A polymorphic type system for logic programs

Abstract

This thesis develops a polymorphic type system for logic programs. Our approach is semantically oriented. We define a type language with precise semantics. Type inference rules are derived from the semantics of the type language and the semantics of logic programs. Algorithms for automatic type construction are developed based on the type inference rules. Soundness of the inference rules guarantees the soundness of the algorithms. A prototype system is implemented using a logic programming language Prolog.

Logic programs has no standard notion of error. Thus, in order to introduce types into logic programs, a notion of type error should be defined first. In our type system, error is the guaranteed failure. Then, types of predicates are supersets of relations defined by the predicates. Such types can be incorporated into logic programs without changing the syntax and semantics of logic programs.

The developed type system assumes that no type declarations or type definitions are available from programs. Types are automatically inferred by static program analysis. Regular trees constitute an effective type language for automatic type inference due to their expressive power and availability of many useful algorithms.

Our type system realizes type polymorphism by using implication and universal quantification as type constructs. Compared with other work, our polymorphic types have well-defined set-theoretic semantics and more expressive power. Our framework can be used for semantic analyses of logic programs for other purpose.

The developed polymorphic type system shows that logic programs can have logically sound and practically useful type systems. Moreover, we recognize that our type system has a generality as a basis for static semantic analyses of logic programs for various purpose.