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 multimethods in the tradition of CLOS [12]. Instead of using extensible records as a foundation for object-oriented extensions of functional languages, we propose to reinterpret 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 quantified polymorphic constrained types. Constraints are conjunctions of inequalities between monotypes built from type constructors organized into extensible and partially ordered classes. We give type checking rules for a small, explicitly typed functional language á la XML [20] with multi-methods, show that the resulting system has decidable minimal types, and discuss subject reduction. Finally, we propose a new object-oriented programming language based on the ML≤ type system.

Abstract interpretation is a formal method that enables the static determination (i.e. at compile-time) of the dynamic properties (i.e. at run-time) of programs. We present an abstract interpretation-based method, called abstract debugging, which enables the static and formal debugging of programs, prior to their execution, by finding the origin of potential bugs as well as necessary conditions for these bugs not to occur at run-time. We show how invariant assertions and intermittent assertions, such as termination, can be used to formally debug programs. Finally, we show how abstract debugging can be effectively and efficiently applied to higher-order imperative programs with exceptions and jumps to non-local labels, and present the Syntox system that enables the abstract debugging of the Pascal language by the determination of the range of the scalar variables of programs.

Abstract The essential part of abstract interpretation is to build a machine-representable abstract domain expressing interesting properties about the possible states reached by a program at runtime. Many techniques have been developed which assume that one knows in advance the class of properties that are of interest. There are cases however when there are no a priori indications about the 'best' abstract properties to use. We introduce a new framework that enables non-unique representations of abstract program properties to be used, and expose a method, called dynamic partitioning, that allows the dynamic determination of interesting abstract domains using data structures built over simpler domains. Finally, we show how dynamic partitioning can be used to compute non-trivial approximations of functions over infinite domains and give an application to the computation of minimal function graphs.