Dennis M. Volpano and Geoffrey S. Smith. On the complexity of ML typability with overloading. In Conference on Functional Programming Languages and Computer Architecture, volume 523 of Lecture Notes in Computer Science, pages 15--28. Springer-Verlag, August 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the type of an object using ( I ) are satisfiable. As we have already mentioned, an object of type ) ae can only be used if we 17 can provide evidence for the predicate . If no such evidence can be obtained, then any object with this type is useless. This problem was noted by Volpano and Smith [VS91] for the special case of the system of type classes described in [WB89] With this in mind, they gave a stronger definition of well typing that includes testing for satisfiability of an inferred type scheme and showed that this makes the process of determining whether a particular term is ....

Dennis Volpano and Geoffrey Smith. On the complexity of ML typability with overloading. Proceedings of the 5th ACM conference on Functional Programming Languages and Computer Architecture. Lecture notes in computer science 523, Springer Verlag, 1991.

....in type expressions and leads to a particularly simple implementation. In addition, this permits further useful extensions such as the possibility of defining overlapping instances. Several researchers, including this author, have investigated the theory and formal properties of type classes [8, 30, 29, 36, 44, 45, 50, 53] and there has 27 also been some experience with practical implementations [14, 28, 46, 5] and applications [27, 38, 13] Since these topics are so well documented, we will concentrate here only on the special features in the implementation of Gofer. We will also assume that the reader is ....

D. Volpano and G. Smith. On the complexity of ML typability with overloading. In 5th ACM conference on Functional Programming Languages and Computer Architecture, New York, 1991. Springer-Verlag. Lecture Notes in Computer Science, 523.

....which we have not addressed here. For example, the introduction of theories into the language leads to a new quality of inference, since the problem of nding an assertion for an assumption is generally undecidable. The reasoning behind this is similar to that concerning predicate types given in [16, 17]. 4 Conclusion Opal 2 is the result of discussions in our group based on the experiences (good as well as bad) we had with Opal 1. Several extensions of Opal 1 were introduced during recent years, but further progress was not possible without losing compatibility with the original language. So ....

Dennis M. Volpano and Georey S. Smith. On the Complexity of ML Typability with Overloading. Technical Report TR91-1210, Cornell University, May 1991.

....named collections (Haskell s type Supported by NSERC Operating Grant 0105568. 1 classes [16] The foundations for this construct are expressed in terms of an underlying ML like minilanguage (ignoring the operational semantics of the mini language) with polytypes enriched with type predicates [19, 33, 10, 32], basically implicit operator parameters which may constrain instantiations of the type variables. In this paper we introduce a moderately novel approach to parametric overloading, based on using structured kinds to constrain type variables. We introduce open kinds, which constrain the operations ....

....the bindings for bound variables must be communicated to the global implementation of an overloaded operation. 7 Related Work There have been many approaches to combining overloadingand parametric polymorphism. The most prominent approach has been that of type predicates and Haskell classes [19, 33, 10, 32, 27, 8, 20, 26]. In fact Kaes seminal paper used a simple form of kinds, where a type variable was annotated with overloaded identifiers indicating that the variable could only be instantiated with a type permitted by all the specified identifiers [19] Kaes paper contained many good insights, including the ....

Denis Volpano and Geoffrey Smith. On the complexity of ML typability with overloading. In Proceedings of ACM Symposium on Functional Programming and Computer Architecture, pages 15--28. Springer-Verlag, 1991. Lecture Notes in Computer Science 523.

....about type variables but tags the type variables directly. The original version of type classes as presented by Wadler and Blott [14] was significantly more powerful than what went into Haskell, the reason being that the original system was undecidable, as shown later by Volpano and Smith [13]. The relationship to Haskell proper is discussed in Section 2. Nipkow and Snelting [12] realized that type inference for type classes can be formulated as an extension of ordinary ML style type inference with order sorted unification, i.e. simply by changing the algebra of types and the ....

D. M. Volpano and G. S. Smith. On the complexity of ML typability with overloading. In Proc. 5th ACM Conf. Functional Programming Languages and Computer Architecture, pages 15--28. LNCS 523, 1991.

....to fail as a result. However, while this may be useful in some applications, it is not required; in the general case, testing for satisfiability of a predicate set is undecidable and we would not be able to guarantee termination of the type inference algorithm (see the work of Volpano and Smith [20], for example) For similar reasons, while we expect the results of simplifying and improving functions to satisfy certain correctness conditions, we do not insist that they are optimal ; in the general case, there may not be any effective way to find such optimal solutions. Our approach is to ....

D. Volpano and G. Smith. On the complexity of ML typability with overloading. In 5th ACM conference on Functional Programming Languages and Computer Architecture, New York, 1991. Springer-Verlag. Lecture Notes in Computer Science, 523.

....[Kae88] The type system of Haskell is certainly its most innovative feature, and has provoked much discussion. There has been closely related work by Rouaix [Rou90] and Comack and Wright [CW90] and work directly inspired by type classes includes Nipkow and Snelting [NS91] Volpano and Smith [VS91] Jones [Jon92a, Jon93] Nipkow and Prehofer [NP93] Odersky and Laufer [OdLa91] Laufer [Lau92, Lau93] and Chen, Hudak and Odersky [CHO92] The paper presents a source language (lambda calculus with implicit typing and with overloading) and a target language (polymorphic lambda calculus with ....

D. M. Volpano and G. S. Smith, On the complexity of ML typability with overloading. In Functional Programming Languages and Computer Architecture, Boston, August 1991, LNCS 523, Springer-Verlag.

....example is the treatment of overloading proposed by Wadler and Blott [25] in which overloading is represented by introducing so called dictionary ab stractions and applications. This basic idea has been used in all current implementations of Haskell type classes [8] and has been widely studied [1, 9, 10, 12, 17, 18, 21, 23, 24]. This paper is motivated by the observation that both ideas can be dealt with in the same framework, allowing us to exploit the connections between the two systems so that results and ideas originally developed with one application in mind can also be applied to the other. More precisely, we show ....

D. Volpano and G. Smith. On the complexity of ML typability with overloading. In 5th ACM conference on Functional Programming Languages and Computer Architecture. Lecture notes in computer science 523. Springer Verlag. 1991.

....] The type system of Haskell is certainly its most innovative feature, and has provoked much discussion. There has been closely related work by Rouaix [ Rou90 ] and Comack and Wright [ CW90 ] and work directly inspired by type classes includes Nipkow and Snelting [ NS91 ] Volpano and Smith [ VS91 ] Jones [ Jon92a, Jon93 ] Nipkow and Prehofer [ NP93 ] Odersky and Laufer [ OdLa91 ] Laufer [ Lau92, Lau93 ] and Chen, Hudak and Odersky [ CHO92 ] The paper presents a source language (lambda calculus with implicit typing and with overloading) and a target language (polymorphic lambda ....

D. M. Volpano and G. S. Smith, On the complexity of ML typability with overloading. In Functional Programming Languages and Computer Architecture, Boston, August 1991, LNCS 523, Springer-Verlag.

....work is supported by the GRASP Project. Authors address: Computing Science Dept, Glasgow University, Glasgow, Scotland. Email: fcvh, kh, simonpj, wadlerg uk.ac.glasgow.dcs 1 Miranda is a trademark of Research Software Limited. 2 HALL, HAMMOND, PEYTON JONES, WADLER [NS91] Volpano and Smith [VS91], and Jones [Jon92] There has also been a good deal of traffic concerning type classes on the Haskell mailing list. The original type inference rules given in [WB89] were deliberately rather spare, and were not intended to reflect the Haskell language precisely. As a result, there has been some ....

D. M. Volpano and G. S. Smith, On the complexity of ML typability with overloading. In Functional Programming Languages and Computer Architecture, Boston, August 1991, LNCS 523, Springer-Verlag.

....0 a 0 . Since characters are not usually regarded as numeric values, we might expect this term to produce a type error. Instead, the standard type inference algorithm assigns a principal type of (Char 2 Num) Char Char to this term. Examples like this were presented by Volpano and Smith [21] as criticisms of the original Wadler and Blott proposals for type class overloading [22] and used to motivate the use of slightly different set of typing rules that would reject such terms. In fact, the Haskell type system already has this behaviour. A similar effect can be obtained by arranging ....

....the type inference algorithm to fail as a result. However, while this may be useful in some applications, it is not required; in the general case, testing for satisfiability of a predicate set is undecidable and we would not be able to guarantee termination of the type inference algorithm (see [21], for example) For similar reasons, while we expect the results of simplifying and improving functions to satisfy certain correctness conditions, we do not insist that they are optimal ; in the general case, there may not be any effective way to find such optimal solutions. Our approach is to ....

D. Volpano and G. Smith. On the complexity of ML typability with overloading. In 5th ACM conference on Functional Programming Languages and Computer Architecture, New York, 1991. Springer-Verlag. Lecture Notes in Computer Science, 523.

....is its unique successor, if it has one. 6 Satisfiability Checking We say that a constraint set B is satisfiable with respect to an assumption set A if there is a substitution S such that A BS. Unfortunately, this turns out to be an undecidable problem, even in the absence of subtyping [14, 18]. This forces us to impose restrictions on overloading and or subtyping. In practice, overloadings come in fairly restricted forms. For example, the overloadings of would typically be : char char bool ; real real bool ; 8ff with : ff ff bool : seq(ff) seq(ff) bool ....

Dennis M. Volpano and Geoffrey S. Smith. On the complexity of ML typability with overloading. In Conference on Functional Programming Languages and Computer Architecture, volume 523 of Lecture Notes in Computer Science, pages 15--28. Springer-Verlag, August 1991.

....C is satisfiable with respect to A. The size of E is at most exponential in jAj. Whether E is unifiable can be decided in linear time so CS SAT is in NEXPTIME. For hardness, let B = fc p(n) 1 : ffl q 0 a 1 a 2 Delta Delta Delta an fflg in the PTIME reduction of Theorem 4. 2 in [VoS91]; a 1 a 2 Delta Delta Delta an is an input string x to a nondeterministic Turing machine M of exponential time complexity. Then B is satisfiable under A x iff M accepts x. Next we consider the complexity of CS SAT with the style of overloading permitted in the lazy functional programming ....

Volpano, D.M. and Smith, G.S., On the Complexity of ML Typability with Overloading, Proc. 5th Conf. on Functional Programming Languages and Computer Architecture, LNCS 523, Springer-Verlag, pp. 15-28, 1991.

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Dennis M. Volpano and Geoffrey S. Smith. On the complexity of ml typability with overloading. Technical Report TR91-1210, Cornell University, Computer Science Department, May 1991.

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Dennis M. Volpano and Geoffrey S. Smith. On the complexity of ML typability with overloading. In Proc. 5th ACM Conf. Functional Programming Languages and Computer Architecture, pages 15--28. LNCS 523, 1991.

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