Abstract

The main contribution of this paper is a partial type-checking algorithm for the system F and its use in a programming language like ML. We dene this system as an extension of the second-order -calculus (system F) verifying the preservation of type during computation (subject-reduction) for -reduction (this result fails for -reduction in system F). Our presentation is based on an original notion of sub-typing which includes all the handling of quantication rules. 1 Introduction. Motivation. Type systems have proved to be useful for many modern functional programming languages such as ML, Miranda, Haskell, . . . . In most cases, the basis of the type system is Milner's algorithm [12]. The main characteristic of these type systems is polymorphism which allows the programmer to write generic functions that can work on arguments of dierent types. However it is often insucient: polymorphic recursion, existential types or the state monad of Haskell are treated using specic exte...

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