This thesis presents the foundations for relational logic programming over polymorphically order-sorted data types. This type discipline combines the notion of parametric polymorphism, which has been developed for higher-order functional programming, with the notion of order-sorted typing, which has been developed for equational first-order specification and programming. Polymorphically order-sorted types are obtained as canonical models of a class of specifications in a suitable logic accommodating sort functions. Algorithms for constraint solving, type checking and type inference are given and proven correct.

We present a concurrent higher-order programming language called Plain and a concomitant static type system. Plain is based on logic variables and computes with possibly partial data structures. The data structures of Plain are procedures, cells, and records. Plain's type system features record-based subtyping, bounded existential polymorphism, and access modalities distinguishing between reading and writing.