Paper: Types for Hereditary Permutators (at LICS 2008)

Authors: 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}
  }