You-Chin Fuh, Prateek Mishra. Type Inference with Subtypes. TCS 73(2): 155-175, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....paper, however, it will be assumed that the principal type property is required, and a solution will be outlined. The approach that will be taken is to add a small language of constraints to types, in a manner similar to schemes more usually used for subtyping, such as the work of Fuh and Mishra [2], and of Mitchell [6] Constrained types will be written in the form 8ff 1 : 8ff n j C 1 ; C k : T , where C = fC 1 ; C k g is a set of constraints on the variables ff 1 : ff n . Furthermore, we will consider a term to be well typed only when it has a type of this form, ....

You-Chin Fuh, Prateek Mishra. Type Inference with Subtypes. TCS 73(2): 155-175, 1990.

....This system presents, in principle, common points with those mentioned above, but the details of constraint resolution, entailment and if it were attempted simpli cation di er widely. Also, note that this system only supports covariant type constructors. Finally, let us mention Fuh and Mishra [FM88, FM89], who were precursors in the area of constraint simpli cation. Their work, however, deals with atomic constraints, as proposed by Mitchell [Mit84] and is of diminished interest today. 7 Conclusion We have given a clean, comprehensive theoretical account of a constraint simpli cation system. ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In H. Ganzinger, editor, Proceedings of the European Symposium on Programming, volume 300 of Lecture Notes in Computer Science, pages 94-114. Springer Verlag, 1988.

....: V n g FV (E with Gamma) x2Dom(E) FV (E(x) with Gamma) The typing rules are given in figure 1. They are very similar to the rules for ML, except for the additional handling of constraints, reminiscent of the treatment of subtyping hypotheses in type inference systems with subtypes [12, 6]. The rules define the proposition term a has type A under assumptions E and constraints Gamma , written E a : A with Gamma. The typing environment E is a partial mapping from term variables to type schemas. We write E[x A] for the environment identical to E, except that x is mapped to A. ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In ESOP '88, volume 300 of Lecture Notes in Computer Science, pages 94--114. Springer Verlag, 1988.

....since inferred type constraints are hard to read even in the absence of objects. The remainder of this section is dedicated to the comparison with three other proposals for adding objects to ML. They all use implicit subtyping, which is, however, restricted to atomic structural subtyping [22, 13]. As a result, they all have the same difficulty with parameterized classes, making it impossible to relate objects created from classes with a different number of parameters, even when the objects have the same interface. For instance, objects of a class string are of incompatible type with ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In ESOP '88, volume 300 of Lecture Notes in Computer Science, pages 94--114. Springer Verlag, 1988.

....is concerned. Many type systems with subtyping have been studied in the literature since the work of Mitchell. Amongst other characteristics, they can be classified according to the structure over which the systems of inequalities are to be solved. Mitchell [Mit84] followed by Fuh and Mishra [FM88,FM89] proposed simple (finite) types as in traditional ML. In this structure, the example above cannot be solved, because of the self application (xx) Amadio and Cardelli [AC93] then put forward recursive types. They are required in the context of object oriented programming if objects are ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In H. Ganzinger, editor, Proceedings of the European Symposium on Programming, volume 300 of Lecture Notes in Computer Science, pages 94--114. Springer Verlag, 1988.

....restrictions due to ML polymorphism. Because subtyping polymorphism goes through lambda abstractions, it could be used to type some of the examples that were wrongly rejected. ML type inference with subtyping polymorphism has been first studied by Mitchell in [Mit84] and later by Mishra and Fuh [FM88, FM89] The LET case has only been treated in [Jat89] But as for recursive 3.4 Extensions 17 types, subtyping has never been studied in the presence of an equational theory. Although the general case of merging subtyping with an equational theory is certainly difficult, we believe that ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In ESOP '88, volume 300 of Lecture Notes in Computer Science, pages 94--114. Springer Verlag, 1988.

....Consequently, they lack the uniformity and generality required for soft typing. Finally, many researchers in the area of static type systems have developed extensions to the ML type system that can type a larger fraction of good programs. In the arena, the work of Mitchell[18] Fuh Mishra[11, 12, 13], and, of course R emy[19] is particularly noteworthy and has exerted a strong influence on our work. 9 Conclusions The principal contribution of this research is the introduction of a new paradigm for program typing called soft typing that combines the best features of static and dynamic ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In Conference Record of the European Symposium on Programming, 1988.

.... is computable in polynomial time [23] Moreover, if ( Sigma; is tree like , then type inference is computable in polynomial time [6] In general, the type inference problem is PSPACE hard [14, 23] Type inference with atomic subtyping has also been studied in combination with ML polymorphism [10, 11]. Objects do not have base types, so type inference with atomic subtyping does not apply to Abadi and Cardelli s calculus. The object types considered in this paper are rather like record types. Type inference for calculi with records but no subtyping has been studied by Wand [24] and Remy ....

You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In Proc. ESOP'88, European Symposium on Programming, pages 94--114. SpringerVerlag (LNCS 300), 1988.

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You-Chin Fuh and Prateek Mishra. Type inference with subtypes. In ESOP '88, volume 300 of Lecture Notes in Computer Science, pages 94--114. Springer Verlag, 1988.

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