Ryan Stansifer. Type inference with subtypes. In Fifteenth ACM Symposium on Principles of Programming Languages, pages 88--97, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are regarded as well typed. For example, in Wadler Blott s system the expression true true is well typed, even though does not work on booleans. Kaes system has similar difficulties. Subtyping (without overloading) has been investigated by (among many others) Mitchell [11] Stansifer [15], Fuh and Mishra [4, 5] and Curtis [2] Mitchell, Stansifer, and Fuh and Mishra consider type inference with subtyping, but their Throughout this paper, we write functions in curried form. languages do not include a let expression; we will see that the presence of let makes it much harder to ....

Ryan Stansifer. Type inference with subtypes. In Fifteenth ACM Symposium on Principles of Programming Languages, pages 88--97, 1988.

....extending languages with type inference in this manner can pose two serious problems: there may be no single most general typings, or worse yet, the type inference problem may become undecidable. 1. 2 Background and Results The viewpoint developed by [Car84] and adopted by many others [Wan87, Sta88, JM88, Rem89] is to think of an object as a record consisting of a finite set of labeled, typed fields. Inheritance is modeled by allowing a function defined on a record to be used automatically on a record with more fields. More specifically, the subclass relation is that a record type y is a ....

....Although there are some algorithmic issues of dealing efficiently with the let construct, we do not address them here. We do not include variant records (tagged unions) although we believe that the subtyping of variants involves issues closely related to the subtyping of records [Car84, Wan87, Sta88, Rem89] We would expect that incorporating variants into our system would not cause any serious difficulties, but we do anticipate that there would be some technical overhead involved. We extend this kernel of ML two ways. We develop a form of extended pattern matching that allows us we type ....

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R. Stansifer. Type inference with subtypes. In Proc. 15-th ACM Syrup. on Priciples of Programming Languages, pages 88-97, January 1988.

....supports certain aspects of method inheritance and provides a typetheoretical basis for object oriented programming. Cardelli and Wegner [1985] extended this approach to a second order type system. Type inference systems with subtyping have also been developed [Fuh and Mishra 1988; Mitchell 1984; Stansifer 1988]. It is, however, not clear whether or not the mechanism for record polymorphism should be coupled with a strong mechanism of subtyping. In the presence of subtyping, a static type no longer represents the exact record structure of a runtime value. For example, a term if true then fA = 1, B = ....

Stansifer, R. 1988. Type inference with subtypes. In Proceedings of the ACM Symposium on Principles of Programming Languages. ACM, New York, 88-97.

....: int] Wand s system, however, does not share ML s feature of existence of principal typing schemes (see [OB88, Wan88] for an analysis of this issue. Based on Wand s general observation, OB88] extended the notion of principal type schemes to include conditions on type variables. See also [Sta88, JM88, Rem89, Wan89] for related studies. This extension allows ML polymorphism to be extended to standard operations on records and variants and also to various database operations such as join and projection. See also [Wan89, CM89, HP91, Rem91] for proposals for other operations on records. ....

R. Stansifer. Type inference with subtypes. In Proc. ACM Symp. on Principles of Programming Languages, pages 88-97, 1988. 23

....HHP93, Mar75] where polymorphism or dependencies on either terms or types is represented by explicit abstractions. 4.2.3 Type Reconstruction Much work has been done with enhancing the ML type reconstruction system. The main threads of this work cover type reconstruction with subtypes [Wan91, Sta88, Oho89, FM90, R 89] type reconstruction with recursive types [CC91] type reconstruction with polymorphic recursion [KTU93a, Hen93] and type reconstruction in stratified polymorphic systems [Lei91, KT92, McC84] There has been some work in dependent type inference [Ell89] that we discuss ....

....types, rather than implicit ML style parametric polymorphism at the outer level, as we do with type schemes. The work on type reconstruction and subtypes covers a range of research that investigates the extension of ML with properties of object oriented and database programming [Wan91, Sta88, Oho89, FM90, R 89] All of these works propose new extensions to ML representing general language facilities and then investigate type reconstruction. There are also many other miscellaneous extensions to ML for which type reconstruction has been extended. 101 4.2.4 Unification and Matching ....

R. Stansifer. Type inference with subtypes. In Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, pages 88--97. ACM, January 1988.

....[Jategaonkar Mitchell 88] give a type system for extendible records in ML, including ML patterns and subtyping on ground (i.e. name equivalent) types. We conjecture that our system can replace the cut restrictions in their system, and that the resulting systems will fit together nicely. Stansifer 88] also contributed a treatment of type inference for records. Reddy 88] gives a semantics for objects as closures which is very close in spirit to ours. He gives a traditional denotational semantics, whereas we give a concrete semantics [Wand 85] a translation into an underlying lambda calculus. ....

Stansifer, R. "Type Inference with Subtypes," Conf. Rec. 15th Ann. ACM Symp. on Principles of Programming Languages (1988), 88--97.

....issues are, of course, important, but (solely due to reasons of lack of space) we refer the interested reader to the last two articles mentioned above for a full treatment of the semantical part of our theory. For readers interested in other issues regarding subtyping in type theory we refer to [CaWe85,FuMi88,KiLa89,Ohor90,Stan88,Wand87]. 3.1 Cardelli type theory In this section we give a brief summary of the system described in [Card84,Card88] Full details of syntactical and proof theoretical aspects can be found in the technical report. 3.1.1 Expressions and Types Types in our version of the Cardelli system are either 1. ....

R. Stansifer, "Type inference with subtypes," in Proceedings Fifteenth Annual ACM Principles of Programming Languages (POPL88), 1988, 88--97.

.... end of our analysis and the algorithm(s) 5 Similar considerations can be applied to other type inference problems to derive systematically reductions to solvability of type constraint systems; in particular, the reductions of Mitchell [Mit84] Wand [Wan87] Fuh and Mishra [FM88] Stansifer [Sta88] Henglein [Hen88b] can be derived in this fashion. for solving these constraints as its back end . We hope that, possibly after some suitable generalization, our constraints are both expressive enough to capture many interesting program analyses and still constrained enough to admit efficient ....

R. Stansifer. Type inference with subtypes. In Proc. 15th ACM Symp. on Principles of Programming Languages, pages 88--97, San Diego, California, Jan. 1988. ACM.

.... type instances of these expressions belong to certain type schemes (e.g. a function like (x: x) has many types, all being instances of the type scheme ff ff) Only recently there have appeared several studies of combining subtyping with type inference (cf. Wand 1987] Fuh, Mishra 1988] and [Stansifer 1988]) but these studies all address only the syntactic aspects. Further investigation is required to determine whether our technique for a semantics of subtyping also applies in this case. The remainder of this paper is organized as follows. In the next section we motivate and formally treat a ....

Stansifer, R.: "Type Inference with Subtypes"; in: Conference Record of the 15 th Annual ACM Symposium on Principles of Programming Languages (POPL 88), 1988, pp.88-97.

....E = E and t t1 and c1 c Proof See the appendix. 4 Related Work Subtyping (see e.g. Cardelli88] adds flexibility to type systems by allowing type coercions to be performed if necessary in the presence of type mismatches. It is often used to captures aspects of object oriented programming [Wand87, Stansifer88]. Subtyping in effect systems has been previously introduced in explicitly typed languages [Gifford87, Consel94] There, a subsumption rule similar to the one presented above was used, but since only type checking was performed, its treatment was simpler than ours. This paper shows that type and ....

Stansifer, R. Type Inference with Subtypes. In ACM Symposium on Principles of Programming Languages, 1988.

.... are important technical differences, the most important of which is that database values have unique types in Machiavelli while they can have multiple types in [Car84b] Based on the idea suggested in [Wan87] Machiavelli achieves the same goals of representing objects and inheritance (see also [Sta88, JM88] for related studies) These differences allow Machiavelli to overcome certain anomalies (see [OB88] which also gives details of the underlying type inference system) Another important extension to these type systems for objects and inheritance is that Machiavelli uniformly integrates ....

R. Stansifer. Type inference with subtypes. In Proc. 15th ACM Symposium on Principles of Programming Languages, pages 88--97, 1988.

....kinded unification) but restrains the set of labels to be finite. Both Wand [71] and R emy [49] later extended this system to infinite sets of labels. Another possibility is the use of row variables introduced by Wand [68, 70] and refined by Jategaonkar and Mitchell [34] and also Stansifer [55]. Although the application of these alternatives to the calculus of objects needs deeper investigation, assigning kinds, as a form of open records, to objects referenced (but not defined) in programs seems quite intuitive. The proof of the equivalence between systems TA [ and TA [ hi already ....

Ryan Stansifer. Type inference with subtypes. In 15th ACM Symposium on Principles of Programming Languages, pages 88--97. ACM Press, 1988.

....designators in record structures. Relatively recently, formalisms for records have been proposed. This started with Cardelli [6] was later extended to a second order calculus [7] and was followed by a number of record type inference systems compatible with ML style polymorphic type inference [22, 20, 13, 19]. Even more recently, a compilation method was proposed by Ohori [18] for an extension of calculus containing polymorphically typed records. Another way to use labels in programming languages has been as keywords for parameter passing in procedure or function calls. This is the case in Common ....

R. Stansifer. Type inference with subtypes. In Proceedings of ACM Symposium on Principles of Programming Languages, pages 88--97 (1988).

....at all. We also provide a complete type inference algorithm for our type system, which is formulated as a rewriting system over sets of type constraints. The algorithm, so to speak, finds bounded quantification[7] by inference. There are already type systems having subtyping such as [14] [16] and [18] Their papers present monomorphic systems, but we expect that it is not so difficult to incorporate parametric polymorphism into their systems. However, essential modifications(like what we did) are necessary in their systems in order to accommodate recursive types. The reason for the ....

....(C5) are inference rules for type constructors. C6) is able to handle recursive types. In addition to the inference rules, we need a set of axioms depending on base types. 3. 3 LUB Type and GLB Type The notion of the least upper bound type and the greatest lower bound type can already be seen in [6, 16]. Lub and glb of types are used to solve a set of subtype constraints in our type inference algorithm. An upper bound of an unknown bounded type is given by the greatest lower bound of its upper bound types. Our definition of lub and glb type is essentially equivalent to Cardelli s. Cardelli ....

Ryan Stansifer. Type Inference with Subtypes. In Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, pages 88--97, 1988.

....with association lists, methods. Formalization of this structure has been actively explored lately. This started with Cardelli [5] was later extended in a second order calculus [6] and resulted in a number of type inference systems to make it compatible with ML style polymorphic type inference [20, 18, 11, 17], and a compilation method was finally given by Ohori in [16] for an extension of calculus containing labeled records. The problem is not completely solved, since the merge operator is still problematic (Ohori s calculus does not contain it) but becomes clearer. On the other hand, the second ....

R. Stansifer. Type inference with subtypes. In Proc. ACM Symposium on Principles of Programming Languages, pages 88--97, 1988.

....and it is shown that the type discipline is consistent with the semantics in the sense that type checking is shown to prevent type errors . Subsequent work has aimed at combining inheritance with richer type disciplines, in particular featuring parametric polymorphism. One direction of research [Wan87, JM88, OB88, Sta88], has investigated expressing inheritance and type inference mechanisms, similarly to the way in which parametric polymorphism is expressed in ML like languages. Another direction of research investigates expressing inheritance through explicit subtyping mechanisms which are part of the ....

R. Stansifer. Type inference with subtypes. In J. Ferrante and P. Mager, editors, Symposium on Principles of Programming Languages, pages 88--97, ACM, 1988.

....designators in record structures. Relatively recently, formalisms for records have been proposed. This started with Cardelli [6] was later extended to a second order calculus [7] and was followed by a number of record type inference systems compatible with ML style polymorphic type inference [22, 20, 13, 19]. Even more recently, a compilation method was proposed by Ohori [18] for an extension of calculus containing polymorphically typed records. Another way to use labels in programming languages has been as keywords for parameterpassing in procedure or function calls. This is the case in Common ....

R. Stansifer. Type inference with subtypes. In Proceedings of ACM Symposium on Principles of Programming Languages, pages 88--97 (1988).

....subtyping. Most of these attempts concentrate on introducing subtyping into the ML core language by providing extendable record types similar to classes with inheritance, and on extending type inference to handle extendable record types. See, for example, the papers by R emy [28] Stansifer [31], and Wand [33] Mitchell, Meldal, and Madhav [27] propose to extend ML modules with subtyping and inheritance. This extension would make ML an objectoriented language with a flexible form of multiple inheritance, parameterized signatures containing function signatures and axioms, functors, ....

Ryan Stansifer. "Type inference with subtypes." In Conference Record of the 15th Annual ACM Symposium on Principles of Programming Languages, San Diego, January 1988.

....lists, methods. Formalization of this structure has been actively explored lately. This started with Cardelli [Car88] was later extended in a second order calculus [CW85] and resulted in a number of type inference systems to make it compatible with ML style polymorphic type inference [Wan88, Sta88, JM88, Rem89] and a compilation method was given by Ohori in [Oho92] for an extension of calculus containing labeled records. On the other hand, the second use of labels, as keywords for parameter passing in functions, as it may be done in Common LISP [Ste84] ADA [Led81] or LIFE [AKP91] and ....

R. Stansifer. Type inference with subtypes. In Proc. ACM Symposium on Principles of Programming Languages, pp. 88--97, 1988.

....Wand [25, 26] analyzed the concept of record polymorphism in the context of ML type inference and introduced the notion of row variables, which allow types to be given to terms involving a natural record extension operator. This work was refined by Jategaonkar and Mitchell [12, 13] and Stansifer [24]. R emy [20] introduced the notion of positive and negative information about record fields and the intuition that increasing either positive or negative information specifying that fields are either definitely present or definitely absent gives more refined types. This intuition, ....

Ryan Stansifer. Type inference with subtypes. In Proceedings of the Fifteenth ACM Symposium on Principles of Programming Languages, pages 88--97, San Diego, CA, January 1988.

....for each primitive type) and we can assume that all fields have type u, a type with just one element. Only the presence or absence of a field will be important in this paper; we are not actually interested in records as data structures. Unfortunately type reconstruction in this system is difficult [2, 4, 8, 10]. The type system r, inspired by the work of R emy [6, 7] is now displayed. This is the system in which we will perform type reconstruction. Type system r has two syntactic categories, or sorts the usual one for types, and an additional sort for fields of records. ff j fl 1 : F 1 ; ....

R. Stansifer. Type inference with subtypes. In Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, pages 88--97. ACM, January 1988.

....is the record obtained by applying every field in e 1 to e 2 . For example, the expression a = v:v; b = v:x:x; c = y: m = y 3 has the value a = 3; b = x:x; c = m = 3 . 6 2. 4 Types Many type systems for the typed lambda calculus augmented with record constructs have been studied [10, 15, 16, 17, 21], and the results in this paper hold for those type systems. Additional type systems are explored in the articles in [1] In other words, the added flexibility of the model we propose in this paper is not contingent upon a particular type system being used. These relatively complex type systems ....

R. Stansifer. Type inference with subtypes. In Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, pages 88--97. ACM, January 1988.

....writing redundant declarations or debugging run time errors, to the user but to let the compiler do more work. To achieve this goal we need strong typing, and type reconstruction as it is done in ML. Together with type reconstruction, however, both inheritance and coercion impose a problem. In [Stansifer 1988], R emy 1989] and [Wand 1989] solutions are presented for how to incorporate class type inheritance into a functional language, the incorporation of these ideas into ML are outlined in [Beaven, Stansifer, Wetklow 1989] A survey of several existing type systems can be found in [Danforth, ....

Stansifer, R., 1988: Type Inference with Subtypes. In Conference Record of the Fifteenth Annual ACM Symposium on Principles of Programming Languages, 13--15 January 1988, San Diego, California, pp. 88--97.

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Ryan Stansifer. Type inference with subtypes. In Proceedings of the Fifteenth ACM Symposium on Principles of Programming Languages, pages 88--97, San Diego, CA, January 1988.

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