The π-calculus offers an attractive basis for concurrent programming. It is small, elegant, and well studied, and supports (via simple encodings) a wide range of high-level constructs including data structures, higher-order functional programming, concurrent control structures, and objects. Moreover, familiar type systems for the -calculus have direct counterparts in the π-calculus, yielding strong, static typing for a high-level language using the π-calculus as its core. This paper describes Pict, a strongly-typed concurrent programming language constructed in terms of an explicitly-typed-calculus core language.

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We propose a general, powerful framework of type systems for the #-calculus, and show that we can obtain as its instances a variety of type systems guaranteeing non-trivial properties like deadlock-freedom and race-freedom. A key idea is to express types and type environments as abstract processes: We can check various properties of a process by checking the corresponding properties of its type environment. The framework clarifies the essence of recent complex type systems, and it also enables sharing of a large amount of work such as a proof of type preservation, making it easy to develop new type systems.

The theory of cut-free sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higher-order programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. To illustrate the new expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency. We also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum.

We propose a new type system for information flow analysis for the

. We propose a typed, higher-order, concurrent linear logic programming called higher-order ACL, which uniformly integrates a variety of mechanisms for concurrent computation based on asynchronous message passing. Higher-order ACL is based on a proof search paradigm according to the principle, proofs as computations, formulas as processes in linear logic. In higher-order ACL, processes as well as functions, and other values can be communicated via messages, which provides high modularity of concurrent programs. Higher-order ACL can be viewed as an asynchronous counterpart of Milner's higher-order, polyadic - calculus. Moreover, higher-order ACL is equipped with an elegant MLstyle type system that ensures (1) well typed programs can never cause type mismatch errors, and (2) there is a type inference algorithm which computes a most general typing for an untyped term. We also demonstrate a power of higher-order ACL by showing several examples of "higher-order concurrent prog...

Interpretation. An alternative way to analyze the behavior of a concurrent program would be to use abstract interpretation [4, 5]. Actually, from a very general viewpoint, our type-based analysis of locks can be seen as a kind of abstract interpretation. We can read a type judgment # P as "# is an abstraction of a concrete process P ." (The relation "#" corresponds to a pair of abstraction /concretization functions.) Indeed, we can regard a type environment as an abstract process: we have defined reductions of type environments in Section 3.7.

Type systems for programming languages help reasoning about program behavior and early finding of bugs. Recent applications of type systems include analysis of various program behaviors such as side effects, resource usage, security properties, and concurrency. This paper is a tutorial of one of such applications: type systems for analyzing behavior of concurrent processes. We start with a simple type system and extend it step by step to obtain more expressive type systems to reason about deadlock-freedom, safe usage of locks, etc.

Linear logic (LL) is the logical foundation of some type-theoretic languages and also of environments for specification and theorem proving. In this paper, we analyse the relationships between the proof net notion of LL and the connection notion used for efficient proof-search in different logics. Aiming at using proof nets as a tool for automated deduction in linear logic, we define a connection-based characterization of provability in Multiplicative Linear Logic (MLL). We show that an algorithm for proof net construction can be seen as a proof-search connection method. This central result is illustrated with a specific algorithm that is able to construct, for a provable MLL sequent, a set of connections, a proof net and a sequent proof. From these results we expect to extend to other LL fragments, we analyse what happens with the additive connectives of LL by tackling the additive fragment in a similar way.

This paper presents a linear logic programming language, called O \Gammaffi , that gives a complete account of an object-oriented calculus with inheritance and override. This language is best understood as a logical counterpart the object and record extensions of functional programming that have recently been proposed in the literature. From these proposals, O \Gammaffi inherits the representation of objects as composite data structures, with attribute and method fields, as well as their interpretation as first-class values. O \Gammaffi also gives a direct logical modeling of the self-application semantics of method invocation that justifies the view of objects as elements of recursive types. As such, the design of O \Gammaffi appears interesting, in perspective, as a basis for developing flexible and powerful type systems for logical object-based languages.