. Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent work it was shown that the denotational semantics of determinate concurrent constraint programming languages forms a fibred categorical structure called a hyperdoctrine, which is used as the basis of the categorical formulation of first-order logic. What this shows is that the combinators of determinate CCP can be viewed as logical connectives. In this paper we extend these ideas to the operational semantics of such languages and thus make available similar analogies for a much broader variety of languages including indeterminate CCP languages and concurrent block-structured imperative languages. CR Classification: F3.1, F3.2, D1.3, D3.3 Key words: Concurrent constraint programming, simula...

We present a framework to support consumable credentials in a logic-based distributed authorization system. Such credentials convey use-limited authority (e.g., to open a door once) or authority to utilize resources that are themselves limited (e.g., to spend money). We design a framework based on linear logic to enforce the consumption of credentials in a distributed system, and to protect credentials from nonproductive consumption as might result from misbehavior or failure. Finally, we give several usage examples in the framework, and evaluate the performance of our implementation for use in a ubiquitous computing deployment at our institution.

We present new proofs of cut elimination for intuitionistic and classical sequent calculi. In both cases the proofs proceed by three nested structural inductions, avoiding the explicit use of multisets and termination measures on sequent derivations. This makes them amenable to elegant and concise representations in LF, which are given in full detail. This work was supported by NSF Grant CCR-9303383 The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of NSF or the U.S. government. Keywords: Logic, Cut Elimination, Logical Framework Contents 1 Introduction 1 2 Intuitionistic Sequent Calculus 2 3 Proof Terms for the Sequent Calculus 8 4 Representing Sequent Derivations in LF 10 5 Admissibility of Cut 13 6 Extension to Classical Logic 18 7 Conclusion 24 A Detailed Admissibility Proofs for Cut 26 A.1 Intuitionistic Calculus : : : : : : : : : : : : : : : : : : :...

The logical framework LF is a constructive type theory of dependent functions that can elegantly encode many other logical systems. Prior work has studied the benefits of extending it to the linear logical framework LLF, for the incorporation linear logic features into the type theory affords good representations of state change. We describe and argue for the usefulness of an extension of LF by features inspired by hybrid logic, which has several benefits. For one, it shows how linear logic features can be decomposed into primitive operations manipulating abstract resource labels. More importantly, it makes it possible to realize a metalogical framework capable of reasoning about stateful deductive systems encoded in the style familiar from prior work with LLF, taking advantage of familiar methodologies used for metatheoretic reasoning in LF.Acknowledgments From the very first computer science course I took at CMU, Frank Pfenning has been an exceptional teacher and mentor. For his patience, breadth of knowledge, and mathematical good taste I am extremely thankful. No less do I owe to the other two major contributors to my programming languages

Recently there has been significant interest in the logic programming community in linear logic, a logic designed with bounded resources in mind. As linear logic is a generalisation of classical logic, a logic programming language based on linear logic subsumes and extends (pure) Prolog. One such language is Lygon, a language based on a certain kind of proof in the linear sequent calculus. However these proofs, whilst providing a logical characterization of the language, still retain some of the non-determinism of the sequent calculus, and hence require further analysis before an implementation can be attempted. In this report we define and discuss a more detailed proof system, which is more deterministic than the original. In particular, this system handles the allocation of resources to different branches of the proof in a lazy manner. The resulting system differs significantly from the original sequent calculus, and so we discuss its properties in some detail. We prove the soundness...

This paper shows how to use Girard’s intuitionistic linear logic extended with arithmetic or other constraints to reason about pointer programs. More specifically, first, the paper defines the proof theory for ILC (Intuitionistic Linear logic with Constraints) and shows it is consistent via a proof of cut elimination. Second, inspired by prior work of O’Hearn, Reynolds and Yang, the paper explains how to interpret linear logical formulas as descriptions of a program store. Third, we define a simple imperative programming language with mutable references and arrays and give verification condition generation rules that produce assertions in ILC. Finally, we identify a fragment of ILC, ILC − , that is both decidable and closed under generation of verification conditions. In other words, if loop invariants are specified in ILC − , then the resulting verification conditions are also in ILC −. Since verification condition generation is syntax-directed, we obtain a decidable procedure for checking properties of pointer programs.

This paper describes an extension of the WAM (Warren Abstract Machine) for a logic programming language called LLP which is based on intuitionisic linear logic. LLP is a subset of Lolli and includes additive and multiplicative conjunction, linear implication in a goal, exponential (!), and the constant 1. The extension of the WAM is mainly for efficient resource management: especially for resource look-up and deletion. In our design, only one table is maintained to keep resources during the execution. Looking-up of a resource is done through a hash table. Deletion of a resource is done by just "marking" the entry in the table. Our prototype compiler produces 25 times faster code compared with a compiled Prolog program which represents resources by a list structure.

The paper reports on an experiment with the major linear logic programming languages defined in the recent years: Lolli, LO and Forum. As a case study, we consider the representation of a class of Petri nets, P/T ! nets, in each of these languages. Keywords: Petri nets, multiset rewriting systems, linear logic, logic programming. 1 Introduction The relationship between linear logic [4] and Petri Nets [8] has been a major object of investigation [2, 3, 6]. It was soon noticed that the monoidal structure of multisets can serve as an abstract link between Petri nets (where markings are multisets and transition are rewrite rules on multisets) and the multiplicative fragment of linear logic (where either\Omega or O is the operation of the monoid and 1 or? is its identity). See [3] for a precise account of this relationship. On the other hand, a number of fragments of linear logic have been cast into logic programming languages with the aim of capturing some of the expressive power provi...

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.

When Miller introduced Forum he called it a specification logic, rather than a logic programming language. In this paper we outline those features that create problems in attempting to implement an interpreter for the language, and describe solutions to those problems. We show how techniques used in the implementation of Lolli can be extended naturally to Forum. Finally, we show two Forum programs in order to demonstrate some of the paradigms that arise in using the language. 1 Introduction Forum, a fragment of Linear Logic introduced by Dale Miller in 1994, is distinguished by two key features. First, it is complete for all of Linear Logic, in the sense that Linear Logic operators that are not part of Forum can be mapped to Forum by a provability-preserving translation. Second, a form of goal-directed proof search (as characterized by uniform proofs) is complete. Historically, logics for which uniform proofs are complete, such as Horn Clauses, Hereditary Harrop Formulas, and Linear H...