Haskell's type system has outgrown its Hindley-Milner roots to the extent that it now stretches to the basics of dependently typed programming. In this paper, we collate and classify techniques for programming with dependent types in Haskell, and contribute some new ones. In particular, through extended examples---merge-sort and rectangular tilings---we show how to exploit Haskell's constraint solver as a theorem prover, delivering code which, as Agda programmers, we envy. We explore the compromises involved in simulating variations on the theme of the dependent function space in an attempt to help programmers put dependent types to work, and to inform the evolving language design both of Haskell and of dependently typed languages more broadly.
{"title":"Hasochism: the pleasure and pain of dependently typed haskell programming","authors":"S. Lindley, Conor McBride","doi":"10.1145/2503778.2503786","DOIUrl":"https://doi.org/10.1145/2503778.2503786","url":null,"abstract":"Haskell's type system has outgrown its Hindley-Milner roots to the extent that it now stretches to the basics of dependently typed programming. In this paper, we collate and classify techniques for programming with dependent types in Haskell, and contribute some new ones. In particular, through extended examples---merge-sort and rectangular tilings---we show how to exploit Haskell's constraint solver as a theorem prover, delivering code which, as Agda programmers, we envy. We explore the compromises involved in simulating variations on the theme of the dependent function space in an attempt to help programmers put dependent types to work, and to inform the evolving language design both of Haskell and of dependently typed languages more broadly.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131690567","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}
Maintaining software in the face of evolving dependencies is a challenging problem, and in addition to good release practices there is a need for automatic dependency analysis tools to avoid errors creeping in. Verified software reveals more semantic information in the form of mechanized proofs of functional specifications, and this can be used for dependency analysis. In this paper we present a scheme for automatic dependency analysis of verified software, which for each program checks that the collection of installed libraries is sufficient to guarantee its functional correctness. We illustrate the scheme with a case study of Haskell packages verified in higher order logic. The dependency analysis reduces the burden of maintaining verified Haskell packages by automatically computing version ranges for the packages they depend on, such that any combination provides the functionality required for correct operation.
{"title":"Maintaining verified software","authors":"Joe Leslie-Hurd","doi":"10.1145/2503778.2503787","DOIUrl":"https://doi.org/10.1145/2503778.2503787","url":null,"abstract":"Maintaining software in the face of evolving dependencies is a challenging problem, and in addition to good release practices there is a need for automatic dependency analysis tools to avoid errors creeping in. Verified software reveals more semantic information in the form of mechanized proofs of functional specifications, and this can be used for dependency analysis. In this paper we present a scheme for automatic dependency analysis of verified software, which for each program checks that the collection of installed libraries is sufficient to guarantee its functional correctness. We illustrate the scheme with a case study of Haskell packages verified in higher order logic. The dependency analysis reduces the burden of maintaining verified Haskell packages by automatically computing version ranges for the packages they depend on, such that any combination provides the functionality required for correct operation.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130979118","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 Glasgow Haskell Compiler (GHC) is a well supported optimizing compiler for the Haskell programming language, along with its own extensions to the language and libraries. Haskell's lazy semantics imposes a runtime model which is in general difficult to implement efficiently. GHC achieves good performance across a wide variety of programs via aggressive optimization taking advantage of the lack of side effects, and by targeting a carefully tuned virtual machine. The Intel Labs Haskell Research Compiler uses GHC as a frontend, but provides a new whole-program optimizing backend by compiling the GHC intermediate representation to a relatively generic functional language compilation platform. We found that GHC's external Core language was relatively easy to use, but reusing GHC's libraries and achieving full compatibility were harder. For certain classes of programs, our platform provides substantial performance benefits over GHC alone, performing 2x faster than GHC with the LLVM backend on selected modern performance-oriented benchmarks; for other classes of programs, the benefits of GHC's tuned virtual machine continue to outweigh the benefits of more aggressive whole program optimization. Overall we achieve parity with GHC with the LLVM backend. In this paper, we describe our Haskell compiler stack, its implementation and optimization approach, and present benchmark results comparing it to GHC.
{"title":"The Intel labs Haskell research compiler","authors":"Hai Liu, Neal Glew, Leaf Petersen, T. A. Anderson","doi":"10.1145/2503778.2503779","DOIUrl":"https://doi.org/10.1145/2503778.2503779","url":null,"abstract":"The Glasgow Haskell Compiler (GHC) is a well supported optimizing compiler for the Haskell programming language, along with its own extensions to the language and libraries. Haskell's lazy semantics imposes a runtime model which is in general difficult to implement efficiently. GHC achieves good performance across a wide variety of programs via aggressive optimization taking advantage of the lack of side effects, and by targeting a carefully tuned virtual machine. The Intel Labs Haskell Research Compiler uses GHC as a frontend, but provides a new whole-program optimizing backend by compiling the GHC intermediate representation to a relatively generic functional language compilation platform. We found that GHC's external Core language was relatively easy to use, but reusing GHC's libraries and achieving full compatibility were harder. For certain classes of programs, our platform provides substantial performance benefits over GHC alone, performing 2x faster than GHC with the LLVM backend on selected modern performance-oriented benchmarks; for other classes of programs, the benefits of GHC's tuned virtual machine continue to outweigh the benefits of more aggressive whole program optimization. Overall we achieve parity with GHC with the LLVM backend. In this paper, we describe our Haskell compiler stack, its implementation and optimization approach, and present benchmark results comparing it to GHC.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129780613","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 novel technique to represent names and binders in Haskell. The dynamic (run-time) representation is based on de Bruijn indices, but it features an interface to write and manipulate variables conviently, using Haskell-level lambdas and variables. The key idea is to use rich types: a subterm with an additional free variable is viewed either as forallν.ν → Term(ɑ + ν) or ϶ν.ν x Term(ν.ν) depending on whether it is constructed or analysed. We demonstrate on a number of examples how this approach permits to express term construction and manipulation in a natural way, while retaining the good properties of representations based on de Bruijn indices.
我们提出了一种在Haskell中表示名称和粘合剂的新技术。动态(运行时)表示基于de Bruijn索引，但它提供了一个接口，可以使用haskell级别的lambdas和变量方便地编写和操作变量。关键思想是使用富类型:带有附加自由变量的子项被视为forallν。ν→术语(ν + ν)或϶ν。ν x terms (ν.ν)取决于它是否被构造或分析。我们通过一些例子展示了这种方法如何允许以自然的方式表达术语构建和操作，同时保留了基于de Bruijn索引的表示的良好性质。
{"title":"Names for free: polymorphic views of names and binders","authors":"Jean-Philippe Bernardy, Nicolas Pouillard","doi":"10.1145/2503778.2503780","DOIUrl":"https://doi.org/10.1145/2503778.2503780","url":null,"abstract":"We propose a novel technique to represent names and binders in Haskell. The dynamic (run-time) representation is based on de Bruijn indices, but it features an interface to write and manipulate variables conviently, using Haskell-level lambdas and variables. The key idea is to use rich types: a subterm with an additional free variable is viewed either as forallν.ν → Term(ɑ + ν) or ϶ν.ν x Term(ν.ν) depending on whether it is constructed or analysed. We demonstrate on a number of examples how this approach permits to express term construction and manipulation in a natural way, while retaining the good properties of representations based on de Bruijn indices.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133724209","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}
R. Bird, J. Gibbons, Stefan Mehner, J. Voigtländer, T. Schrijvers
We present new ways of reasoning about a particular class of effectful Haskell programs, namely those expressed as idiomatic traversals. Starting out with a specific problem about labelling and unlabelling binary trees, we extract a general inversion law, applicable to any monad, relating a traversal over the elements of an arbitrary traversable type to a traversal that goes in the opposite direction. This law can be invoked to show that, in a suitable sense, unlabelling is the inverse of labelling. The inversion law, as well as a number of other properties of idiomatic traversals, is a corollary of a more general theorem characterising traversable functors as finitary containers: an arbitrary traversable object can be decomposed uniquely into shape and contents, and traversal be understood in terms of those. Proof of the theorem involves the properties of traversal in a special idiom related to the free applicative functor.
{"title":"Understanding idiomatic traversals backwards and forwards","authors":"R. Bird, J. Gibbons, Stefan Mehner, J. Voigtländer, T. Schrijvers","doi":"10.1145/2503778.2503781","DOIUrl":"https://doi.org/10.1145/2503778.2503781","url":null,"abstract":"We present new ways of reasoning about a particular class of effectful Haskell programs, namely those expressed as idiomatic traversals. Starting out with a specific problem about labelling and unlabelling binary trees, we extract a general inversion law, applicable to any monad, relating a traversal over the elements of an arbitrary traversable type to a traversal that goes in the opposite direction. This law can be invoked to show that, in a suitable sense, unlabelling is the inverse of labelling. The inversion law, as well as a number of other properties of idiomatic traversals, is a corollary of a more general theorem characterising traversable functors as finitary containers: an arbitrary traversable object can be decomposed uniquely into shape and contents, and traversal be understood in terms of those. Proof of the theorem involves the properties of traversal in a special idiom related to the free applicative functor.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115574885","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}
This paper argues for a new methodology for writing high performance Haskell programs by using Embedded Domain Specific Languages. We exemplify the methodology by describing a complete library, meta-repa, which is a reimplementation of parts of the repa library. The paper describes the implementation of meta-repa and contrasts it with the standard approach to writing high performance libraries. We conclude that even though the embedded language approach has an initial cost of defining the language and some syntactic overhead it gives a more tailored programming model, stronger performance guarantees, better control over optimizations, simpler implementation of fusion and inlining and allows for moving type level programming down to value level programming in some cases. We also provide benchmarks showing that meta-repa is as fast, or faster, than repa. Furthermore, meta-repa also includes push arrays and we demonstrate their usefulness for writing certain high performance kernels such as FFT.
{"title":"An EDSL approach to high performance Haskell programming","authors":"J. Ankner, Josef Svenningsson","doi":"10.1145/2503778.2503789","DOIUrl":"https://doi.org/10.1145/2503778.2503789","url":null,"abstract":"This paper argues for a new methodology for writing high performance Haskell programs by using Embedded Domain Specific Languages.\u0000 We exemplify the methodology by describing a complete library, meta-repa, which is a reimplementation of parts of the repa library. The paper describes the implementation of meta-repa and contrasts it with the standard approach to writing high performance libraries. We conclude that even though the embedded language approach has an initial cost of defining the language and some syntactic overhead it gives a more tailored programming model, stronger performance guarantees, better control over optimizations, simpler implementation of fusion and inlining and allows for moving type level programming down to value level programming in some cases. We also provide benchmarks showing that meta-repa is as fast, or faster, than repa.\u0000 Furthermore, meta-repa also includes push arrays and we demonstrate their usefulness for writing certain high performance kernels such as FFT.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115734481","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 new splittable pseudorandom number generator (PRNG) based on a cryptographic hash function. Splittable PRNGs, in contrast to linear PRNGs, allow the creation of two (seemingly) independent generators from a given random number generator. Splittable PRNGs are very useful for structuring purely functional programs, as they avoid the need for threading around state. We show that the currently known and used splittable PRNGs are either not efficient enough, have inherent flaws, or lack formal arguments about their randomness. In contrast, our proposed generator can be implemented efficiently, and comes with a formal statements and proofs that quantify how 'random' the results are that are generated. The provided proofs give strong randomness guarantees under assumptions commonly made in cryptography.
{"title":"Splittable pseudorandom number generators using cryptographic hashing","authors":"Koen Claessen, Michal H. Palka","doi":"10.1145/2503778.2503784","DOIUrl":"https://doi.org/10.1145/2503778.2503784","url":null,"abstract":"We propose a new splittable pseudorandom number generator (PRNG) based on a cryptographic hash function. Splittable PRNGs, in contrast to linear PRNGs, allow the creation of two (seemingly) independent generators from a given random number generator. Splittable PRNGs are very useful for structuring purely functional programs, as they avoid the need for threading around state. We show that the currently known and used splittable PRNGs are either not efficient enough, have inherent flaws, or lack formal arguments about their randomness. In contrast, our proposed generator can be implemented efficiently, and comes with a formal statements and proofs that quantify how 'random' the results are that are generated. The provided proofs give strong randomness guarantees under assumptions commonly made in cryptography.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"145 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124638521","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 design and implement a library that solves the long-standing problem of combining effects without imposing restrictions on their interactions (such as static ordering). Effects arise from interactions between a client and an effect handler (interpreter); interactions may vary throughout the program and dynamically adapt to execution conditions. Existing code that relies on monad transformers may be used with our library with minor changes, gaining efficiency over long monad stacks. In addition, our library has greater expressiveness, allowing for practical idioms that are inefficient, cumbersome, or outright impossible with monad transformers. Our alternative to a monad transformer stack is a single monad, for the coroutine-like communication of a client with its handler. Its type reflects possible requests, i.e., possible effects of a computation. To support arbitrary effects and their combinations, requests are values of an extensible union type, which allows adding and, notably, subtracting summands. Extending and, upon handling, shrinking of the union of possible requests is reflected in its type, yielding a type-and-effect system for Haskell. The library is lightweight, generalizing the extensible exception handling to other effects and accurately tracking them in types.
{"title":"Extensible effects: an alternative to monad transformers","authors":"O. Kiselyov, A. Sabry, Cameron Swords","doi":"10.1145/2503778.2503791","DOIUrl":"https://doi.org/10.1145/2503778.2503791","url":null,"abstract":"We design and implement a library that solves the long-standing problem of combining effects without imposing restrictions on their interactions (such as static ordering). Effects arise from interactions between a client and an effect handler (interpreter); interactions may vary throughout the program and dynamically adapt to execution conditions. Existing code that relies on monad transformers may be used with our library with minor changes, gaining efficiency over long monad stacks. In addition, our library has greater expressiveness, allowing for practical idioms that are inefficient, cumbersome, or outright impossible with monad transformers.\u0000 Our alternative to a monad transformer stack is a single monad, for the coroutine-like communication of a client with its handler. Its type reflects possible requests, i.e., possible effects of a computation. To support arbitrary effects and their combinations, requests are values of an extensible union type, which allows adding and, notably, subtracting summands. Extending and, upon handling, shrinking of the union of possible requests is reflected in its type, yielding a type-and-effect system for Haskell. The library is lightweight, generalizing the extensible exception handling to other effects and accurately tracking them in types.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126956101","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}
Profiling real-world Haskell programs is hard, as compiler optimizations make it tricky to establish causality between the source code and program behavior. In this paper we attack the root issue by performing a causality analysis of functional programs under optimization. We apply our findings to build a novel profiling infrastructure on top of the Glasgow Haskell Compiler, allowing for performance analysis even of aggressively optimized programs.
{"title":"Causality of optimized Haskell: what is burning our cycles?","authors":"P. Wortmann, D. Duke","doi":"10.1145/2503778.2503788","DOIUrl":"https://doi.org/10.1145/2503778.2503788","url":null,"abstract":"Profiling real-world Haskell programs is hard, as compiler optimizations make it tricky to establish causality between the source code and program behavior. In this paper we attack the root issue by performing a causality analysis of functional programs under optimization. We apply our findings to build a novel profiling infrastructure on top of the Glasgow Haskell Compiler, allowing for performance analysis even of aggressively optimized programs.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121997621","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}
This paper presents the rationale and design of monoid-subclasses. This Haskell library consists of a collection of type classes that generalize the interface of several common data types, most importantly those used to represent strings. We demonstrate that the mathematical theory behind monoid-subclasses can bring substantial practical benefits to the Haskell library ecosystem by generalizing attoparsec, one of the most popular Haskell parsing libraries.
{"title":"Adding structure to monoids: thus hopefully ending Haskell's string type confusion","authors":"Mario BlaEevic","doi":"10.1145/2503778.2503785","DOIUrl":"https://doi.org/10.1145/2503778.2503785","url":null,"abstract":"This paper presents the rationale and design of monoid-subclasses. This Haskell library consists of a collection of type classes that generalize the interface of several common data types, most importantly those used to represent strings. We demonstrate that the mathematical theory behind monoid-subclasses can bring substantial practical benefits to the Haskell library ecosystem by generalizing attoparsec, one of the most popular Haskell parsing libraries.","PeriodicalId":188691,"journal":{"name":"ACM SIGPLAN Symposium/Workshop on Haskell","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126487781","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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