Many program analysis problems can be formulated as graph reachability problems. In the literature, context-free language (CFL) reachability has been the most popular formulation and can be computed in subcubic time. The context-sensitive data-dependence analysis is a fundamental abstraction that can express a broad range of program analysis problems. It essentially describes an interleaved matched-parenthesis language reachability problem. The language is not context-free, and the problem is well-known to be undecidable. In practice, many program analyses adopt CFL-reachability to exactly model the matched parentheses for either context-sensitivity or structure-transmitted data-dependence, but not both. Thus, the CFL-reachability formulation for context-sensitive data-dependence analysis is inherently an approximation. To support more precise and scalable analyses, this paper introduces linear conjunctive language (LCL) reachability, a new, expressive class of graph reachability. LCL not only contains the interleaved matched-parenthesis language, but is also closed under all set-theoretic operations. Given a graph with n nodes and m edges, we propose an O(mn) time approximation algorithm for solving all-pairs LCL-reachability, which is asymptotically better than known CFL-reachability algorithms. Our formulation and algorithm offer a new perspective on attacking the aforementioned undecidable problem - the LCL-reachability formulation is exact, while the LCL-reachability algorithm yields a sound approximation. We have applied the LCL-reachability framework to two existing client analyses. The experimental results show that the LCL-reachability framework is both more precise and scalable than the traditional CFL-reachability framework. This paper opens up the opportunity to exploit LCL-reachability in program analysis.
{"title":"Context-sensitive data-dependence analysis via linear conjunctive language reachability","authors":"Qirun Zhang, Z. Su","doi":"10.1145/3009837.3009848","DOIUrl":"https://doi.org/10.1145/3009837.3009848","url":null,"abstract":"Many program analysis problems can be formulated as graph reachability problems. In the literature, context-free language (CFL) reachability has been the most popular formulation and can be computed in subcubic time. The context-sensitive data-dependence analysis is a fundamental abstraction that can express a broad range of program analysis problems. It essentially describes an interleaved matched-parenthesis language reachability problem. The language is not context-free, and the problem is well-known to be undecidable. In practice, many program analyses adopt CFL-reachability to exactly model the matched parentheses for either context-sensitivity or structure-transmitted data-dependence, but not both. Thus, the CFL-reachability formulation for context-sensitive data-dependence analysis is inherently an approximation. To support more precise and scalable analyses, this paper introduces linear conjunctive language (LCL) reachability, a new, expressive class of graph reachability. LCL not only contains the interleaved matched-parenthesis language, but is also closed under all set-theoretic operations. Given a graph with n nodes and m edges, we propose an O(mn) time approximation algorithm for solving all-pairs LCL-reachability, which is asymptotically better than known CFL-reachability algorithms. Our formulation and algorithm offer a new perspective on attacking the aforementioned undecidable problem - the LCL-reachability formulation is exact, while the LCL-reachability algorithm yields a sound approximation. We have applied the LCL-reachability framework to two existing client analyses. The experimental results show that the LCL-reachability framework is both more precise and scalable than the traditional CFL-reachability framework. This paper opens up the opportunity to exploit LCL-reachability in program analysis.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82534921","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}
What is the right notion of "isomorphism" between types, in a simple type theory? The traditional answer is: a pair of terms that are inverse up to a specified congruence. We firstly argue that, in the presence of effects, this answer is too liberal and needs to be restricted, using Führmann's notion of thunkability in the case of value types (as in call-by-value), or using Munch-Maccagnoni's notion of linearity in the case of computation types (as in call-by-name). Yet that leaves us with different notions of isomorphism for different kinds of type. This situation is resolved by means of a new notion of "contextual" isomorphism (or morphism), analogous at the level of types to contextual equivalence of terms. A contextual morphism is a way of replacing one type with the other wherever it may occur in a judgement, in a way that is preserved by the action of any term with holes. For types of pure λ-calculus, we show that a contextual morphism corresponds to a traditional isomorphism. For value types, a contextual morphism corresponds to a thunkable isomorphism, and for computation types, to a linear isomorphism.
{"title":"Contextual isomorphisms","authors":"P. Levy","doi":"10.1145/3009837.3009898","DOIUrl":"https://doi.org/10.1145/3009837.3009898","url":null,"abstract":"What is the right notion of \"isomorphism\" between types, in a simple type theory? The traditional answer is: a pair of terms that are inverse up to a specified congruence. We firstly argue that, in the presence of effects, this answer is too liberal and needs to be restricted, using Führmann's notion of thunkability in the case of value types (as in call-by-value), or using Munch-Maccagnoni's notion of linearity in the case of computation types (as in call-by-name). Yet that leaves us with different notions of isomorphism for different kinds of type. This situation is resolved by means of a new notion of \"contextual\" isomorphism (or morphism), analogous at the level of types to contextual equivalence of terms. A contextual morphism is a way of replacing one type with the other wherever it may occur in a judgement, in a way that is preserved by the action of any term with holes. For types of pure λ-calculus, we show that a contextual morphism corresponds to a traditional isomorphism. For value types, a contextual morphism corresponds to a thunkable isomorphism, and for computation types, to a linear isomorphism.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"73 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78751512","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 present Turnstile, a metalanguage for creating typed embedded languages. To implement the type system, programmers write type checking rules resembling traditional judgment syntax. To implement the semantics, they incorporate elaborations into these rules. Turnstile critically depends on the idea of linguistic reuse. It exploits a macro system in a novel way to simultaneously type check and rewrite a surface program into a target language. Reusing a macro system also yields modular implementations whose rules may be mixed and matched to create other languages. Combined with typical compiler and runtime reuse, Turnstile produces performant typed embedded languages with little effort.
{"title":"Type systems as macros","authors":"Stephen Chang, Alex Knauth, B. Greenman","doi":"10.1145/3009837.3009886","DOIUrl":"https://doi.org/10.1145/3009837.3009886","url":null,"abstract":"We present Turnstile, a metalanguage for creating typed embedded languages. To implement the type system, programmers write type checking rules resembling traditional judgment syntax. To implement the semantics, they incorporate elaborations into these rules. Turnstile critically depends on the idea of linguistic reuse. It exploits a macro system in a novel way to simultaneously type check and rewrite a surface program into a target language. Reusing a macro system also yields modular implementations whose rules may be mixed and matched to create other languages. Combined with typical compiler and runtime reuse, Turnstile produces performant typed embedded languages with little effort.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73627477","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}
Lucas Brutschy, Dimitar Dimitrov, Peter Müller, Martin T. Vechev
Developing and reasoning about systems using eventually consistent data stores is a difficult challenge due to the presence of unexpected behaviors that do not occur under sequential consistency. A fundamental problem in this setting is to identify a correctness criterion that precisely captures intended application behaviors yet is generic enough to be applicable to a wide range of applications. In this paper, we present such a criterion. More precisely, we generalize conflict serializability to the setting of eventual consistency. Our generalization is based on a novel dependency model that incorporates two powerful algebraic properties: commutativity and absorption. These properties enable precise reasoning about programs that employ high-level replicated data types, common in modern systems. To apply our criterion in practice, we also developed a dynamic analysis algorithm and a tool that checks whether a given program execution is serializable. We performed a thorough experimental evaluation on two real-world use cases: debugging cloud-backed mobile applications and implementing clients of a popular eventually consistent key-value store. Our experimental results indicate that our criterion reveals harmful synchronization problems in applications, is more effective at finding them than prior approaches, and can be used for the development of practical, eventually consistent applications.
{"title":"Serializability for eventual consistency: criterion, analysis, and applications","authors":"Lucas Brutschy, Dimitar Dimitrov, Peter Müller, Martin T. Vechev","doi":"10.1145/3009837.3009895","DOIUrl":"https://doi.org/10.1145/3009837.3009895","url":null,"abstract":"Developing and reasoning about systems using eventually consistent data stores is a difficult challenge due to the presence of unexpected behaviors that do not occur under sequential consistency. A fundamental problem in this setting is to identify a correctness criterion that precisely captures intended application behaviors yet is generic enough to be applicable to a wide range of applications. In this paper, we present such a criterion. More precisely, we generalize conflict serializability to the setting of eventual consistency. Our generalization is based on a novel dependency model that incorporates two powerful algebraic properties: commutativity and absorption. These properties enable precise reasoning about programs that employ high-level replicated data types, common in modern systems. To apply our criterion in practice, we also developed a dynamic analysis algorithm and a tool that checks whether a given program execution is serializable. We performed a thorough experimental evaluation on two real-world use cases: debugging cloud-backed mobile applications and implementing clients of a popular eventually consistent key-value store. Our experimental results indicate that our criterion reveals harmful synchronization problems in applications, is more effective at finding them than prior approaches, and can be used for the development of practical, eventually consistent applications.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78111919","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}
When using a proof assistant to reason in an embedded logic -- like separation logic -- one cannot benefit from the proof contexts and basic tactics of the proof assistant. This results in proofs that are at a too low level of abstraction because they are cluttered with bookkeeping code related to manipulating the object logic. In this paper, we introduce a so-called proof mode that extends the Coq proof assistant with (spatial and non-spatial) named proof contexts for the object logic. We show that thanks to these contexts we can implement high-level tactics for introduction and elimination of the connectives of the object logic, and thereby make reasoning in the embedded logic as seamless as reasoning in the meta logic of the proof assistant. We apply our method to Iris: a state of the art higher-order impredicative concurrent separation logic. We show that our method is very general, and is not just limited to program verification. We demonstrate its generality by formalizing correctness proofs of fine-grained concurrent algorithms, derived constructs of the Iris logic, and a unary and binary logical relation for a language with concurrency, higher-order store, polymorphism, and recursive types. This is the first formalization of a binary logical relation for such an expressive language. We also show how to use the logical relation to prove contextual refinement of fine-grained concurrent algorithms.
{"title":"Interactive proofs in higher-order concurrent separation logic","authors":"R. Krebbers, Amin Timany, L. Birkedal","doi":"10.1145/3009837.3009855","DOIUrl":"https://doi.org/10.1145/3009837.3009855","url":null,"abstract":"When using a proof assistant to reason in an embedded logic -- like separation logic -- one cannot benefit from the proof contexts and basic tactics of the proof assistant. This results in proofs that are at a too low level of abstraction because they are cluttered with bookkeeping code related to manipulating the object logic. In this paper, we introduce a so-called proof mode that extends the Coq proof assistant with (spatial and non-spatial) named proof contexts for the object logic. We show that thanks to these contexts we can implement high-level tactics for introduction and elimination of the connectives of the object logic, and thereby make reasoning in the embedded logic as seamless as reasoning in the meta logic of the proof assistant. We apply our method to Iris: a state of the art higher-order impredicative concurrent separation logic. We show that our method is very general, and is not just limited to program verification. We demonstrate its generality by formalizing correctness proofs of fine-grained concurrent algorithms, derived constructs of the Iris logic, and a unary and binary logical relation for a language with concurrency, higher-order store, polymorphism, and recursive types. This is the first formalization of a binary logical relation for such an expressive language. We also show how to use the logical relation to prove contextual refinement of fine-grained concurrent algorithms.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77940978","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}
Ravichandhran Madhavan, Sumith Kulal, Viktor Kunčak
We present a new approach for specifying and verifying resource utilization of higher-order functional programs that use lazy evaluation and memoization. In our approach, users can specify the desired resource bound as templates with numerical holes e.g. as steps ≤ ? * size(l) + ? in the contracts of functions. They can also express invariants necessary for establishing the bounds that may depend on the state of memoization. Our approach operates in two phases: first generating an instrumented first-order program that accurately models the higher-order control flow and the effects of memoization on resources using sets, algebraic datatypes and mutual recursion, and then verifying the contracts of the first-order program by producing verification conditions of the form ∃ ∀ using an extended assume/guarantee reasoning. We use our approach to verify precise bounds on resources such as evaluation steps and number of heap-allocated objects on 17 challenging data structures and algorithms. Our benchmarks, comprising of 5K lines of functional Scala code, include lazy mergesort, Okasaki's real-time queue and deque data structures that rely on aliasing of references to first-class functions; lazy data structures based on numerical representations such as the conqueue data structure of Scala's data-parallel library, cyclic streams, as well as dynamic programming algorithms such as knapsack and Viterbi. Our evaluations show that when averaged over all benchmarks the actual runtime resource consumption is 80% of the value inferred by our tool when estimating the number of evaluation steps, and is 88% for the number of heap-allocated objects.
{"title":"Contract-based resource verification for higher-order functions with memoization","authors":"Ravichandhran Madhavan, Sumith Kulal, Viktor Kunčak","doi":"10.1145/3009837.3009874","DOIUrl":"https://doi.org/10.1145/3009837.3009874","url":null,"abstract":"We present a new approach for specifying and verifying resource utilization of higher-order functional programs that use lazy evaluation and memoization. In our approach, users can specify the desired resource bound as templates with numerical holes e.g. as steps ≤ ? * size(l) + ? in the contracts of functions. They can also express invariants necessary for establishing the bounds that may depend on the state of memoization. Our approach operates in two phases: first generating an instrumented first-order program that accurately models the higher-order control flow and the effects of memoization on resources using sets, algebraic datatypes and mutual recursion, and then verifying the contracts of the first-order program by producing verification conditions of the form ∃ ∀ using an extended assume/guarantee reasoning. We use our approach to verify precise bounds on resources such as evaluation steps and number of heap-allocated objects on 17 challenging data structures and algorithms. Our benchmarks, comprising of 5K lines of functional Scala code, include lazy mergesort, Okasaki's real-time queue and deque data structures that rely on aliasing of references to first-class functions; lazy data structures based on numerical representations such as the conqueue data structure of Scala's data-parallel library, cyclic streams, as well as dynamic programming algorithms such as knapsack and Viterbi. Our evaluations show that when averaged over all benchmarks the actual runtime resource consumption is 80% of the value inferred by our tool when estimating the number of evaluation steps, and is 88% for the number of heap-allocated objects.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82029036","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 type soundness proofs are taught in every graduate PL class, the gap between realistic languages and what is accessible to formal proofs is large. In the case of Scala, it has been shown that its formal model, the Dependent Object Types (DOT) calculus, cannot simultaneously support key metatheoretic properties such as environment narrowing and subtyping transitivity, which are usually required for a type soundness proof. Moreover, Scala and many other realistic languages lack a general substitution property. The first contribution of this paper is to demonstrate how type soundness proofs for advanced, polymorphic, type systems can be carried out with an operational semantics based on high-level, definitional interpreters, implemented in Coq. We present the first mechanized soundness proofs in this style for System F and several extensions, including mutable references. Our proofs use only straightforward induction, which is significant, as the combination of big-step semantics, mutable references, and polymorphism is commonly believed to require coinductive proof techniques. The second main contribution of this paper is to show how DOT-like calculi emerge from straightforward generalizations of the operational aspects of F, exposing a rich design space of calculi with path-dependent types inbetween System F and DOT, which we dub the System D Square. By working directly on the target language, definitional interpreters can focus the design space and expose the invariants that actually matter at runtime. Looking at such runtime invariants is an exciting new avenue for type system design.
{"title":"Type soundness proofs with definitional interpreters","authors":"Nada Amin, Tiark Rompf","doi":"10.1145/3009837.3009866","DOIUrl":"https://doi.org/10.1145/3009837.3009866","url":null,"abstract":"While type soundness proofs are taught in every graduate PL class, the gap between realistic languages and what is accessible to formal proofs is large. In the case of Scala, it has been shown that its formal model, the Dependent Object Types (DOT) calculus, cannot simultaneously support key metatheoretic properties such as environment narrowing and subtyping transitivity, which are usually required for a type soundness proof. Moreover, Scala and many other realistic languages lack a general substitution property. The first contribution of this paper is to demonstrate how type soundness proofs for advanced, polymorphic, type systems can be carried out with an operational semantics based on high-level, definitional interpreters, implemented in Coq. We present the first mechanized soundness proofs in this style for System F and several extensions, including mutable references. Our proofs use only straightforward induction, which is significant, as the combination of big-step semantics, mutable references, and polymorphism is commonly believed to require coinductive proof techniques. The second main contribution of this paper is to show how DOT-like calculi emerge from straightforward generalizations of the operational aspects of F, exposing a rich design space of calculi with path-dependent types inbetween System F and DOT, which we dub the System D Square. By working directly on the target language, definitional interpreters can focus the design space and expose the invariants that actually matter at runtime. Looking at such runtime invariants is an exciting new avenue for type system design.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88478979","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}
Operators in multi-tenant cloud datacenters require support for diverse and complex end-to-end policies, such as, reachability, middlebox traversals, isolation, traffic engineering, and network resource management. We present Genesis, a datacenter network management system which allows policies to be specified in a declarative manner without explicitly programming the network data plane. Genesis tackles the problem of enforcing policies by synthesizing switch forwarding tables. It uses the formal foundations of constraint solving in combination with fast off-the-shelf SMT solvers. To improve synthesis performance, Genesis incorporates a novel search strategy that uses regular expressions to specify properties that leverage the structure of datacenter networks, and a divide-and-conquer synthesis procedure which exploits the structure of policy relationships. We have prototyped Genesis, and conducted experiments with a variety of workloads on real-world topologies to demonstrate its performance.
{"title":"Genesis: synthesizing forwarding tables in multi-tenant networks","authors":"Kausik Subramanian, Loris D'antoni, Aditya Akella","doi":"10.1145/3009837.3009845","DOIUrl":"https://doi.org/10.1145/3009837.3009845","url":null,"abstract":"Operators in multi-tenant cloud datacenters require support for diverse and complex end-to-end policies, such as, reachability, middlebox traversals, isolation, traffic engineering, and network resource management. We present Genesis, a datacenter network management system which allows policies to be specified in a declarative manner without explicitly programming the network data plane. Genesis tackles the problem of enforcing policies by synthesizing switch forwarding tables. It uses the formal foundations of constraint solving in combination with fast off-the-shelf SMT solvers. To improve synthesis performance, Genesis incorporates a novel search strategy that uses regular expressions to specify properties that leverage the structure of datacenter networks, and a divide-and-conquer synthesis procedure which exploits the structure of policy relationships. We have prototyped Genesis, and conducted experiments with a variety of workloads on real-world topologies to demonstrate its performance.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"30 21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87076890","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}
The goal of this paper is to develop a form of functional arrays (sequences) that are as efficient as imperative arrays, can be used in parallel, and have well defined cost-semantics. The key idea is to consider sequences with functional value semantics but non-functional cost semantics. Because the value semantics is functional, "updating" a sequence returns a new sequence. We allow operations on "older" sequences (called interior sequences) to be more expensive than operations on the "most recent" sequences (called leaf sequences). We embed sequences in a language supporting fork-join parallelism. Due to the parallelism, operations can be interleaved non-deterministically, and, in conjunction with the different cost for interior and leaf sequences, this can lead to non-deterministic costs for a program. Consequently the costs of programs can be difficult to analyze. The main result is the derivation of a deterministic cost dynamics which makes analyzing the costs easier. The theorems are not specific to sequences and can be applied to other data types with different costs for operating on interior and leaf versions. We present a wait-free concurrent implementation of sequences that requires constant work for accessing and updating leaf sequences, and logarithmic work for accessing and linear work for updating interior sequences. We sketch a proof of correctness for the sequence implementation. The key advantages of the present approach compared to current approaches is that our implementation requires no changes to existing programming languages, supports nested parallelism, and has well defined cost semantics. At the same time, it allows for functional implementations of algorithms such as depth-first search with the same asymptotic complexity as imperative implementations.
{"title":"Parallel functional arrays","authors":"Ananya Kumar, G. Blelloch, R. Harper","doi":"10.1145/3009837.3009869","DOIUrl":"https://doi.org/10.1145/3009837.3009869","url":null,"abstract":"The goal of this paper is to develop a form of functional arrays (sequences) that are as efficient as imperative arrays, can be used in parallel, and have well defined cost-semantics. The key idea is to consider sequences with functional value semantics but non-functional cost semantics. Because the value semantics is functional, \"updating\" a sequence returns a new sequence. We allow operations on \"older\" sequences (called interior sequences) to be more expensive than operations on the \"most recent\" sequences (called leaf sequences). We embed sequences in a language supporting fork-join parallelism. Due to the parallelism, operations can be interleaved non-deterministically, and, in conjunction with the different cost for interior and leaf sequences, this can lead to non-deterministic costs for a program. Consequently the costs of programs can be difficult to analyze. The main result is the derivation of a deterministic cost dynamics which makes analyzing the costs easier. The theorems are not specific to sequences and can be applied to other data types with different costs for operating on interior and leaf versions. We present a wait-free concurrent implementation of sequences that requires constant work for accessing and updating leaf sequences, and logarithmic work for accessing and linear work for updating interior sequences. We sketch a proof of correctness for the sequence implementation. The key advantages of the present approach compared to current approaches is that our implementation requires no changes to existing programming languages, supports nested parallelism, and has well defined cost semantics. At the same time, it allows for functional implementations of algorithms such as depth-first search with the same asymptotic complexity as imperative implementations.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90580709","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}
Arthur Azevedo de Amorim, Marco Gaboardi, Justin Hsu, Shin-ya Katsumata, Ikram Cherigui
Program sensitivity measures how robust a program is to small changes in its input, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formalize program sensitivity is in terms of metrics on the input and output spaces, requiring that an r-sensitive function map inputs that are at distance d to outputs that are at distance at most r · d. Program sensitivity is thus an analogue of Lipschitz continuity for programs. Reed and Pierce introduced Fuzz, a functional language with a linear type system that can express program sensitivity. They show soundness operationally, in the form of a metric preservation property. Inspired by their work, we study program sensitivity and metric preservation from a denotational point of view. In particular, we introduce metric CPOs, a novel semantic structure for reasoning about computation on metric spaces, by endowing CPOs with a compatible notion of distance. This structure is useful for reasoning about metric properties of programs, and specifically about program sensitivity. We demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz.
{"title":"A semantic account of metric preservation","authors":"Arthur Azevedo de Amorim, Marco Gaboardi, Justin Hsu, Shin-ya Katsumata, Ikram Cherigui","doi":"10.1145/3009837.3009890","DOIUrl":"https://doi.org/10.1145/3009837.3009890","url":null,"abstract":"Program sensitivity measures how robust a program is to small changes in its input, and is a fundamental notion in domains ranging from differential privacy to cyber-physical systems. A natural way to formalize program sensitivity is in terms of metrics on the input and output spaces, requiring that an r-sensitive function map inputs that are at distance d to outputs that are at distance at most r · d. Program sensitivity is thus an analogue of Lipschitz continuity for programs. Reed and Pierce introduced Fuzz, a functional language with a linear type system that can express program sensitivity. They show soundness operationally, in the form of a metric preservation property. Inspired by their work, we study program sensitivity and metric preservation from a denotational point of view. In particular, we introduce metric CPOs, a novel semantic structure for reasoning about computation on metric spaces, by endowing CPOs with a compatible notion of distance. This structure is useful for reasoning about metric properties of programs, and specifically about program sensitivity. We demonstrate metric CPOs by giving a model for the deterministic fragment of Fuzz.","PeriodicalId":20657,"journal":{"name":"Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72963169","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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