The Subtyping Problem for Second-Order Types Is Undecidable

Abstract

Among various forms of subtyping, one that seems to be quite fundamental for the analysis of polymorphic languages is induced by the containment relation of Mitchell [6]. An expression of a universal type, say ∀ασ , can be understood as having all types that are polymorphic instances of ∀α σ . If we choose the second-order polymorphic lambda-calculus as the basic language, then (taking into account the possibility of polymorphic generalization) we may formalize the notion of containment as ∀α1 · · · ∀αn σ ∀β1 · · · ∀βm σ (ρ1/α1, . . . , ρn/αn), (1)

DOI: 10.1006/inco.2001.2950

Cite this paper

@inproceedings{Tiuryn1996TheSP, title={The Subtyping Problem for Second-Order Types Is Undecidable}, author={Jerzy Tiuryn and Pawel Urzyczyn}, booktitle={Inf. Comput.}, year={1996} }