Introduction to generalized type systems

Abstract

AbstractProgramming languages often come with type systems. Some of these are simple, others are sophisticated. As a stylistic representation of types in programming languages several versions of typed lambda calculus are studied. During the last 20 years many of these systems have appeared, so there is some need of classification. Working towards a taxonomy, Barendregt (1991) gives a fine-structure of the theory of constructions (Coquand and Huet 1988) in the form of a canonical cube of eight type systems ordered by inclusion. Berardi (1988) and Terlouw (1988) have independently generalized the method of constructing systems in the λ-cube. Moreover, Berardi (1988, 1990) showed that the generalized type systems are flexible enough to describe many logical systems. In that way the well-knownpropositions-as-typesinterpretation obtains a nice canonical form.