## Paper: Types for Hereditary Permutators (at LICS 2008)

**Makoto Tatsuta**

### Abstract

This paper answers the open problem of finding a type system that characterizes hereditary permutators. First this paper shows that there does not exist such a type system by showing that the set of hereditary permutators 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 countably infinite set of types such that a term has every type in the set if and only if the term is a hereditary permutator. By the same technique for the first claim, this paper also shows that a set of normalizing terms in infinite lambda-calculus is not recursively enumerable if it contains some term having a computable infinite path,and shows the set of streams is not recursively enumerable.

### BibTeX

@InProceedings{Tatsuta-TypesforHereditaryP, author = {Makoto Tatsuta}, title = {Types for Hereditary Permutators}, booktitle = {Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008)}, year = {2008}, month = {June}, pages = {83--92}, location = {Pittsburgh, PA, USA}, publisher = {IEEE Computer Society Press} }