; IEEE-CS - DATC IEEE Computer Society, Jul 2014, Vienna, Austria. ⟨10.1145/2603088.2603115⟩. ⟨hal-00991147⟩