Intersection Types and Counting

Paweł Parys
(University of Warsaw)

We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of a derivation of a type for this lambda-term, in this type system.

Our approach is presented in the particular case of the language finiteness problem for nondeterministic higher-order recursion schemes (HORSes): given a nondeterministic HORS, decide whether the set of all finite trees generated by this HORS is finite. We give a type system such that the HORS can generate a tree of an arbitrarily large finite size if and only if in the type system we can obtain derivations that are arbitrarily large, in an appropriate sense; the latter condition can be easily decided.

In Naoki Kobayashi: Proceedings Eighth Workshop on Intersection Types and Related Systems (ITRS 2016), Porto, Portugal, 26th June 2016, Electronic Proceedings in Theoretical Computer Science 242, pp. 48–63.
Published: 7th February 2017.

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