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60
Session Types as Intuitionistic Linear Propositions
"... Several type disciplines for πcalculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculu ..."
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Cited by 61 (17 self)
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Several type disciplines for πcalculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic. Our type system is based on a new interpretation of linear propositions as session types, and provides the first purely logical account of all (both shared and linear) features of session types. We show that our type discipline is useful from a programming perspective, and ensures session fidelity, absence of deadlocks, and a tight operational correspondence between πcalculus reductions and cut elimination steps. 1
Focusing the inverse method for linear logic
 Proceedings of CSL 2005
, 2005
"... 1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10 ..."
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Cited by 51 (15 self)
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1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10
An Authorization Logic with Explicit Time
, 2008
"... We present an authorization logic that permits reasoning with explicit time. Following a prooftheoretic approach, we study the metatheory of the logic, including cut elimination. We also demonstrate formal connections to proofcarrying authorization’s existing approach for handling time and commen ..."
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Cited by 30 (12 self)
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We present an authorization logic that permits reasoning with explicit time. Following a prooftheoretic approach, we study the metatheory of the logic, including cut elimination. We also demonstrate formal connections to proofcarrying authorization’s existing approach for handling time and comment on the enforceability of our logic in the same framework. Finally, we illustrate the expressiveness of the logic through examples, including those with complex interactions between time, authorization, and mutable state.
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 27 (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
Consumable Credentials in LogicBased Access Control
 CARNEGIE MELLON UNIVERSITY
, 2006
"... We present a framework to support consumable credentials in a logicbased distributed authorization system. Such credentials convey uselimited 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 ..."
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Cited by 27 (10 self)
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We present a framework to support consumable credentials in a logicbased distributed authorization system. Such credentials convey uselimited 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.
A proofcarrying file system
, 2009
"... This paper presents the design and implementation of PCFS, a file system that uses formal proofs and capabilities to efficiently enforce access policies expressed in a rich logic. Salient features include backwards compatibility with existing programs and automatic enforcement of access rules that d ..."
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Cited by 26 (13 self)
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This paper presents the design and implementation of PCFS, a file system that uses formal proofs and capabilities to efficiently enforce access policies expressed in a rich logic. Salient features include backwards compatibility with existing programs and automatic enforcement of access rules that depend on both time and system state. We rigorously prove that enforcement using capabilities is correct, and evaluate the file system’s performance.
Hybridizing a logical framework
 In International Workshop on Hybrid Logic 2006 (HyLo 2006), Electronic Notes in Computer Science
, 2006
"... 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 r ..."
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Cited by 25 (1 self)
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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
Linear Logical Algorithms
"... Abstract. Bottomup logic programming can be used to declaratively specify many algorithms in a succinct and natural way, and McAllester and Ganzinger have shown that it is possible to define a cost semantics that enables reasoning about the running time of algorithms written as inference rules. Pre ..."
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Cited by 16 (5 self)
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Abstract. Bottomup logic programming can be used to declaratively specify many algorithms in a succinct and natural way, and McAllester and Ganzinger have shown that it is possible to define a cost semantics that enables reasoning about the running time of algorithms written as inference rules. Previous work with the programming language Lollimon demonstrates the expressive power of logic programming with linear logic in describing algorithms that have imperative elements or that must repeatedly make mutually exclusive choices. In this paper, we identify a bottomup logic programming language based on linear logic that is amenable to efficient execution and describe a novel cost semantics that can be used for complexity analysis of algorithms expressed in linear logic. Key words: Bottomup logic programming, forward reasoning, linear logic, deductive databases, cost semantics, abstract running time 1
Towards Concurrent Type Theory
 INVITED TALK AT TLDI’12
, 2012
"... We review progress in a recent line of research that provides a concurrent computational interpretation of (intuitionistic) linear logic. Propositions are interpreted as session types, sequent proofs as processes in the πcalculus, cut reductions as process reductions, and vice versa. The strong pro ..."
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Cited by 15 (7 self)
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We review progress in a recent line of research that provides a concurrent computational interpretation of (intuitionistic) linear logic. Propositions are interpreted as session types, sequent proofs as processes in the πcalculus, cut reductions as process reductions, and vice versa. The strong prooftheoretic foundation of this type system provides immediate opportunities for uniform generalization, specifically, to embed terms from a functional type theory. The resulting system satisfies the properties of type preservation, progress, and termination, as expected from a language derived via a CurryHoward isomorphism. While very expressive, the language is strictly stratified so that dependent types for functional terms can be enforced during communication, but neither processes nor channels can appear in functional terms. We briefly speculate on how this limitation might be overcome to arrive at a fully dependent concurrent type theory.
Linear Logical Relations for SessionBased Concurrency
"... Abstract. In prior work we proposed an interpretation of intuitionistic linear logic propositions as session types for concurrent processes. The type system obtained from the interpretation ensures fundamental properties of sessionbased typed disciplines—most notably, type preservation, session fid ..."
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Cited by 13 (8 self)
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Abstract. In prior work we proposed an interpretation of intuitionistic linear logic propositions as session types for concurrent processes. The type system obtained from the interpretation ensures fundamental properties of sessionbased typed disciplines—most notably, type preservation, session fidelity, and global progress. In this paper, we complement and strengthen these results by developing a theory of logical relations. Our development is based on, and is remarkably similar to, that for functional languages, extended to an (intuitionistic) linear type structure. A main result is that welltyped processes always terminate (strong normalization). We also introduce a notion of observational equivalence for sessiontyped processes. As applications, we prove that all proof conversions induced by the logic interpretation actually express observational equivalences, and explain how type isomorphisms resulting from linear logic equivalences are realized by coercions between interface types of sessionbased concurrent systems. 1