## Anti-Symmetry of Higher-Order Subtyping (1999)

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Venue: | In Proceedings of the 8th Annual Conference on Computer Science Logic (CSL’99), J. Flum and M. RodríguezArtalejo, Eds. Springer-Verlag LNCS 1683 |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Compagnoni99anti-symmetryof,

author = {Adriana Compagnoni and Healfdene Goguen},

title = {Anti-Symmetry of Higher-Order Subtyping},

booktitle = {In Proceedings of the 8th Annual Conference on Computer Science Logic (CSL’99), J. Flum and M. RodríguezArtalejo, Eds. Springer-Verlag LNCS 1683},

year = {1999},

pages = {420--438}

}

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### Abstract

. This paper shows that the subtyping relation of a higherorder lambda calculus, F ! , is anti-symmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial order|reexive, transitive, and anti-symmetric up to -equality. While a subtyping relation is reexive and transitive by denition, anti-symmetry is a derived property. The result, which may seem obvious to the nonexpert, is technically challenging, and had been an open problem for almost a decade. In this context, typed operational semantics for subtyping oers a powerful new technology to solve the problem: of particular importance is our extended rule for the well-formedness of types with head variables. The paper also gives a presentation of F ! without a relation for -equality, apparently the rst such, and shows its equivalence with the traditional presentation. 1 Introduction Object-oriented programming languages such as Smalltalk, C++, Modula 3, and ...