School of Computer Science; Carnegie Mellon University
SVM HeaderParse 0.2
Pittsburgh, PA 15213-3890, USA
SVM HeaderParse 0.1
F is a typed -calculus with subtyping and bounded second-order polymorphism. First proposed by Cardelli and Wegner, it has been widely studied as a core calculus for type systems with subtyping. Curien and Ghelli proved the partial correctness of a recursive procedure for computing minimal types of F terms and showed that the termination of this procedure is equivalent to the termination of its major component, a procedure for checking the subtype relation between F types. This procedure was thought to terminate on all inputs, but the discovery of a subtle bug in a purported proof of this claim recently reopened the question of the decidability of subtyping, and hence of typechecking. This question is settled here in the negative, using a reduction from the halting problem for two-counter Turing machines to show that the subtype relation of F is undecidable. 1 Introduction The notion of bounded quantification was introduced by Cardelli and Wegner  in the language Fun. Based on i...