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We study the problem of type inference for a family of polymorphic type disciplines containing the power of Core-ML. This family comprises all levels of the strati cation of the second-order lambda-calculus by \ r a n k " o f t ypes. We s h o w that typability is an undecidable problem at every rank k 3 of this strati cation. While it was already known that typability is decidable at rank 2, no direct and easy-to-implement algorithm was available. To design such an algorithm, we d e v elop adoi:10.1145/182409.182456 dblp:conf/lfp/KfouryW94 fatcat:b56pwql3qzgldahjpzvfdbetky