Satish R. Thatte. Semantics of type classes revisited. In Proc. 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... open kinds bear some similarity to the approaches followed by Chen et al. [8] and Nipkow and Prehofer [26] which constrain type variables in the type rules by sets of class names, while closed kinds bear some similarity to the approach suggested by Thatte for the semantics of type classes [31]. Our approach is novel in considering the combination of open and closed kinds, and their explication in the types of polymorphic functions. In the next section we provide several examples to motivate this, including a new approach to combining parametric overloading with Standard ML modules, and ....

....example, what is the semantic notion of parametricity for such a calculus [22, 21] Our approach suggests that this is a worthwhile avenue of study for logicians interested in parametricity properties. Recently an interesting new approach has been proposed for the semantics of type classes [31]. This approach has some similarity to the system of closed kinds as originally introduced in [13] and to the semantics for closed kinds presented here. The point of departure for [31] is to consider the greatest fixed point rather than the least fixed point as denoting the proper semantics for ....

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Satish Thatte. Semantics of type classes revisited. In Proceedings of ACM Symposium on Lisp and Functional Programming, pages 208--219. ACM Press, 1994.

....Volpano s critique does not apply to open world systems in general. An alternative treatment of overloading regards it as a special case of dynamic typing, using a typecase construct to discriminate between overloaded variants [DRW95, HM95] A semantics along these lines was studied by Thatte [Tha94] Thatte s semantics maps programs to an explicitly typed polymorphic language similar to XML [MH88] Type classes denote sets of recursive types in this language. By contrast, our semantics maps to an untyped language where types and type schemes denote ideals. Outline The rest of this paper is ....

Satish R. Thatte. Semantics of type classes revisited. In Proc. Conference on Lisp and Functional Programming, pages 208--219, 1994.

.... parametric polymorphism and dynamic typing may co exist safely in one calculus; this was not previously considered possible 2 (Girard 1972) Our proposal bears some relationship to recent proposals for adding dynamic typing to ML like languages (including other work done by the author) Thatte (1994) and Duggan and Ophel (1994) propose semantics for Haskell style parametric overloading based on overloaded functions which implicitly use a typecase construct to dispatch based on run time type parameters. Dubois et al. 1995) have also considered an approach to parametric overloading based on ....

....typing with objects. Harper and Morrisett do not consider subtyping, and it appears difficult to define narrow for object types, using their typecase, in a language with subtyping. As pointed out in the introduction, our work is related to recent work in parametric overloading. Thatte s proposal (Thatte 1994) is somewhat unrealistic in that the semantics requires a global program analysis to build the semantic definitions of overloaded functions, and so it is not applicable to the separate compilation of reusable software components. Independently of and contemporaneously with Thatte s work, Duggan ....

Thatte, S. (1994). Semantics of type classes revisited. In Proceedings of ACM Symposium on Lisp and Functional Programming, pp. 208--219. ACM Press.

....there are terms in Exell that do not have a unique semantics. For example, the term show (read True ) either evaluates to the string True or fails, depending on the choice of the type of the subexpression read True . This problem is called (semantic) incoherence (Blott, 1991, Jones, 1993a, Thatte, 1994) and occurs when unbound method dictionaries are generCONS TEST PAT Figure 12: Translation rules for expressions involving existential types G S , E K ( b m :T m .t t t n ( G S , t i : T i T i C 1 i . C k i i , i 1. m = G S E , K : ....

Thatte, S. 1994. Semantics of type classes revisited. In Proc. ACM Conf. Lisp and Functional Programming.

....corresponding to a proof that a type satisfies the constraints of the qualification. From a practical point of view it appears that both mechanisms can be used to solve similar problems, but the exact relationship between the two approaches is not clear. Recently Duggan and Ophel [14] and Thatte [50] have independently suggested semantics for type classes that are similar in spirit to our proposal. In particular both approaches represent the restriction of a class as a user defined, possibly recursive, kind definition in a predicative language. Both sets of authors are concerned with ....

S. R. Thatte. Semantics of type classes revisited. In Proc. 1994 ACM Conference on LISP and Functional Programming, pages 208--219, Orlando, June 1994. ACM.

....of structural recursion on types at both the term and the type level. Intensional type analysis is required at the type, as well as the term, level in order to track the type of intensionally polymorphic operations. This feature distinguishes our approach from other approaches based on typecase [49, 28]. The form of intensional analysis that we provide is sufficiently strong to perform non trivial type based code selection, but it is sufficiently weak that termination of operations that analyze types is assured. This means that the compiler may always open code intensionally polymorphic ....

....Ohori and Kato s paper [42] for further details. 6 Other Applications In this section, we sketch several other applications of intensional polymorphism. 6.1 Type Classes The language Haskell [25] provides the ability to define a class of types with associated operations called methods. See [51, 27, 49, 7] for various papers related to type classes. The canonical example is the class of types that admit equality (also known as equality types in SML [36] Consider adding a distinguished type void (with associated constructor Void) in such a way that void is empty . By empty, we mean that no ....

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Satish R. Thatte. Semantics of type classes revisited. In Proc. 1994 ACM Conference on LISP and Functional Programming, pages 208--219, Orlando, June 1994. ACM.

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Satish R. Thatte. Semantics of type classes revisited. In Proc. 1994.

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