NII Technical Report (NII-2007-010E)：Types for Hereditary Permutators

This paper answers the open problem of finding a type system that characterizes hereditary permutators, which is the problem 20 in the TLCA list of open problems. First this paper shows that there does not exist such a type system by showing that the set of hereditary permutatos is not recursively enumerable. The set of positive primitive recursive functions is used to prove it. Secondly this paper gives a best-possible solution by providing a set of types such that a term has every type in the set if and only if the term is a hereditary permutator. Intersection types and the Omega type is used to handle infinite computation in lambda terms.