We present a new approach to proving type soundness for Hindley/Milner-style polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations. 1 Type Soundness Static type systems for programming languages attempt to prevent the occurrence of type errors during execution. A definition of type error depends on a specific language and type system, but always includes the use of a function on arguments for which it is not defined, and the attempted application of a non-function. ...

The simple and elegant Hindley/Milner polymorphic type discipline is the basis of the type system of Standard ML, but ML's imperative features are a blight on this otherwise clean landscape. Polymorphism and imperative features cannot freely coexist without compromising type safety, hence Standard ML assigns imperative types of limited polymorphism to procedures that use references, exceptions, or continuations. Several other solutions exist, but all introduce new kinds of types that complicate the type system, contaminate module signatures, and violate abstraction by revealing the pure or imperative nature of a procedure in its type. We propose a seemingly radical alternative: by restricting polymorphism to values, imperative procedures have the same types as their behaviorally equivalent functional counterparts. Although the resulting type system does not accept all expressions typable in the purely functional sublanguage, this limitation is seldom encountered in practice. The vast m...

Hindley/Milner-style polymorphism is a simple, natural, and flexible type discipline for functional languages, but incorporating imperative extensions is difficult. We present a new technique for typing references in the presence of polymorphism by inferring a concise summary of each expression's allocation behavior---a type effect. A simple technique for proving soundness with respect to a reduction semantics demonstrates that the type system prevents type errors. By establishing that the system corresponds to an alternate system better suited to implementation, we obtain an algorithm to perform type and effect inference. 1 Polymorphism and References Hindley/Milner-style polymorphism [8, 12] is a simple, natural, and flexible type discipline for functional languages, but incorporating imperative extensions is difficult. While a number of systems for typing reference cells exist [3, 10, 16, 17, 18], we have devised a more direct approach based on inferring a concise summary of each ...