Polytypic values possess polykinded types (2000) [88 citations — 21 self]
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@INPROCEEDINGS{Hinze00polytypicvalues,author = {Ralf Hinze},
title = {Polytypic values possess polykinded types},
booktitle = {Science of Computer Programming},
year = {2000},
pages = {2--27},
publisher = {Springer-Verlag}
}
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Abstract:
Abstract. A polytypic value is one that is dened by induction on the structure of types. In Haskell types are assigned so-called kinds that distinguish between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to polytypic programming were restricted in that they only allowed to parameterize values by types of one xed kind. In this paper we show how to dene values that are indexed by types of arbitrary kinds. It turns out that these polytypic values possess types that are indexed by kinds. We present several examples that demonstrate that the additional exibility is useful in practice. One paradigmatic example is the mapping function, which describes the functorial action on arrows. A single polytypic denition yields mapping functions for datatypes of arbitrary kinds including rstand higher-order functors. Polytypic values enjoy polytypic properties. Using kind-indexed logical relations we prove among other things that the polytypic mapping function satises suitable generalizations of the functorial laws. 1
