Typing the Use of Resources in a Concurrent Calculus (Extended Abstract)

We introduce a new type system for the blue calculus - a variant of the π-calculus that directly contains the Λ-calculus. Our notion of type is built upon a combination of Curry-Church simple types and Hennessy-Milner logic with recursion. We interpret a modality (u)T as the type of a process offering a resource of type T on the name u. In the typing system this is used in a kind of logical cut rule, ensuring that a message to the name u will meet a corresponding offer. We show that our calculus is type safe, that is, types are preserved along the computations.

[1]  Marino Miculan,et al.  Modal /spl mu/-types for processes , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[2]  Roberto M. Amadio,et al.  An Asynchronous Model of Locality, Failure and Process Mobility , 1997, COORDINATION.

[3]  F. Cardone,et al.  Two extensions of Curry's type inference system , 1990 .

[4]  Gérard Boudol.  The π-calculus in direct style , 1997, POPL '97.

[5]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[6]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[7]  M. Nivat.  Fiftieth volume of theoretical computer science , 1988 .

[8]  Kohei Honda,et al.  An Interaction-based Language and its Typing System , 1994, PARLE.

[9]  Oscar Nierstrasz,et al.  Regular types for active objects , 1993, OOPSLA '93.

[10]  Jean-Yves Girard,et al.  On the Unity of Logic , 1993, Ann. Pure Appl. Log..

[11]  Nobuko Yoshida,et al.  Graph Types for Monadic Mobile Processes , 1996, FSTTCS.

[12]  Benjamin C. Pierce,et al.  Linearity and the pi-calculus , 1996, POPL '96.

[13]  Roberto M. Amadio,et al.  Toward a Modal Theory of Types for the pi-Calculus , 1996, FTRTFT.

[14]  Cédric Fournet,et al.  The reflexive CHAM and the join-calculus , 1996, POPL '96.

[15]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[16]  Kim G. Larsen,et al.  Proof Systems for Satisfiability in Hennessy-Milner Logic with Recursion , 1990, Theor. Comput. Sci..

[17]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[18]  Naoki Kobayashi,et al.  A partially deadlock-free typed process calculus , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[19]  David N. Turner,et al.  The polymorphic Pi-calculus : theory and implementation , 1996 .

[20]  Rajagopal Nagarajan,et al.  Interaction categories and the foundations of typed concurrent programming , 1996, NATO ASI DPD.