Vasco T. Vasconcelos and Kohei Honda. Principal typing schemes in a polyadic ß-calculus. In Proceedings CONCUR'93, July 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....behavior of the whole system and they are not able to express nondeterminism. The use of logical languages like the modal calculus to express sequences [4] results in a complex type checking system which supports finite types only. Types in the object based process model of Vasconcelos and Honda [12, 13] also cannot describe the sequencing of messages. The calculi proposed by Abadi and Cardelli [1] focus on sequential object oriented systems; hence, sequencing of messages is not even a topic for these calculi. A concurrent version of one of these calculi is presented in [5] simply This work ....

Vasco T. Vasconcelos and Kohei Honda. Principal typing schemes in a polyadic ß-calculus. In Proceedings CONCUR'93, July 1993.

....is compatible, P is compatible and 8n 2 N : Gamma n Pn : process then t Gamma t P : process. For any pre type S the set f T j S v T g is finite. Given some Gamma P : process (perhaps with types containing only GG capabilities, inferred by an algorithm along the lines of [Gay93, VH93, Tur96] one can therefore compute the least upper bound of f P 0 j P v P 0 Gamma P 0 : process g. For the example above this gives T = l LL l GammaL 1) t (l LL l LL 1) l LL l GammaL 1. A more efficient algorithm will clearly be required in practice. 5 Conclusion We conclude by ....

Vasco Thudichum Vasconcelos and Kohei Honda. Principal typing schemes in a polyadic ß-calculus. In Proceedings of CONCUR '93. LNCS 715, pages 524--538, 1993.

....introduces an operator to express recursion, and an ML style let constructor allowing to associate an agent to an agentvariable, and use the latter several times in a program. The essence of the monomorphic type system is the assignment of types to names, and multiple name type pairs to programs [14]. The polymorphic type system incorporates a form of abstraction over types, and inference rules allowing to introduce and eliminate the abstraction operator. The extended system preserves most of the syntactic properties of the monomorphic system, including subject reduction and computability of ....

....of polymorphism. In fact, an agent constant can be used to instantiate processes with different name structures for the names in the instantiated process. This name structure, arising in name passing calculi by the simple fact that names carry names, is captured by the notion of types for names [2, 7, 11, 13, 14]. Then we are in presence of a case To appear in 5th Parallel Architectures and Languages Europe, LNCS. Springer Verlag, July 1994. of predicative polymorphism where names in the instantiated processes have different types, instances of a more general (polymorphic) type for the agent. The ....

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Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß-calculus. In 4th International Conference on Concurrency Theory, volume 715 of LNCS, pages 524--538. Springer-Verlag, August 1993. Also as Keio University Report CS 92-002.

.... number of refined type systems for calculi have been studied, addressing polymorphism [FLMR97, LW95, PS97, Tur96, Vas94] directionality [Ode95, PS96] linearity and receptiveness [Ama97, KPT96, San97] deadlock freedom [Kob97] object encodings [San96] confluence [Nie96, NS97] type inference [Gay93, VH93] and other phenomena (this is far from exhaustive) Each allows some particular behavioural discipline of processes to be expressed. It may be useful to contrast typing for calculi with the more standard typing for calculi. A simply typed calculus might have types T : Int fi fi fi T ....

Vasco Thudichum Vasconcelos and Kohei Honda. Principal typing schemes in a polyadic ß-calculus. In Proceedings of CONCUR '96. LNCS 715, pages 524--538, 1993.

.... The present report is the summary of a brief investigation on the nature of the name agentvariable structures that arise in the higher order calculus [4] The result that types (in the sense of [6] for higher order agents do not add much to what was already know for the polyadic calculus [6, 7] is in conformity with Sangiorgi s conclusions at the behavior level [4] To extend the framework of types for the polyadic calculus into the higher order scenario, all we have to do is to introduce a new type constructor [ff 1 Delta Delta Delta ff n ] n describing a process abstracted in a ....

....ff n ] n describing a process abstracted in a sequence of n names of types ff 1 ; ff n , respectively. Recall that the type of a name capable of carrying a sequence of n names of types ff 1 ; ff n is denoted by (ff 1 Delta Delta Delta ff n ) n . The typing system proposed in [6, 7] adapts easily to the new setting, and so does the typing reconstruction algorithm. Sangiorgi describes a higher order calculus where legal agents must be syntactically correct (we call these pre agents) and must verify a system of formation rules. In contrast, we present a system of inference ....

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Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß- calculus. CS 92-4, Keio University, November 1992.

....Keio University 3 14 1 Hiyoshi Kohoku ku Yokohama 223 Japan September 22, 1993 Abstract We study a typing assignment system for the higher order calculus. The system proposed is a straightforward extension of the typing system for the polyadic calculus proposed by Kohei Honda and the author [6], by introducing a new type constructor for agents (i.e. processes abstracted on some sequence of names and variables. We also present an efficient typing reconstruction algorithm to extract the most general typing of an agent or to detect its inexistence, and prove its correctness with respect ....

....correspondence between Sangiorgi s sorting system [4] and the typing assignment system. Introduction The present report is the summary of a brief investigation on the nature of the name agentvariable structures that arise in the higher order calculus [4] The result that types (in the sense of [6]) for higher order agents do not add much to what was already know for the polyadic calculus [6, 7] is in conformity with Sangiorgi s conclusions at the behavior level [4] To extend the framework of types for the polyadic calculus into the higher order scenario, all we have to do is to ....

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Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß- calculus. In E. Best, editor, Proceedings of CONCUR'93, pages 524--538, SpringerVerlag, August 1993. LNCS 715.

....infinite behaviour. 4 1. INTRODUCTION The type systems. The calculus is untyped, or more precisely, implicitly typed. In contrast with calculi where terms are assigned types, in name passing calculi it is names which are assigned types; terms are assigned sets of name type pairs called typings [65]. Simple types are built from type variables and the labels in terms, by means of a single constructor: a record. A type variable is a type, and, if l 1 ; l n are n pairwise distinct labels, and ff 1 ; ff n are n sequences of types, then [l 1 : ff 1 ; l n : ff n ] ....

....6 1. INTRODUCTION TA [ TA [ hi TA [ TA [ hi TA ( TA TA SR p p p p p p p P I Gamma p p p p p p p P I p p p p p p p PT p p p p p SN p Three systems where included for reference. System TA ( is the type system for the polyadic calculus developed by Honda and myself [64, 65]. System TA is the simple type system for the calculus, and system TA is the recursive type system for the calculus developed by Cardone and Coppo [15, 16] The new acronym, SN, stands for the strong normalization property of the calculus that says that typable terms are strongly ....

[Article contains additional citation context not shown here]

Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß-calculus. In 4th International Conference on Concurrency Theory, volume 715 of LNCS, pages 524-- 538. Springer-Verlag, August 1993. Also as Keio University Report CS 92--004.

....6 1. INTRODUCTION TA [ TA [ hi TA [ TA [ hi TA ( TA TA SR p p p p p p p P I Gamma p p p p p p p P I p p p p p p p PT p p p p p SN p Three systems where included for reference. System TA ( is the type system for the polyadic calculus developed by Honda and myself [64, 65]. System TA is the simple type system for the calculus, and system TA is the recursive type system for the calculus developed by Cardone and Coppo [15, 16] The new acronym, SN, stands for the strong normalization property of the calculus that says that typable terms are strongly ....

....given sort may carry. A sort check system allows to verify whether a process is well sorted against a given sorting. Sorts and types are indeed close notions. There is however an important difference: sorts induce a notion of name matching, as opposed to the notion of structure matching for types [64, 65]. A typing assignment system for the polyadic calculus, based on type assignment systems for the calculus, was presented by Honda and myself [64, 65] While both the sort check and the typing assignment systems ensure that wellsorted (or typable) programs do not encounter errors at runtime, the ....

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Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß-calculus. CS 92--004, Keio University, November 1992. Abridged version in [65].

....117. Springer Verlag, July 1994. They provide for recursion and, through an ML like let constructor, allow to declare an agent once and use it several times in a given process. T yCO grows from the basic calculus of objects and its monomorphic typing system [17] by introducing recursive types [2, 14, 16], and a form of predicative polymorphism [3, 15] Then, we incorporate datatype declarations, and values constructed from these declarations, in the style of ML [9] Miranda [13] and Haskell [6] Further values are the application of values to values, and a form of name abstraction. Together, ....

....Processes representing natural numbers and lists are two examples of a more general class of processes containing recurring name structures that cannot be typed in TA. To type such processes we introduce a new type constructor t:ff denoting the infinite tree solution of the equation t = ff [2, 14, 16]. In this way, the set of recursive types is defined by adding to the syntax of simple types a production t:ff, for any type variable t and any recursive type ff. If ff is a type, denote by ff its associated infinite tree. An interpretation of recursive types as infinite trees naturally ....

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Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß-calculus. In 4th International Conference on Concurrency Theory, volume 715 of LNCS, pages 524--538. Springer-Verlag, August 1993. Also as Keio University Report CS 92-002.

....Then there is Gamma such that P Gamma where, for any Gamma 0 with P Gamma 0 , Gamma 0 is a substitution instance of Gamma. Moreover such Gamma can be found effectively. The proof uses the most common type scheme between two schemes and checks each inference rule. In [20], an algorithm which efficiently computes the most general type scheme for a restricted system, which is essentially Milner s polyadic calculus in [17] is presented and proved to be correct with respect to its typing system. The algorithm is easily adaptable to the system in the present paper. ....

Vasco, V. and Honda, K., Principal typing scheme for polyadic ß-Calculus, in this volume.

.... by Milner s polyadic calculus [4] Honda s calculus [3] and Hewitt s actor model [1] we present a basic object calculus where the notions of objects, asynchronous messages and concurrency are primitive, and introduce a type discipline along the lines of Honda [2] and Vasconcelos and Honda [7] for the (untyped) calculus, enjoying the properties that programs that verify the discipline will never run into errors of the kind message not understood , and that there is an effectively computable notion of principal typings from which all typings that make a process well typed can be ....

....of which composed of a label l i , a sequence of formal parameters x i and an arbitrary process as the method body. Processes are put together by means of the usual concurrent composition. Scope restriction and replication complete the set of constructors the calculus is built from. Following [2, 7], types are assigned to names, and not to processes, the latter being assigned multiple name type pairs, constituting a typing for the process. Types are built from variables by means of a single constructor [l 1 : ff 1 ; l n : ff n ] representing a name associated with an object ....

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Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß- calculus. In E. Best, editor, Proceedings of CONCUR'93, pages 524--538, SpringerVerlag, August 1993. LNCS 715.

....of the unique solution of a single system of regular equations [2] From such a system we can easily build S and ob. It is then easy to prove that we have a : s and x n : ob(s) for some sort s, if and only if fa : ae) n ; x n : aeg 0 for some sequence of infinite types ae (refer to [14] for details) Using this correspondence between sortings and typings, it is easy to prove that a located agent in standard form [10] is well sorted if and only if the corresponding process in our calculus is typable (again, refer to [14] for details) As an example, let us solve the system of ....

.... aeg 0 for some sequence of infinite types ae (refer to [14] for details) Using this correspondence between sortings and typings, it is easy to prove that a located agent in standard form [10] is well sorted if and only if the corresponding process in our calculus is typable (again, refer to [14] for details) As an example, let us solve the system of regular equations induced by the sorting to handle lists as in [10] 8 : list = cons, nil) 2 cons = val, list) 2 nil = 0 The system is solved equation by equation. By substituting the right hand side of the second and third ....

Vasco T. Vasconcelos and Kohei Honda. Principal typing-schemes in a polyadic ß-calculus. CS 92-4, Keio University, 1992.

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