Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Infinite &lgr;-calculus and types
Theoretical Computer Science - Special issue: Gentzen
A Type Theoretical View of Böhm-Trees
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Data Types, Infinity and Equality in System AF2
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Normalisation is Insensible to \lambda-Term Identity or Difference
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Compositional characterisations of λ-terms using intersection types
Theoretical Computer Science - Mathematical foundations of computer science 2000
Untyped recursion schemes and infinite intersection types
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
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Klop's Problem is finding a type for characterizing hereditary head normalizing terms, that is, lambda-terms whose Böhm trees do not contain the bottom. This paper proves that this problem does not have any solution by showing that the set of those terms is not recursively enumerable. This paper also gives a best-possible solution by providing an intersection type system with a countably infinite set of types such that typing in all these types characterizes hereditary head normalizing terms. By using the same technique, this paper also shows that the set of lambda-terms normalizing by infinite reduction is not recursively enumerable.