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A Model for Formal Parametric Polymorphism: A PER Interpretation for System R

Summary: A Model for Formal Parametric Polymorphism:
A PER Interpretation for System R
Roberto Bellucci 1;3 , Mart'in Abadi 2 , Pierre­Louis Curien 1
1 LIENS, CNRS ­ D'epartement de Math'ematiques et Informatique de l'Ecole Normale Sup'erieure
45, rue d'Ulm, 75005 Paris, France
2 Digital Equipment Corporation, Systems Research Center, 130 Lytton Avenue, Palo Alto,
California 94301, USA
3 Dipartimento di Matematica, Via del Capitano 15, 53100 Siena, Italy
Abstract. System R is an extension of system F that formalizes Reynolds' notion of
relational parametricity. In system R, considerably more –­terms can be proved equal
than in system F : for example, the encoded weak products of F are strong products
in R. Also, many ``theorems for free'' `a la Wadler can be proved formally in R. In this
paper we describe a semantics for system R. As a first step, we give a precise and general
reconstruction of the per model of system F of Bainbridge et al., presenting it as a
categorical model in the sense of Seely. Then we interpret system R in this model.
1 From Models of F to Models of R
The principle of parametricity has gone through many avatars. First Strachey distinguished
parametric polymorphism and ad hoc polymorphism [Str67]. Strachey described parametric
polymorphism as the pure polymorphism of functions like append, which works on lists of any
type uniformly. In contrast, a function like print examines and branches on the types of its


Source: Abadi, Martín - Department of Computer Science, University of California at Santa Cruz


Collections: Computer Technologies and Information Sciences