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We study an extension of the Hindley-Milner system with explicit type scheme annotations and type declarations. The system can express polymorphic function arguments, user-defined data types with abstract components, and structure types with polymorphic fields. More generally, all programs of the polymorphic lambda calculus can be encoded by a translation between typing derivations. We show that type reconstruction in this system can be reduced to the decidable problem of first-order unification under a mixed prefix.

We demonstrate the pragmatic value of the principal typing property, a property more general than ML's principal type property, by studying a type system with principal typings. The type system is based on rank 2 intersection types and is closely related to ML. Its principal typing property provides elegant support for separate compilation, including "smartest recompilation" and incremental type inference, and for accurate type error messages. Moreover, it motivates a novel rule for typing recursive definitions that can type many examples of polymorphic recursion.

Type classes and overloading are shown to be independent concepts that can both be added to simple higher-order logics in the tradition of Church and Gordon, without demanding more logical expressiveness. In particular, model-theoretic issues are not affected. Our metalogical results may serve as a foundation of systems like Isabelle/Pure that offer the user Haskell-style order-sorted polymorphism as an extended syntactic feature. The latter can be used to describe simple abstract theories with a single carrier type and a fixed signature of operations.

Based on our experience with modelling and verifying microarchitectural designs within Haskell, this paper examines our use of Haskell as host for an embedded language. In particular, we highlight our use of Haskell's lazy lists, type classes, lazy state monad, and unsafePerformIO, and point to several areas where Haskell could be improved in the future. We end with an example of a benefit gained by bringing the functional perspective to microarchitectural modelling.

We study the type inference problem for a system with type classes as in the functional programming language Haskell. Type classes are an extension of ML-style polymorphism with overloading. We generalize Milner's work on polymorphism byintroducing a separate context constraining the type variables in a typing judgement. This leads to simple type inference systems and algorithms which closely resemble those for ML. In particular we present a new unification algorithm which is an extension of syntactic unification with constraint solving. The existence of principal types follows from an analysis of this unification algorithm.

A formal verification of the soundness and completeness of Milner's type inference algorithm W for simply typed lambda-terms is presented. Particular attention is paid to the notorious issue of "new" variables. The proofs are carried out in Isabelle/HOL, the HOL instantiation of the generic theorem prover Isabelle.

Syntactic Control of Interference (SCI) [17] has long been studied asabasis for interference-free programming, with cleaner reasoning properties and semantics than traditional imperative languages. This paper improves upon Huang and Reddy's type inference system [7] for SCI-based languages in two signi cant ways. First, we eliminate the need for explicit coercion operators in terms. Second, we consider adding let-bound polymorphism, which appears to be nontrivial in the presence of interference control. SCI can be adapted to a wide variety of languages, and our techniques should be applicable to any such language with SCI-based interference control. 1

This paper first discusses the advantages of sorts in algebraic specification languages. It gives a brief introduction into polymorphism approaches used in functional programming languages to weaken the strength of traditional sort systems. We then sketch a universally polymorphic specification language which combines all polymorphism concepts within one universal approach. The approach is based on qualified sorts which generalize the Haskell sort classes to n-ary sort predicates. To describe the properties of arbitrary sort predicates we use a separate Horn-Clause specification. In an introductory example we show how to model sort classes with our approach. A further example...