Towards a Practical Programming Language Based on the Polymorphic Lambda Calculus

The value of polymorphism in programming languages has been demonstrated by languages such as ML [19]. Recent e cient implementations of ML have shown that a language with implicit polymorphism can be practical [1]. The core of ML's type system is limited, however, by the fact that only instances of polymorphic functions may be passed as arguments to other functions, but not the polymorphic functions themselves. This has serious practical consequences, particularly for modular programming. For this reason, ML incorporates the generic let construct which cannot be de ned in terms of -abstraction and other extensions to the basic Hindley-Milner type system [12, 18], such as the module system [16]. More powerful type systems allowing explicit quanti cation over types, such as the second-order polymorphic -calculus [11, 27] (which we refer to as F 2 ), are free of such limitations. Thus, it is natural to ask whether they too can form the basis for practical programming languages.