The Undecidability of Mitchell's Subtyping Relationship
نویسنده
چکیده
Mitchell de ned and axiomatized a subtyping relationship (also known as containment, coercibility, or subsumption) over the types of System F (with \!" and \8"). This subtyping relationship is quite simple and does not involve bounded quanti cation. Tiuryn and Urzyczyn quite recently proved this subtyping relationship to be undecidable. This paper supplies a new undecidability proof for this subtyping relationship. First, a new syntax-directed axiomatization of the subtyping relationship is dened. Then, this axiomatization is used to prove a reduction from the undecidable problem of semi-uni cation to subtyping. The undecidability of subtyping implies the undecidability of type checking for System F extended with Mitchell's subtyping, also known as \F plus eta".
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Typability is Undecidable for F+Eta
System F is the well-known polymorphically-typed -calculus with universal quanti ers (\8"). F+ is System F extended with the eta rule, which says that if termM can be given type and M -reduces to N , then N can also be given the type . Adding the eta rule to System F is equivalent to adding the subsumption rule using the subtyping (\containment") relation that Mitchell de ned and axiomatized [M...
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