Intersection Types and Counting [article]

Paweł Parys
2017 arXiv   pre-print
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 λ-term corresponds to some property of a derivation of a type for this λ-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
more » ... ll 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.
arXiv:1701.05303v1 fatcat:oz3y6fo3pja6viylgr2tnsxn2y