On Typability for Rank-2 Intersection Types with Polymorphic Recursion

Authors:
Tachio Terauchi;Alex Aiken
Affiliations:
University of California, Berkeley, USA;Stanford University, USA
Venue:
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Year:
2006

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Cited 3

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Strict intersection types for the Lambda Calculus

ACM Computing Surveys (CSUR)
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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Abstract

We show that typability for a natural form of polymorphic recursive typing for rank-2 intersection types is undecidable. Our proof involves characterizing typability as a context free language (CFL) graph problem, which may be of independent interest, and reduction from the boundedness problem for Turing machines. We also show a property of the type system which, in conjunction with the undecidability result, disproves a misconception about the Milner- Mycroft type system. We also show undecidability of a related program analysis problem.