The Subtyping Problem for Second-Order Types Is Undecidable


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} }