Type Checking Higher - Order Polymorphic Multi - MethodsFran

We present a new predicative and decidable type system , called ML , suitable for languages that integrate functional programming and parametric polymorphism in the tradition of ML 21, 28], and class-based object-oriented programming and higher-order multi-methods in the tradition of CLOS 12]. Instead of using ex-tensible records as a foundation for object-oriented extensions of functional languages, we propose to rein-terpret ML datatype declarations as abstract and concrete class declarations, and to replace pattern matching on run-time values by dynamic dispatch on run-time types. ML is based on universally quantiied polymor-phic constrained types. Constraints are conjunctions of inequalities between monotypes built from type con-structors organized into extensible and partially ordered classes. We give type checking rules for a small, explicitly typed functional language a la XML 20] with multi-methods, show that the resulting system has de-cidable minimal types, and discuss subject reduction. Finally, we propose a new object-oriented programming language based on the ML type system.