## Semantics of Parametric Polymorphism in Imperative Programming Languages

### BibTeX

@MISC{Dunphy_semanticsof,

author = {Brian P. Dunphy and Uday S. Reddy},

title = {Semantics of Parametric Polymorphism in Imperative Programming Languages},

year = {}

}

### OpenURL

### Abstract

Ada and Modula-3 have included facilities for parametric polymorphism and, more recently, C++ and Java have also added similar facilities. In this paper, we examine the issues of defining denotational semantics for imperative programming languages with polymorphism. We use the framework of reflexive graphs of categories previously developed for a general axiomatization of relational parametricity constraints implicit in polymorphic functions. We specialize it to the context of imperative programming languages, which in turn involve parametricity constraints implicit in local variables. The two levels of parametricity inherent in such languages can be captured in a pleasing way in ”higher-order ” reflexive graphs. 1

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Citation Context ...yer. To carry out such sophisticated constructions, one needs a suitably general mathematical theory of functors enriched with relational parametricity. Such a theory was defined in our previous work =-=[8, 9]-=- based on O’Hearn and Tennent’s reflexive graph categories [20]. We make essential use of this framework. After defining the constructions, we were surprise to discover that the traditional Reynolds-O... |

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