Davi Barbosa, Julien Cretin, Nate Foster, M. Greenberg, B. Pierce
Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well as one mapping updated views back to updated sources. One thorny issue that has not received sufficient attention in the design of bidirectional languages is alignment. In general, to correctly propagate an update to a view, a lens needs to match up the pieces of the view with the corresponding pieces of the underlying source, even after data has been inserted, deleted, or reordered. However, existing bidirectional languages either support only simple strategies that fail on many examples of practical interest, or else propose specific strategies that are baked deeply into the underlying theory. We propose a general framework of matching lenses that parameterizes lenses over arbitrary heuristics for calculating alignments. We enrich the types of lenses with "chunks" identifying reorderable pieces of the source and view that should be re-aligned after an update, and we formulate behavioral laws that capture essential constraints on the handling of chunks. We develop a core language of matching lenses for strings, together with a set of "alignment combinators" that implement a variety of alignment strategies.
{"title":"Matching lenses: alignment and view update","authors":"Davi Barbosa, Julien Cretin, Nate Foster, M. Greenberg, B. Pierce","doi":"10.1145/1863543.1863572","DOIUrl":"https://doi.org/10.1145/1863543.1863572","url":null,"abstract":"Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well as one mapping updated views back to updated sources.\u0000 One thorny issue that has not received sufficient attention in the design of bidirectional languages is alignment. In general, to correctly propagate an update to a view, a lens needs to match up the pieces of the view with the corresponding pieces of the underlying source, even after data has been inserted, deleted, or reordered. However, existing bidirectional languages either support only simple strategies that fail on many examples of practical interest, or else propose specific strategies that are baked deeply into the underlying theory.\u0000 We propose a general framework of matching lenses that parameterizes lenses over arbitrary heuristics for calculating alignments. We enrich the types of lenses with \"chunks\" identifying reorderable pieces of the source and view that should be re-aligned after an update, and we formulate behavioral laws that capture essential constraints on the handling of chunks. We develop a core language of matching lenses for strings, together with a set of \"alignment combinators\" that implement a variety of alignment strategies.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"1025 1","pages":"193-204"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77167324","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 describe the design, implementation, and use of a machine-certified framework for correct compilation and execution of programs in garbage-collected languages. Our framework extends Leroy's Coq-certified Compcert compiler and Cminor intermediate language. We add: (i) a new intermediate language, GCminor, that includes primitives for allocating memory in a garbage-collected heap and for specifying GC roots; (ii) a precise, low-level specification for a Cminor library for garbage collection; and (iii) a proven semantics-preserving translation from GCminor to Cminor plus the GC library. GCminor neatly encapsulates the interface between mutator and collector code, while remaining simple and flexible enough to be used with a wide variety of source languages and collector styles. Front ends targeting GCminor can be implemented using any compiler technology and any desired degree of verification, including full semantics preservation, type preservation, or informal trust. As an example application of our framework, we describe a compiler for Haskell that translates the Glasgow Haskell Compiler's Core intermediate language to GCminor. To support a simple but useful memory safety argument for this compiler, the front end uses a novel combination of type preservation and runtime checks, which is of independent interest.
{"title":"A certified framework for compiling and executing garbage-collected languages","authors":"Andrew McCreight, T. Chevalier, A. Tolmach","doi":"10.1145/1863543.1863584","DOIUrl":"https://doi.org/10.1145/1863543.1863584","url":null,"abstract":"We describe the design, implementation, and use of a machine-certified framework for correct compilation and execution of programs in garbage-collected languages. Our framework extends Leroy's Coq-certified Compcert compiler and Cminor intermediate language. We add: (i) a new intermediate language, GCminor, that includes primitives for allocating memory in a garbage-collected heap and for specifying GC roots; (ii) a precise, low-level specification for a Cminor library for garbage collection; and (iii) a proven semantics-preserving translation from GCminor to Cminor plus the GC library. GCminor neatly encapsulates the interface between mutator and collector code, while remaining simple and flexible enough to be used with a wide variety of source languages and collector styles. Front ends targeting GCminor can be implemented using any compiler technology and any desired degree of verification, including full semantics preservation, type preservation, or informal trust.\u0000 As an example application of our framework, we describe a compiler for Haskell that translates the Glasgow Haskell Compiler's Core intermediate language to GCminor. To support a simple but useful memory safety argument for this compiler, the front end uses a novel combination of type preservation and runtime checks, which is of independent interest.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"85 1","pages":"273-284"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87544502","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 a technique for higher-order representation of substructural logics such as linear or modal logic. We show that such logics can be encoded in the (ordinary) Logical Framework, without any linear or modal extensions. Using this encoding, metatheoretic proofs about such logics can easily be developed in the Twelf proof assistant.
{"title":"Higher-order representation of substructural logics","authors":"Karl Crary","doi":"10.1145/1863543.1863565","DOIUrl":"https://doi.org/10.1145/1863543.1863565","url":null,"abstract":"We present a technique for higher-order representation of substructural logics such as linear or modal logic. We show that such logics can be encoded in the (ordinary) Logical Framework, without any linear or modal extensions. Using this encoding, metatheoretic proofs about such logics can easily be developed in the Twelf proof assistant.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"27 13","pages":"131-142"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91404604","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}
G. Keller, M. Chakravarty, Roman Leshchinskiy, S. Jones, B. Lippmeier
We present a novel approach to regular, multi-dimensional arrays in Haskell. The main highlights of our approach are that it (1) is purely functional, (2) supports reuse through shape polymorphism, (3) avoids unnecessary intermediate structures rather than relying on subsequent loop fusion, and (4) supports transparent parallelisation. We show how to embed two forms of shape polymorphism into Haskell's type system using type classes and type families. In particular, we discuss the generalisation of regular array transformations to arrays of higher rank, and introduce a type-safe specification of array slices. We discuss the runtime performance of our approach for three standard array algorithms. We achieve absolute performance comparable to handwritten C code. At the same time, our implementation scales well up to 8 processor cores.
{"title":"Regular, shape-polymorphic, parallel arrays in Haskell","authors":"G. Keller, M. Chakravarty, Roman Leshchinskiy, S. Jones, B. Lippmeier","doi":"10.1145/1863543.1863582","DOIUrl":"https://doi.org/10.1145/1863543.1863582","url":null,"abstract":"We present a novel approach to regular, multi-dimensional arrays in Haskell. The main highlights of our approach are that it (1) is purely functional, (2) supports reuse through shape polymorphism, (3) avoids unnecessary intermediate structures rather than relying on subsequent loop fusion, and (4) supports transparent parallelisation.\u0000 We show how to embed two forms of shape polymorphism into Haskell's type system using type classes and type families. In particular, we discuss the generalisation of regular array transformations to arrays of higher rank, and introduce a type-safe specification of array slices.\u0000 We discuss the runtime performance of our approach for three standard array algorithms. We achieve absolute performance comparable to handwritten C code. At the same time, our implementation scales well up to 8 processor cores.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"36 1","pages":"261-272"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90540907","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}
Modern proof assistants such as Coq and Isabelle provide high degrees of expressiveness and assurance because they support formal reasoning in higher-order logic and supply explicit machine-checkable proof objects. Unfortunately, large scale proof development in these proof assistants is still an extremely difficult and time-consuming task. One major weakness of these proof assistants is the lack of a single language where users can develop complex tactics and decision procedures using a rich programming model and in a typeful manner. This limits the scalability of the proof development process, as users avoid developing domain-specific tactics and decision procedures. In this paper, we present VeriML - a novel language design that couples a type-safe effectful computational language with first-class support for manipulating logical terms such as propositions and proofs. The main idea behind our design is to integrate a rich logical framework - similar to the one supported by Coq - inside a computational language inspired by ML. The language design is such that the added features are orthogonal to the rest of the computational language, and also do not require significant additions to the logic language, so soundness is guaranteed. We have built a prototype implementation of VeriML including both its type-checker and an interpreter. We demonstrate the effectiveness of our design by showing a number of type-safe tactics and decision procedures written in VeriML.
{"title":"VeriML: typed computation of logical terms inside a language with effects","authors":"Antonis Stampoulis, Zhong Shao","doi":"10.1145/1863543.1863591","DOIUrl":"https://doi.org/10.1145/1863543.1863591","url":null,"abstract":"Modern proof assistants such as Coq and Isabelle provide high degrees of expressiveness and assurance because they support formal reasoning in higher-order logic and supply explicit machine-checkable proof objects. Unfortunately, large scale proof development in these proof assistants is still an extremely difficult and time-consuming task. One major weakness of these proof assistants is the lack of a single language where users can develop complex tactics and decision procedures using a rich programming model and in a typeful manner. This limits the scalability of the proof development process, as users avoid developing domain-specific tactics and decision procedures.\u0000 In this paper, we present VeriML - a novel language design that couples a type-safe effectful computational language with first-class support for manipulating logical terms such as propositions and proofs. The main idea behind our design is to integrate a rich logical framework - similar to the one supported by Coq - inside a computational language inspired by ML. The language design is such that the added features are orthogonal to the rest of the computational language, and also do not require significant additions to the logic language, so soundness is guaranteed. We have built a prototype implementation of VeriML including both its type-checker and an interpreter. We demonstrate the effectiveness of our design by showing a number of type-safe tactics and decision procedures written in VeriML.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"223 1","pages":"333-344"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76697407","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 monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library's interface is similar to those of many other parser combinator libraries, with two important differences: one is that the interface clearly specifies which parts of the constructed parsers may be infinite, and which parts have to be finite, using dependent types and a combination of induction and coinduction; and the other is that the parser type is unusually informative. The library comes with a formal semantics, using which it is proved that the parser combinators are as expressive as possible. The implementation is supported by a machine-checked correctness proof.
{"title":"Total parser combinators","authors":"Nils Anders Danielsson","doi":"10.1145/1863543.1863585","DOIUrl":"https://doi.org/10.1145/1863543.1863585","url":null,"abstract":"A monadic parser combinator library which guarantees termination of parsing, while still allowing many forms of left recursion, is described. The library's interface is similar to those of many other parser combinator libraries, with two important differences: one is that the interface clearly specifies which parts of the constructed parsers may be infinite, and which parts have to be finite, using dependent types and a combination of induction and coinduction; and the other is that the parser type is unusually informative.\u0000 The library comes with a formal semantics, using which it is proved that the parser combinators are as expressive as possible. The implementation is supported by a machine-checked correctness proof.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"1 1","pages":"285-296"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83707773","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 leading implementations of graph reduction all target conventional processors designed for low-level imperative execution. In this paper, we present a processor specially designed to perform graph-reduction. Our processor -- the Reduceron -- is implemented using off-the-shelf reconfigurable hardware. We highlight the low-level parallelism present in sequential graph reduction, and show how parallel memories and dynamic analyses are used in the Reduceron to achieve an average reduction rate of 0.55 function applications per clock-cycle.
{"title":"The reduceron reconfigured","authors":"Matthew Naylor, C. Runciman","doi":"10.1145/1863543.1863556","DOIUrl":"https://doi.org/10.1145/1863543.1863556","url":null,"abstract":"The leading implementations of graph reduction all target conventional processors designed for low-level imperative execution. In this paper, we present a processor specially designed to perform graph-reduction. Our processor -- the Reduceron -- is implemented using off-the-shelf reconfigurable hardware. We highlight the low-level parallelism present in sequential graph reduction, and show how parallel memories and dynamic analyses are used in the Reduceron to achieve an average reduction rate of 0.55 function applications per clock-cycle.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"11 1","pages":"75-86"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82842789","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}
Gilad Arnold, J. Hölzl, A. Köksal, R. Bodík, Shmuel Sagiv
Sparse matrix formats are typically implemented with low-level imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variable-free functional language (LL) in which even advanced formats can be expressed naturally, as a pipeline-style composition of smaller construction steps. We translate LL programs to Isabelle/HOL and describe a proof system based on parametric predicates for tracking relationship between mathematical vectors and their concrete representations. This proof theory automatically verifies full functional correctness of many formats. We show that it is reusable and extensible to hierarchical sparse formats.
{"title":"Specifying and verifying sparse matrix codes","authors":"Gilad Arnold, J. Hölzl, A. Köksal, R. Bodík, Shmuel Sagiv","doi":"10.1145/1863543.1863581","DOIUrl":"https://doi.org/10.1145/1863543.1863581","url":null,"abstract":"Sparse matrix formats are typically implemented with low-level imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variable-free functional language (LL) in which even advanced formats can be expressed naturally, as a pipeline-style composition of smaller construction steps. We translate LL programs to Isabelle/HOL and describe a proof system based on parametric predicates for tracking relationship between mathematical vectors and their concrete representations. This proof theory automatically verifies full functional correctness of many formats. We show that it is reusable and extensible to hierarchical sparse formats.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"1 1","pages":"249-260"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89317015","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}
S. Hidaka, Zhenjiang Hu, K. Inaba, H. Kato, Kazutaka Matsuda, Keisuke Nakano
Bidirectional transformations provide a novel mechanism for synchronizing and maintaining the consistency of information between input and output. Despite many promising results on bidirectional transformations, these have been limited to the context of relational or XML (tree-like) databases. We challenge the problem of bidirectional transformations within the context of graphs, by proposing a formal definition of a well-behaved bidirectional semantics for UnCAL, i.e., a graph algebra for the known UnQL graph query language. The key to our successful formalization is full utilization of both the recursive and bulk semantics of structural recursion on graphs. We carefully refine the existing forward evaluation of structural recursion so that it can produce sufficient trace information for later backward evaluation. We use the trace information for backward evaluation to reflect in-place updates and deletions on the view to the source, and adopt the universal resolving algorithm for inverse computation and the narrowing technique to tackle the difficult problem with insertion. We prove our bidirectional evaluation is well-behaved. Our current implementation is available online and confirms the usefulness of our approach with nontrivial applications.
{"title":"Bidirectionalizing graph transformations","authors":"S. Hidaka, Zhenjiang Hu, K. Inaba, H. Kato, Kazutaka Matsuda, Keisuke Nakano","doi":"10.1145/1863543.1863573","DOIUrl":"https://doi.org/10.1145/1863543.1863573","url":null,"abstract":"Bidirectional transformations provide a novel mechanism for synchronizing and maintaining the consistency of information between input and output. Despite many promising results on bidirectional transformations, these have been limited to the context of relational or XML (tree-like) databases. We challenge the problem of bidirectional transformations within the context of graphs, by proposing a formal definition of a well-behaved bidirectional semantics for UnCAL, i.e., a graph algebra for the known UnQL graph query language. The key to our successful formalization is full utilization of both the recursive and bulk semantics of structural recursion on graphs. We carefully refine the existing forward evaluation of structural recursion so that it can produce sufficient trace information for later backward evaluation. We use the trace information for backward evaluation to reflect in-place updates and deletions on the view to the source, and adopt the universal resolving algorithm for inverse computation and the narrowing technique to tackle the difficult problem with insertion. We prove our bidirectional evaluation is well-behaved. Our current implementation is available online and confirms the usefulness of our approach with nontrivial applications.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"12 1","pages":"205-216"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86087216","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}
Several recent security-typed programming languages, such as Aura, PCML5, and Fine, allow programmers to express and enforce access control and information flow policies. In this paper, we show that security-typed programming can be embedded as a library within a general-purpose dependently typed programming language, Agda. Our library, Aglet, accounts for the major features of existing security-typed programming languages, such as decentralized access control, typed proof-carrying authorization, ephemeral and dynamic policies, authentication, spatial distribution, and information flow. The implementation of Aglet consists of the following ingredients: First, we represent the syntax and proofs of an authorization logic, Garg and Pfenning's BL0, using dependent types. Second, we implement a proof search procedure, based on a focused sequent calculus, to ease the burden of constructing proofs. Third, we represent computations using a monad indexed by pre- and post-conditions drawn from the authorization logic, which permits ephemeral policies that change during execution. We describe the implementation of our library and illustrate its use on a number of the benchmark examples considered in the literature.
{"title":"Security-typed programming within dependently typed programming","authors":"Jamie Morgenstern, Daniel R. Licata","doi":"10.1145/1863543.1863569","DOIUrl":"https://doi.org/10.1145/1863543.1863569","url":null,"abstract":"Several recent security-typed programming languages, such as Aura, PCML5, and Fine, allow programmers to express and enforce access control and information flow policies. In this paper, we show that security-typed programming can be embedded as a library within a general-purpose dependently typed programming language, Agda. Our library, Aglet, accounts for the major features of existing security-typed programming languages, such as decentralized access control, typed proof-carrying authorization, ephemeral and dynamic policies, authentication, spatial distribution, and information flow. The implementation of Aglet consists of the following ingredients: First, we represent the syntax and proofs of an authorization logic, Garg and Pfenning's BL0, using dependent types. Second, we implement a proof search procedure, based on a focused sequent calculus, to ease the burden of constructing proofs. Third, we represent computations using a monad indexed by pre- and post-conditions drawn from the authorization logic, which permits ephemeral policies that change during execution. We describe the implementation of our library and illustrate its use on a number of the benchmark examples considered in the literature.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"11 1","pages":"169-180"},"PeriodicalIF":0.0,"publicationDate":"2010-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78111244","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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