Gay, S. J., A sort inference algorithm for the polyadic #-calculus, in: Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (1993), pp. 429--438.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of subject sorts and from a sorting a total function of sorts into sequences of sorts Milner de nes a type system that assigns sorts to the free names of a process. The system enjoys a Subject Reduction property, and supports recursion. Gay developed a type inference algorithm for sorting [Gay93] Independently, Vasconcelos and Honda gave a typing system for sorting, together with an ecient typing algorithm [VH93] Polymorphism is also considered in sorting. Turner studies impredicative polymorphism, encoding the System F in polymorphic pi calculus [Tur96] Vasconcelos proposes a ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In 20th Annual Symposium on Principles of Programming Languages (POPL) (Charleston, SC). ACM, 1993.

....by programs, as well as the more pragmatic requirement that well typedness must be automatically and efficiently verifiable. Milner s sort discipline plays an essential role in later papers on properties of the calculus [Wal92, San92] it has been further studied by Turner [Tur94] Gay [Gay93], and Vasconcelos and Honda [VH93] who consider the problem of inferring most general sortings. Our typing discipline retains the basic character of Milner s, while extending it in two dimensions. First, we replace by name matching of sorts with the more straightforward notion of structural ....

....theoretical properties of our type system rather than to propose a pragmatic notation for programming, we adopt an explicitly typed presentation in which every bound name is annotated with a sorting. The algorithmic problem of inferring these annotations is deferred to future investigation (c.f. [Tur94, Gay93, VH93]) Our basic syntactic categories are defined by the grammar in Figure 1. We use the metavariables S, T , and U for sorts; P , Q, and R for process expressions; Gamma and Delta for sorting assumptions (or sortings) and a, b, c, etc. for channels (or names) For most of the paper, the only type ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

....cost at run time. Given the relative rarity of these constructs in our programs, we choose not to provide this degree of fairness in the Pict library implementing choice. 3 Type System The Pict type system has its roots in the theoretical literature on type systems for the calculus [Mil91, Gay93, VH93, PS93, Tur96] and for functional languages, among which its most immediate predecessors are Quest [Car91] and Amber [Car86] The treatment of subtyping and higher order polymorphism is based on recent work on static type systems for object oriented languages [Car84, Bru94, CHC90, PT94, ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

....all reasons for oe 6 if seq ( ae seq (oe) A type ae not satisfying the conditions of Def. 7 is constructed for each reason [16] ut 5 Related Work Most work on types in concurrent systems is based on Milner s calculus [8, 7] and similar calculi. The problems of inferring most general types [4, 19] and subtyping [11, 12, 18, 3, 17] were considered. But these type systems cannot represent message sequences and ensure statically that all sent messages are acceptable. A large amount of work based on path expressions and process algebra shows that reasoning about the order of messages in ....

S. J. Gay. A sort inference algorithm for the polyadic -calculus. In Conference Record of the 20th Symposium on Principles of Programming Languages, Jan. 1993.

....programming languages: labeled records, integers, booleans, and so on. These are all included in the syntax and typing rules listed in the appendices. Some other useful extensions, such as subtyping, recursive types, and polymorphism, are described (in various combinations) in the literature (c.f. [Mil89, Gay93, PS93, VH93, Tur93]) Indeed, recent work on static type systems for sequential objectoriented languages (c.f. Car88, Bru93, PT93] indicates that a general treatment of the object oriented features that we introduce in Section 7 might be based on a combination of all of these features. 4 Process Typing A type ....

....found in [VH93] for a system extended with recursive types. Proofs for a system including both recursive types and polymorphism appear in [Tur93] and for a system with recursive types and subtyping in [PS93] As in the simply typed calculus, simply typed calculus processes have principal types [Gay93, Tur93, VH93]. This leads naturally to an equivalent of ML style polymorphism [DM82] for the calculus extended with let. The well known problematic interaction between ML type inference and imperative features does not arise here because the bodies of process definitions are not evaluated until they are ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

....manipulated by programs, as well as the more pragmatic requirement that well typedness must be automatically and efficiently verifiable. Milner s sort discipline plays an essential role in later papers on properties of the calculus [25, 23] it has been further studied by Turner [24] and Gay [8], who consider most general sortings. Our typing discipline retains the basic character of Milner s, while extending it in two dimensions. First, we replace by name matching of sorts with the more straightforward notion of structural matching, a technical modification that allows a substantially ....

....theoretical properties of our type system rather than to propose a pragmatic notation for programming, we adopt an explicitly typed presentation in which every bound name is annotated with a sorting. The algorithmic problem of inferring these annotations is deferred to future investigation (c.f. [24, 8]) Our basic syntactic categories are defined by the following abstract grammar: channel sorts S : S 1 : S n ) I tagged tuple j A: S recursive sort j A sort variable I O tags I : Gamma input only j output only j Sigma either process types X : ok ok process process ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

....above algorithm is equivalent to that proposed by Vasconcelos and Honda (modulo the fact that we do not do type inference for recursive types) Note that in the case of a closed term P our algorithms already coincide, since Vasconcelos and Honda s algorithm returns a trivial type for P . Gay [Gay93] has developed an algorithm which infers principle sorts for terms in Milner s sort system. The algorithm is based on a unification algorithm for sorts. For example, we can unify the sorts A and D below CHAPTER 10. RELATED WORK 166 A 7 [B; C] B 7 [A] C 7 [ D 7 [E; F ] E 7 [D] F 7 [ ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In ACM Symposium on Principles of Programming Languages, 1993.

....programming with inheritance and method overriding. Therefore, our type system of HACL is highly useful not only in HACL itself, but also in other concurrent languages based on message passing. Although type systems for concurrent calculi have been recently investigated by many researchers[5][9] 18] 23] 24] we 1 From our experience in programming using concurrent object oriented language ABCL[25] we have long recognized that it is very cumbersome to make such topologies between concurrent objects using only first order concurrent objects. 2 believe that our formulation is one of ....

....also useful for the abstract interpretation, because it gives information to decide which arguments can be dropped during abstract interpretation. Typed Concurrent Calculi Recently, type systems for concurrent calculi such as polyadic calculus and object calculus, were proposed by several people[5][9] 18] 23] 24] Gay s sorting algorithm[5] can be considered a specific instance of the basic type system of HACL, where base types are restricted to only o, and letpolymorphism and higher order processes are dropped. Pierce and Sangiorgi[18] introduced I O modes to calculus in a different ....

[Article contains additional citation context not shown here]

Gay, S. J., "A Sort Inference Algorithm for the Polyadic -calculus," in Proceedings of ACM SIGACT/SIGPLAN Symposium on Principles of Programming Language, pp. 429--438, 1993.

....who also shows a strong correspondence between the polymorphic pi and lambda calculi by demonstrating that Milner s translations of lambda terms into untyped pi calculus both preserve and reAEect polymorphic typing. Process calculi with weaker ML style polymorphism have been developed by Gay [Gay93] and Vasconcelos and Honda [VH93] A rather dioeerent style of polymorphism is considered by Liu and Walker [LW95] Many other type systems have been proposed for process calculi. One that particularly invites comparison with the present system is the pi calculus with input output modalities ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

....who also shows a strong correspondence between the polymorphic pi and lambda calculi by demonstrating that Milner s translations of lambda terms into untyped pi calculus both preserve and reflect polymorphic typing. Process calculi with weaker ML style polymorphism have been developed by Gay [Gay93] and Vasconcelos and Honda [VH93] A rather different style of system is considered by Liu and Walker [LW95] here, polymorphism arises not from type quantification, but by explicitly declaring the possible set of types of values that a given channel may carry. Typing itself does not guarantee ....

Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

....based on name matching. Name matching (or, by name matching) determines sort equality by relying on the syntactical names assigned to communication channels (or names) in a given process, instead of no structure. An algorithm to infer the most general sorting of a term has been reported by Gay in [6]. Milner s original idea is further extended and explored by Liu and Walker in [7] where an input sorting and an output sorting are distinguished. On the other hand, typing systems based on structure matching are introduced in [16, 12] In the structure matching (or, by structure matching) type ....

....is safe. Definition 3.1 A sorting judgment (by name matching) on 6 is an expression of the form: 0 ; Omega P : where 0 ; Omega is a sorting, P is a process, and ( is the special symbol standing for well behavedness of a process. 2 An object sorting is usually called a sorting [10,6,7]. As usual at most one sort is assigned to a name in 0 and at most one object sort is assigned to each polarized subject sort, the subject sort with the polarity, in Omega . So that 0 (a) and Omega (s ) denote the assigned subject sort to a and the object sort to s , respectively. Let ....

Gay, S.J., A sort inference algorithm for the polyadic -calculus, in 20th POPL, 1993.

....systems have been presented in this style. 4 Turner [31] gives an environment presentation of the simple type system, and also considers recursive types explicitly; his treatment of recursive types is similar to Pierce and Sangiorgi s. The problem of type reconstruction has been studied by Gay [3] and Vasconcelos and Honda [33] 3 Input Output Types Pierce and Sangiorgi [23, 24] proposed a refinement of the simple type system, in which the type of a channel not only specifies the types of channels which may be transmitted along it, but also the direction in which messages may flow. Each ....

....as PolyId = i fXg[x : X; r : b[X ] r [x] PolyIdClient = r : b[T ] i fTg[x; r] r [y : T ] and the type of i is bfXg[X;b[X ] It is straightforward to formalise typing rules and the reduction relation for this system, and to prove Subject Reduction. In the work of Gay [3] and Vasconcelos and Honda [33] on type reconstruction for the simple type system, the result of type reconstruction is a typing of a process in an environment containing type variables which can be instantiated once and for all to yield a valid monomorphic typing judgement. Turner s system is ....

S. J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings, 20th ACM Symposium on Principles of Programming Languages. ACM Press, 1993.

....of this technique. 1 Introduction Following its early success as a framework for the investigation of the foundations of various concurrent programming styles, the calculus [8] has also become established as a vehicle for the exploration of type systems for concurrent programming languages [7, 1, 10, 5, 4, 14]. Inter process communication in the calculus is based on point to point transmission of messages along named channels, and many proposed type systems have started from the assignment of types to channels, so that the type of a channel determines what kind of message it can carry. Because ....

....thread receives a session channel along a channel called port and uses it to interact with a client. thread = port [x : S 1 ] server newserver = thread client1body = y negate : y [2] y [a : int] 0 client1 = y : S 2 )port [y] client1body client2body = z plus : z [1] : z [2] z [b : int] 0 client2 = z : S 2 )port [z] client2body Now port : b[S 1 ] newserver j client1 j client2 3 is a valid typing judgement. Because port does not have a sequential type, it can be used by all three processes. When this system is executed, client1 sends ....

S. J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings, 20th ACM Symposium on Principles of Programming Languages. ACM Press, 1993.

....of this technique. 1 Introduction Following its early success as a framework for the investigation of the foundations of various concurrent programming styles, the calculus [12] has also become established as a vehicle for the exploration of type systems for concurrent programming languages [2, 7, 9, 11, 15, 21]. Inter process communication in the calculus is based on point to point transmission of messages along named channels, and many proposed type systems have started from the assignment of types to channels, so that the type of a channel determines what kind of message it can carry. Because ....

....labels are the same as those in S, and the pattern of inputs (x [a : int] and outputs (x [a b] matches that in S. The usage annotation of 1 on S indicates that only one side of x is being used by server. One possible definition of a client is client = x negate : x [2] : x [a : int] 0 2 and we can derive the typing judgement x : S 1 client: Note the use of to select from the available options, and that the subsequent pattern of inputs and outputs matches the specification in S. This client does not do anything with the value received from the ....

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S. J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings, 20th ACM Symposium on Principles of Programming Languages. ACM Press, 1993.

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Gay, S. J., A sort inference algorithm for the polyadic #-calculus, in: Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages (1993), pp. 429--438.

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S. J. Gay. A sort inference algorithm for the polyadic -calculus. In Proc. of POPL, pages 429--438, 1993.

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Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of ACM SIGPLAN /SIGACT Symposium on Principles of Programming Languages, pages 429--438, 1993.

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Simon J. Gay. A sort inference algorithm for the polyadic -calculus. In Proceedings of the Twentieth ACM Symposium on Principles of Programming Languages, January 1993.

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S. J. Gay. A sort inference algorithm for the polyadic - calculus. In Proceedings of ACM SIGPLAN/SIGACT Symposium on Principles of Programming Languages, pages 429--438, 1993.

No context found.

S. J. Gay. A sort inference algorithm for the polyadic #-calculus. In Proceedings of ACM SIGPLAN /SIGACT Symposium on Principles of Programming Languages, pages 429--438, 1993.

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Simon J. Gay. A sort inference algorithm for the polyadic - calculus. In ACM Symposium on Principles of Programming Languages `93, 1993.

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Simon J. Gay. A sort inference algorithm for the polyadic #-calculus. In ACM SIGACT / SIGPLAN Symposium on Principles of Programming Languages, pages 429--438, 1993.

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