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40
A concurrent logical framework I: Judgments and properties
, 2003
"... The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous con ..."
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Cited by 74 (25 self)
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The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives# of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #, & and #.
A symmetric modal lambda calculus for distributed computing
 IN PROCEEDINGS OF THE 19TH IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS
, 2004
"... We present a foundational language for distributed programming, called Lambda 5, that addresses both mobilityof code and locality of resources. In order to construct our system, we appeal to the powerful propositionsastypes interpretation of logic. Specifically, we take the possible worlds of the ..."
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Cited by 50 (12 self)
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We present a foundational language for distributed programming, called Lambda 5, that addresses both mobilityof code and locality of resources. In order to construct our system, we appeal to the powerful propositionsastypes interpretation of logic. Specifically, we take the possible worlds of the intuitionistic modal logic IS5 to be nodes ona network, and the connectives 2 and 3 to reflect mobility and locality, respectively. We formulate a novel systemof natural deduction for IS5, decomposing the introduction and elimination rules for 2 and 3, thereby allowing thecorresponding programs to be more direct. We then give an operational semantics to our calculus that is typesafe, logically faithful, and computationally realistic.
A Judgmental Analysis of Linear Logic
, 2003
"... We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, ext ..."
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Cited by 49 (27 self)
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We reexamine the foundations of linear logic, developing a system of natural deduction following MartinL of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing from both classical linear logic and Hyland and de Paiva's full intuitionistic linear logic. We also provide a corresponding sequent calculus that admits a simple proof of the admissibility of cut by a single structural induction. Finally, we show how to interpret classical linear logic (with or without the MIX rule) in our system, employing a form of doublenegation translation.
A Coverage Checking Algorithm for LF
, 2003
"... Coverage checking is the problem of deciding whether any closed term of a given type is an instance of at least one of a given set of patterns. It can be used to verify if a function defined by pattern matching covers all possible cases. This problem has a straightforward solution for the first ..."
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Cited by 39 (12 self)
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Coverage checking is the problem of deciding whether any closed term of a given type is an instance of at least one of a given set of patterns. It can be used to verify if a function defined by pattern matching covers all possible cases. This problem has a straightforward solution for the firstorder, simplytyped case, but is in general undecidable in the presence of dependent types. In this paper we present a terminating algorithm for verifying coverage of higherorder, dependently typed patterns.
A Concurrent Logical Framework: The Propositional Fragment
, 2003
"... We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations ..."
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Cited by 31 (3 self)
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We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations. This separation leads to a tractable notion of definitional equality that identifies computations di#ering only in the order of execution of independent steps. From a logical point of view our type theory can be seen as a novel combination of lax logic and dual intuitionistic linear logic. An encoding of a small Petri net exemplifies the representation methodology, which can be summarized as "concurrent computations as monadic expressions ".
A linear logic of authorization and knowledge
 In Proceedings of the 11th European Symposium on Research in Computer Security
, 2006
"... ..."
Modal Types for Mobile Code
, 2008
"... In this dissertation I argue that modal type systems provide an elegant and practical means for controlling local resources in spatially distributed computer programs. A distributed program is one that executes in multiple physical or logical places. It usually does so because those places have loca ..."
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Cited by 19 (0 self)
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In this dissertation I argue that modal type systems provide an elegant and practical means for controlling local resources in spatially distributed computer programs. A distributed program is one that executes in multiple physical or logical places. It usually does so because those places have local resources that can only be used in those locations. Such resources can include processing power, proximity to data, hardware, or the physical presence of a user. Programmers that write distributed applications therefore need to be able to reason about the places in which their programs will execute. This work provides an elegant and practical way to think about such programs in the form of a type system derived from modal logic. Modal logic allows for reasoning about truth from multiple simultaneous perspectives. These perspectives, called "worlds," are identified with the locations in the distributed program. This enables the programming language to be simultaneously aware of the various hosts involved in a program, their
Modal proofs as distributed programs
 13th European Symposium on Programming
, 2003
"... We develop a new foundation for distributed programming languages by defining an intuitionistic, modal logic and then interpreting the modal proofs as distributed programs. More specifically, the proof terms for the various modalities have computational interpretations as remote procedure calls, com ..."
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Cited by 18 (1 self)
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We develop a new foundation for distributed programming languages by defining an intuitionistic, modal logic and then interpreting the modal proofs as distributed programs. More specifically, the proof terms for the various modalities have computational interpretations as remote procedure calls, commands to broadcast computations to all nodes in the network, commands to use portable code, and finally, commands to invoke computational agents that can find their own way to safe places in the network where they can execute. We prove some simple metatheoretic results about our logic as well as a safety theorem that demonstrates that the deductive rules act as a sound type system for a distributed programming language. 1
A mechanically verified, sound and complete theorem prover for first order logic
 In Theorem Proving in Higher Order Logics, 18th International Conference, TPHOLs 2005, volume 3603 of Lecture Notes in Computer Science
, 2005
"... Abstract. We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable, allowing us to derive an algorithm to test for first order validity. This algorithm may be e ..."
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Cited by 13 (0 self)
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Abstract. We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable, allowing us to derive an algorithm to test for first order validity. This algorithm may be executed in Isabelle/HOL using the rewrite engine. Alternatively the algorithm has been ported to OCaML. 1
On the specification of sequent systems
 IN LPAR 2005: 12TH INTERNATIONAL CONFERENCE ON LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE AND REASONING, NUMBER 3835 IN LNAI
, 2005
"... Recently, linear Logic has been used to specify sequent calculus proof systems in such a way that the proof search in linear logic can yield proof search in the specified logic. Furthermore, the metatheory of linear logic can be used to draw conclusions about the specified sequent calculus. For e ..."
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Cited by 13 (6 self)
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Recently, linear Logic has been used to specify sequent calculus proof systems in such a way that the proof search in linear logic can yield proof search in the specified logic. Furthermore, the metatheory of linear logic can be used to draw conclusions about the specified sequent calculus. For example, derivability of one proof system from another can be decided by a simple procedure that is implemented via bounded logic programmingstyle search. Also, simple and decidable conditions on the linear logic presentation of inference rules, called homogeneous and coherence, can be used to infer that the initial rules can be restricted to atoms and that cuts can be eliminated. In the present paper we introduce Llinda, a logical framework based on linear logic augmented with inference rules for definition (fixed points) and induction. In this way, the above properties can be proved entirely inside the framework. To further illustrate the power of Llinda, we extend the definition of coherence and provide a new, semiautomated proof of cutelimination for Girard’s Logic of Unicity (LU).