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Conjunctional type assignment in programming languages

The aim of this work is to widen ML-type polymorphism to a more comprehensive form. Polymorphic type systems as proposed by Milner and implemented in the programming language Standard ML offer rich types, unobtrusive compile time type checking, and type safety in functional languages. However, straightforward application of such a type system to languages can inhibit seriously the characteristic polymorphic nature of an argument occurring twice or more in a function definition. We describe the problems and present a formal type discipline for polymorphic expressions in the context of a simple programming language, and a compile time type-checking algorithm R which enforces the discipline. The algorithm, which is sound and (we believe) complete, introduces a new operator 2229 for handling conjunction types. We also suggest an idea about a unification algorithm for handling type expressions with or without 2229-operators [gho87b].