The type concept of the logic programming language PROTOS-L supports sorts, subsort relationships and parametric polymorphism. Due to the order-sortedness types are also present at run time, replacing parts of the deduction process required in an unsorted version by efficient type computations. Together with the polymorphism most of the flexibility of untyped logic programming carries over to the order-sorted approach. The operational semantics of PROTOS-L is based on polymorphic order-sorted resolution. Starting from an abstract specification, we show how this operational semantics can be implemented efficiently by an extension of the Warren Abstract Machine and give a detailed description of all instructions and low-level procedures responsible for type handling. Since the extension leaves the WAM's AND/OR structure unchanged, it allows for all WAM optimizations like last call optimization, environment trimming, etc. Moreover, the extension is orthogonal in the sense that any program part not exploiting the facilities of computing with subtypes is executed with almost the same efficiency as on the original WAM.

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Abstract. Subtyping tends to undermine the effects of parametric polymorphism as far as the static detection of type errors is concerned. Starting with this observation we present a new approach for type checking logic programs to overcome these difficulties. The two basic ideas are, first, to interpret a predicate type declaration as an approximation for the success set of the predicate. Second, declarations are extended with type constraints such that they can be more refined than in other conventional type systems. The type system has been implemented in a system called Typical which provides a type checker for Standard Prolog enriched with type annotations.

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