We introduce the concept of behavioral separation as a general principle for disciplining interference in higher-order imperative concurrent programs, and present a type-based approach that systematically develops the concept in the context of an ML-like language extended with concurrency and synchronization primitives. Behavioral separation builds on notions originally introduced for behavioral type systems and separation logics, but shifts the focus from the separation of static program state properties towards the separation of dynamic usage behaviors of runtime values. Behavioral separation types specify how values may be safely used by client code, and can enforce fine-grained interference control disciplines while preserving compositionality, information hiding, and flexibility. We illustrate how our type system, even if based on a small set of general primitives, is already able to tackle fairly challenging program idioms, involving aliasing at various types, concurrency with first-class threads, manipulation of linked data structures, behavioral borrowing, and invariant-based separation.
{"title":"The type discipline of behavioral separation","authors":"Luís Caires, J. Seco","doi":"10.1145/2429069.2429103","DOIUrl":"https://doi.org/10.1145/2429069.2429103","url":null,"abstract":"We introduce the concept of behavioral separation as a general principle for disciplining interference in higher-order imperative concurrent programs, and present a type-based approach that systematically develops the concept in the context of an ML-like language extended with concurrency and synchronization primitives. Behavioral separation builds on notions originally introduced for behavioral type systems and separation logics, but shifts the focus from the separation of static program state properties towards the separation of dynamic usage behaviors of runtime values. Behavioral separation types specify how values may be safely used by client code, and can enforce fine-grained interference control disciplines while preserving compositionality, information hiding, and flexibility. We illustrate how our type system, even if based on a small set of general primitives, is already able to tackle fairly challenging program idioms, involving aliasing at various types, concurrency with first-class threads, manipulation of linked data structures, behavioral borrowing, and invariant-based separation.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88295866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Effects are fundamental to programming languages. Even the lambda calculus has effects, and consequently the two famous evaluation strategies produce different semantics. As such, much research has been done to improve our understanding of effects. Since Moggi introduced monads for his computational lambda calculus, further generalizations have been designed to formalize increasingly complex computational effects, such as indexed monads followed by layered monads followed by parameterized monads. This succession prompted us to determine the most general formalization possible. In searching for this formalization we came across many surprises, such as the insufficiencies of arrows, as well as many unexpected insights, such as the importance of considering an effect as a small component of a whole system rather than just an isolated feature. In this paper we present our semantic formalization for producer effect systems, which we call a productor, and prove its maximal generality by focusing on only sequential composition of effectful computations, consequently guaranteeing that the existing monadic techniques are specializations of productors.
{"title":"The sequential semantics of producer effect systems","authors":"R. Tate","doi":"10.1145/2429069.2429074","DOIUrl":"https://doi.org/10.1145/2429069.2429074","url":null,"abstract":"Effects are fundamental to programming languages. Even the lambda calculus has effects, and consequently the two famous evaluation strategies produce different semantics. As such, much research has been done to improve our understanding of effects. Since Moggi introduced monads for his computational lambda calculus, further generalizations have been designed to formalize increasingly complex computational effects, such as indexed monads followed by layered monads followed by parameterized monads. This succession prompted us to determine the most general formalization possible. In searching for this formalization we came across many surprises, such as the insufficiencies of arrows, as well as many unexpected insights, such as the importance of considering an effect as a small component of a whole system rather than just an isolated feature. In this paper we present our semantic formalization for producer effect systems, which we call a productor, and prove its maximal generality by focusing on only sequential composition of effectful computations, consequently guaranteeing that the existing monadic techniques are specializations of productors.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86263496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. Hur, Georg Neis, Derek Dreyer, Viktor Vafeiadis
Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonly-known lattice-theoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e. breaking proofs into separate pieces that can be developed in isolation), and they do not support incremental reasoning (i.e. developing proofs interactively by starting from the goal and generalizing the coinduction hypothesis repeatedly as necessary). In this paper, we show how to support coinductive proofs that are both compositional and incremental, using a dead simple construction we call the parameterized greatest fixed point. The basic idea is to parameterize the greatest fixed point of interest over the accumulated knowledge of "the proof so far". While this idea has been proposed before, by Winskel in 1989 and by Moss in 2001, neither of the previous accounts suggests its general applicability to improving the state of the art in interactive coinductive proof. In addition to presenting the lattice-theoretic foundations of parameterized coinduction, demonstrating its utility on representative examples, and studying its composition with "up-to" techniques, we also explore its mechanization in proof assistants like Coq and Isabelle. Unlike traditional approaches to mechanizing coinduction (e.g. Coq's cofix), which employ syntactic "guardedness checking", parameterized coinduction offers a semantic account of guardedness. This leads to faster and more robust proof development, as we demonstrate using our new Coq library, Paco.
{"title":"The power of parameterization in coinductive proof","authors":"C. Hur, Georg Neis, Derek Dreyer, Viktor Vafeiadis","doi":"10.1145/2429069.2429093","DOIUrl":"https://doi.org/10.1145/2429069.2429093","url":null,"abstract":"Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonly-known lattice-theoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e. breaking proofs into separate pieces that can be developed in isolation), and they do not support incremental reasoning (i.e. developing proofs interactively by starting from the goal and generalizing the coinduction hypothesis repeatedly as necessary).\u0000 In this paper, we show how to support coinductive proofs that are both compositional and incremental, using a dead simple construction we call the parameterized greatest fixed point. The basic idea is to parameterize the greatest fixed point of interest over the accumulated knowledge of \"the proof so far\". While this idea has been proposed before, by Winskel in 1989 and by Moss in 2001, neither of the previous accounts suggests its general applicability to improving the state of the art in interactive coinductive proof.\u0000 In addition to presenting the lattice-theoretic foundations of parameterized coinduction, demonstrating its utility on representative examples, and studying its composition with \"up-to\" techniques, we also explore its mechanization in proof assistants like Coq and Isabelle. Unlike traditional approaches to mechanizing coinduction (e.g. Coq's cofix), which employ syntactic \"guardedness checking\", parameterized coinduction offers a semantic account of guardedness. This leads to faster and more robust proof development, as we demonstrate using our new Coq library, Paco.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82199558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a general framework for abstraction with respect to quantitative properties, such as worst-case execution time, or power consumption. Our framework provides a systematic way for counter-example guided abstraction refinement for quantitative properties. The salient aspect of the framework is that it allows anytime verification, that is, verification algorithms that can be stopped at any time (for example, due to exhaustion of memory), and report approximations that improve monotonically when the algorithms are given more time. We instantiate the framework with a number of quantitative abstractions and refinement schemes, which differ in terms of how much quantitative information they keep from the original system. We introduce both state-based and trace-based quantitative abstractions, and we describe conditions that define classes of quantitative properties for which the abstractions provide over-approximations. We give algorithms for evaluating the quantitative properties on the abstract systems. We present algorithms for counter-example based refinements for quantitative properties for both state-based and segment-based abstractions. We perform a case study on worst-case execution time of executables to evaluate the anytime verification aspect and the quantitative abstractions we proposed.
{"title":"Quantitative abstraction refinement","authors":"Pavol Cerný, T. Henzinger, Arjun Radhakrishna","doi":"10.1145/2429069.2429085","DOIUrl":"https://doi.org/10.1145/2429069.2429085","url":null,"abstract":"We propose a general framework for abstraction with respect to quantitative properties, such as worst-case execution time, or power consumption. Our framework provides a systematic way for counter-example guided abstraction refinement for quantitative properties. The salient aspect of the framework is that it allows anytime verification, that is, verification algorithms that can be stopped at any time (for example, due to exhaustion of memory), and report approximations that improve monotonically when the algorithms are given more time.\u0000 We instantiate the framework with a number of quantitative abstractions and refinement schemes, which differ in terms of how much quantitative information they keep from the original system. We introduce both state-based and trace-based quantitative abstractions, and we describe conditions that define classes of quantitative properties for which the abstractions provide over-approximations. We give algorithms for evaluating the quantitative properties on the abstract systems. We present algorithms for counter-example based refinements for quantitative properties for both state-based and segment-based abstractions. We perform a case study on worst-case execution time of executables to evaluate the anytime verification aspect and the quantitative abstractions we proposed.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73994212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Delphine Demange, Vincent Laporte, Lei Zhao, S. Jagannathan, David Pichardie, J. Vitek
Recent advances in verification have made it possible to envision trusted implementations of real-world languages. Java with its type-safety and fully specified semantics would appear to be an ideal candidate; yet, the complexity of the translation steps used in production virtual machines have made it a challenging target for verifying compiler technology. One of Java's key innovations, its memory model, poses significant obstacles to such an endeavor. The Java Memory Model is an ambitious attempt at specifying the behavior of multithreaded programs in a portable, hardware agnostic, way. While experts have an intuitive grasp of the properties that the model should enjoy, the specification is complex and not well-suited for integration within a verifying compiler infrastructure. Moreover, the specification is given in an axiomatic style that is distant from the intuitive reordering-based reasonings traditionally used to justify or rule out behaviors, and ill suited to the kind of operational reasoning one would expect to employ in a compiler. This paper takes a step back, and introduces a Buffered Memory Model (BMM) for Java. We choose a pragmatic point in the design space sacrificing generality in favor of a model that is fully characterized in terms of the reorderings it allows, amenable to formal reasoning, and which can be efficiently applied to a specific hardware family, namely x86 multiprocessors. Although the BMM restricts the reorderings compilers are allowed to perform, it serves as the key enabling device to achieving a verification pathway from bytecode to machine instructions. Despite its restrictions, we show that it is backwards compatible with the Java Memory Model and that it does not cripple performance on TSO architectures.
{"title":"Plan B: a buffered memory model for Java","authors":"Delphine Demange, Vincent Laporte, Lei Zhao, S. Jagannathan, David Pichardie, J. Vitek","doi":"10.1145/2429069.2429110","DOIUrl":"https://doi.org/10.1145/2429069.2429110","url":null,"abstract":"Recent advances in verification have made it possible to envision trusted implementations of real-world languages. Java with its type-safety and fully specified semantics would appear to be an ideal candidate; yet, the complexity of the translation steps used in production virtual machines have made it a challenging target for verifying compiler technology. One of Java's key innovations, its memory model, poses significant obstacles to such an endeavor. The Java Memory Model is an ambitious attempt at specifying the behavior of multithreaded programs in a portable, hardware agnostic, way. While experts have an intuitive grasp of the properties that the model should enjoy, the specification is complex and not well-suited for integration within a verifying compiler infrastructure. Moreover, the specification is given in an axiomatic style that is distant from the intuitive reordering-based reasonings traditionally used to justify or rule out behaviors, and ill suited to the kind of operational reasoning one would expect to employ in a compiler. This paper takes a step back, and introduces a Buffered Memory Model (BMM) for Java. We choose a pragmatic point in the design space sacrificing generality in favor of a model that is fully characterized in terms of the reorderings it allows, amenable to formal reasoning, and which can be efficiently applied to a specific hardware family, namely x86 multiprocessors. Although the BMM restricts the reorderings compilers are allowed to perform, it serves as the key enabling device to achieving a verification pathway from bytecode to machine instructions. Despite its restrictions, we show that it is backwards compatible with the Java Memory Model and that it does not cripple performance on TSO architectures.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90326665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Gordon, Mihhail Aizatulin, J. Borgström, Guillaume Claret, T. Graepel, A. Nori, S. Rajamani, Claudio V. Russo
A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic programming abstraction, a typed Bayesian model, which is based on a pair of probabilistic expressions for the prior and sampling distributions. A sampler for a model is an algorithm to compute synthetic data from its sampling distribution, while a learner for a model is an algorithm for probabilistic inference on the model. Models, samplers, and learners form a generic programming pattern for model-based inference. They support the uniform expression of common tasks including model testing, and generic compositions such as mixture models, evidence-based model averaging, and mixtures of experts. A formal semantics supports reasoning about model equivalence and implementation correctness. By developing a series of examples and three learner implementations based on exact inference, factor graphs, and Markov chain Monte Carlo, we demonstrate the broad applicability of this new programming pattern.
{"title":"A model-learner pattern for bayesian reasoning","authors":"A. Gordon, Mihhail Aizatulin, J. Borgström, Guillaume Claret, T. Graepel, A. Nori, S. Rajamani, Claudio V. Russo","doi":"10.1145/2429069.2429119","DOIUrl":"https://doi.org/10.1145/2429069.2429119","url":null,"abstract":"A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic programming abstraction, a typed Bayesian model, which is based on a pair of probabilistic expressions for the prior and sampling distributions. A sampler for a model is an algorithm to compute synthetic data from its sampling distribution, while a learner for a model is an algorithm for probabilistic inference on the model. Models, samplers, and learners form a generic programming pattern for model-based inference. They support the uniform expression of common tasks including model testing, and generic compositions such as mixture models, evidence-based model averaging, and mixtures of experts. A formal semantics supports reasoning about model equivalence and implementation correctness. By developing a series of examples and three learner implementations based on exact inference, factor graphs, and Markov chain Monte Carlo, we demonstrate the broad applicability of this new programming pattern.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79928942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
While separation logic is acknowledged as an enabling technology for large-scale program verification, most of the existing verification tools use only a fragment of separation logic that excludes separating implication. As the first step towards a verification tool using full separation logic, we develop a nested sequent calculus for Boolean BI (Bunched Implications), the underlying theory of separation logic, as well as a theorem prover based on it. A salient feature of our nested sequent calculus is that its sequent may have not only smaller child sequents but also multiple parent sequents, thus producing a graph structure of sequents instead of a tree structure. Our theorem prover is based on backward search in a refinement of the nested sequent calculus in which weakening and contraction are built into all the inference rules. We explain the details of designing our theorem prover and provide empirical evidence of its practicality.
{"title":"A theorem prover for Boolean BI","authors":"Jonghyun Park, Jeongbong Seo, Sungwoo Park","doi":"10.1145/2429069.2429095","DOIUrl":"https://doi.org/10.1145/2429069.2429095","url":null,"abstract":"While separation logic is acknowledged as an enabling technology for large-scale program verification, most of the existing verification tools use only a fragment of separation logic that excludes separating implication. As the first step towards a verification tool using full separation logic, we develop a nested sequent calculus for Boolean BI (Bunched Implications), the underlying theory of separation logic, as well as a theorem prover based on it. A salient feature of our nested sequent calculus is that its sequent may have not only smaller child sequents but also multiple parent sequents, thus producing a graph structure of sequents instead of a tree structure. Our theorem prover is based on backward search in a refinement of the nested sequent calculus in which weakening and contraction are built into all the inference rules. We explain the details of designing our theorem prover and provide empirical evidence of its practicality.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79741892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Even with the assistance of computer tools, the formalized de-scription and verification of research-level mathematics remains a daunting task, not least because of the talent with which mathema-ticians combine diverse theories to achieve their ends. By combin-ing tools and techniques from type theory, language design, and software engineering we have managed to capture enough of these practices to formalize the proof of the Odd Order theorem, a landmark result in Group Theory.
{"title":"Engineering mathematics: the odd order theorem proof","authors":"Georges Gonthier","doi":"10.1145/2429069.2429071","DOIUrl":"https://doi.org/10.1145/2429069.2429071","url":null,"abstract":"Even with the assistance of computer tools, the formalized de-scription and verification of research-level mathematics remains a daunting task, not least because of the talent with which mathema-ticians combine diverse theories to achieve their ends. By combin-ing tools and techniques from type theory, language design, and software engineering we have managed to capture enough of these practices to formalize the proof of the Odd Order theorem, a landmark result in Group Theory.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84751789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
From Owicki-Gries' Resource Invariants and Jones' Rely/Guarantee to modern variants based on Separation Logic, axiomatic logics for concurrency require auxiliary state to explicitly relate the effect of all threads to the global invariant on the shared resource. Unfortunately, auxiliary state gives the proof of an individual thread access to the auxiliaries of all other threads. This makes proofs sensitive to the global context, which prevents local reasoning and compositionality. To tame this historical difficulty of auxiliary state, we propose subjective auxiliary state, whereby each thread is verified using a self view (i.e., the thread's effect on the shared resource) and an other view (i.e., the collective effect of all the other threads). Subjectivity generalizes auxiliary state from stacks and heaps to user-chosen partial commutative monoids, which can eliminate the dependence on the global thread structure. We employ subjectivity to formulate Subjective Concurrent Separation Logic as a combination of subjective auxiliary state and Concurrent Separation Logic. The logic yields simple, compositional proofs of coarse-grained concurrent programs that use auxiliary state, and scales to support higher-order recursive procedures that can themselves fork new threads. We prove the soundness of the logic with a novel denotational semantics of action trees and a definition of safety using rely/guarantee transitions over a large subjective footprint. We have mechanized the denotational semantics, logic, metatheory, and a number of examples by a shallow embedding in Coq.
{"title":"Subjective auxiliary state for coarse-grained concurrency","authors":"Ruy Ley-Wild, Aleksandar Nanevski","doi":"10.1145/2429069.2429134","DOIUrl":"https://doi.org/10.1145/2429069.2429134","url":null,"abstract":"From Owicki-Gries' Resource Invariants and Jones' Rely/Guarantee to modern variants based on Separation Logic, axiomatic logics for concurrency require auxiliary state to explicitly relate the effect of all threads to the global invariant on the shared resource. Unfortunately, auxiliary state gives the proof of an individual thread access to the auxiliaries of all other threads. This makes proofs sensitive to the global context, which prevents local reasoning and compositionality.\u0000 To tame this historical difficulty of auxiliary state, we propose subjective auxiliary state, whereby each thread is verified using a self view (i.e., the thread's effect on the shared resource) and an other view (i.e., the collective effect of all the other threads). Subjectivity generalizes auxiliary state from stacks and heaps to user-chosen partial commutative monoids, which can eliminate the dependence on the global thread structure.\u0000 We employ subjectivity to formulate Subjective Concurrent Separation Logic as a combination of subjective auxiliary state and Concurrent Separation Logic. The logic yields simple, compositional proofs of coarse-grained concurrent programs that use auxiliary state, and scales to support higher-order recursive procedures that can themselves fork new threads. We prove the soundness of the logic with a novel denotational semantics of action trees and a definition of safety using rely/guarantee transitions over a large subjective footprint. We have mechanized the denotational semantics, logic, metatheory, and a number of examples by a shallow embedding in Coq.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88775695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbit-finite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojanczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and `definite description' over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallel-or, to a programming language for recursively defined higher-order functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higher-order functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.
{"title":"Full abstraction for nominal Scott domains","authors":"Steffen Lösch, A. Pitts","doi":"10.1145/2429069.2429073","DOIUrl":"https://doi.org/10.1145/2429069.2429073","url":null,"abstract":"We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbit-finite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojanczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and `definite description' over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallel-or, to a programming language for recursively defined higher-order functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higher-order functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.","PeriodicalId":20683,"journal":{"name":"Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86223567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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