功能性parametricity

[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science Pub Date : 1992-01-01 DOI:10.1109/LICS.1992.185555

P. Freyd, E. Robinson, G. Rosolini

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引用次数: 0

摘要

作者考虑将参数化类型视为从某个参数化范畴到另一个类型范畴的任意函子，并将元素语义作为自然变换。他们表明，在合理的假设下，这只有在参数化范畴是群形时才有可能。这暗示了半参数形式多态性的语义。他们讨论了在PER模型中对这种形式的参数的解释，并表明它与表面上由非自然性推导出来的更强的形式是一致的

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Functional parametricity

The authors consider the idea of treating a parametrized type as an arbitrary functor from some parametrizing category to a category of types, and giving elements semantics as natural transformations. They show that under reasonable hypotheses this is only possible when the parametrizing category is a groupoid. This suggests a semantics for a semiparametric form of polymorphism. They discuss the interpretation of this form of parametricity in a PER model, and show that it coincides with the ostensibly stronger form derived from dinaturality.<>

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[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science

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