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Summary: On Typability for Rank-2 Intersection Types with Polymorphic Recursion
Tachio Terauchi
EECS Department
University of California, Berkeley
Alex Aiken
Computer Science Department
Stanford University
Abstract
We show that typability for a natural form of polymor-
phic recursive typing for rank-2 intersection types is unde-
cidable. Our proof involves characterizing typability as a
context free language (CFL) graph problem, which may be
of independent interest, and reduction from the bounded-
ness problem for Turing machines. We also show a property
of the type system which, in conjunction with the undecid-
ability result, disproves a misconception about the Milner-
Mycroft type system. We also show undecidability of a re-
lated program analysis problem.
1 Introduction
Among the interesting aspects of intersection types is the
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