This paper describes a flexible type system which combines overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes -- a natural generalization of type classes in Haskell. We present a wide range of examples which demonstrate the usefulness of such a system. In particular, we show how constructor classes can be used to support the use of monads in a functional language. The underlying type system permits higher-order polymorphism but retains many of many of the attractive features that have made the use of Hindley/Milner type systems so popular. In particular, there is an effective algorithm which can be used to calculate principal types without the need for explicit type or kind annotations. A prototype implementation has been developed providing, amongst other things, the first concrete implementation of monad comprehensions known to us at the time of writing. 1 An overloaded map function Many functional programs use the map ...

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The meaning of programs in a language with implicit overloading can be described by translating them into a second language that makes the use of overloading explicit. A single program may have many distinct translations and it is important to show that any two translations are semantically equivalent to ensure that the meaning of the original program is well-defined. This property is commonly known as coherence. This paper deals with an implicitly typed language that includes support for parametric polymorphism and overloading based on a system of qualified types. Typical applications include Haskell type classes, extensible records and subtyping. In the general case, it is possible to find examples for which the coherence property does not hold. Extending the development of a type inference algorithm for this language to include the calculation of translations, we give a simple syntactic condition on the principal type scheme of a term that is sufficient to guarantee coherence for a large class of programs. One of the most interesting aspects of this work is the use of terms in the target language to provide a semantic interpretation for the ordering relation between types that is used to establish the existence of principal types. On a practical level, our results explain the importance of unambiguous type schemes in Haskell.

One of the most novel features in the functional programming language Haskell is the system of type classes used to support a combination of overloading and polymorphism. Current implementations of type class overloading are based on the use of dictionary values, passed as extra parameters to overloaded functions. Unfortunately, this can have a significant effect on run-time performance, for example, by reducing the effectiveness of important program analyses and optimizations. This paper describes how a simple partial evaluator can be used to avoid the need for dictionary values at run-time by generating specialized versions of overloaded functions. This eliminates the run-time costs of overloading. Furthermore, and somewhat surprisingly given the presence of multiple versions of some functions, for all of the examples that we have tried so far, specialization actually leads to a reduction in the size of compiled programs.

It has long been suggested that parametric polymorphism might be implemented by generating a distinct version of the code for each monomorphic instance of a function that is used in a given program. However, most implementations avoid this approach for fear that it could lead to a substantial increase in the size of the compiled program -- a so-called code explosion -- and that it would complicate the process of separate compilation. An alternative, used in many systems, is to have a single implementation of each polymorphic function and use a uniform (or boxed) representation for all values. This avoids the risk of code explosion but makes it more difficult to support parametric overloading. In addition, the use of boxed representations for even the most primitive values may carry a significant run-time cost. This paper presents a new approach that lies between these two extremes. The resulting system can be used to obtain an efficient implementation of overloading and to avoid the ...

Abstract. The ML type system was originally introduced as a means of identifying a class of terms in a simple untyped language, often referred to as core-ML, whose evaluation could be guaranteed not to “go wrong”. In subsequent work, the terms of core-ML have also been viewed as a ‘convenient shorthand ’ for programs in typed languages. Notable examples include studies of ML polymorphism and investigations of overloading, motivated by the use of type classes in Haskell. In this paper, we show how qualified types, originally developed to study type class overloading, can be used to explore the relationship between core-ML programs and their translations in an explicitly typed language. Viewing these two distinct applications as instances of a single framework has obvious advantages; many of the results that have been established for one can also be applied to the other. We concentrate particularly on the issue of coherence, establishing sufficient conditions to guarantee that all possible translations of a given core-ML term are equivalent. One of the key features of this work is the use of conversions, similar to Mitchell’s retyping functions, to provide an interpretation of the ordering between type schemes in the target language. 1

for qualified types