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# henglein96a

Fritz Henglein. Syntactic Properties of Polymorphic Subtyping. TOPPS Report D-293 DIKU, University of Copenhagen, May 1996.

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## Abstract

In this paper we study polymorphic subtyping, where the subtyping theory is \emph{not} required to be structural. We observe that type schemes with subtyping qualifications are strictly necessary in order to obtain principal typing. We identify a new instance relation on typing judgements, the \emph{halbstark} relation. It is a hybrid, lying in strength between Mitchell's original instance relation and Fuh and Mishra's lazy instance relation. We present a sound and complete type inference algorithm in the style of Milner's Algorithm W. The significance of the halbstark relation emerges from the fact that the algorithm is \emph{generic} in that it admits replacing typing judgements by \emph{any} halbstark-equivalent judgements at any point. This provides a generalized correctness argument for Algorithm W independent of any particular constraint simplification strategy chosen. Finally, we show that polymorphic typing judgements are preserved under let-unfolding, let-folding, and $\eta$-reduction, but not in general under $\beta$-reduction. The latter holds, though, if the subtyping discipline has the \emph{decomposition} property, which says that two function types are in a subtype relation only if their domain and range types are in the appropriate contra-/covariant subtype relation

Fritz Henglein

## BibTex Reference

@TechReport{henglein96a,
Author = {Henglein, Fritz},
Title = {Syntactic Properties of Polymorphic Subtyping},
Institution = {DIKU, University of Copenhagen},
Address = {Universitetsparken 1, DK-2100 Copenhagen, Denmark},
Month = {May},
Year = {1996}
}

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