{"title":"A theory of gradual effect systems","authors":"Felipe Bañados, Ronald Garcia, É. Tanter","doi":"10.1145/2692915.2628149","DOIUrl":"https://doi.org/10.1145/2692915.2628149","url":null,"abstract":"","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"53 1","pages":"283-295"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74316541","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}
{"title":"Functional programming for dynamic and large data with self-adjusting computation","authors":"Yan Chen, Umut A. Acar, Kanat Tangwongsan","doi":"10.1145/2692915.2628150","DOIUrl":"https://doi.org/10.1145/2692915.2628150","url":null,"abstract":"","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"16 1","pages":"227-240"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73249064","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}
Expressing algorithms using immutable arrays greatly simplifies the challenges of automatic SIMD vectorization, since several important classes of dependency violations cannot occur. The Haskell programming language provides libraries for programming with immutable arrays, and compiler support for optimizing them to eliminate the overhead of intermediate temporary arrays. We describe an implementation of automatic SIMD vectorization in a Haskell compiler which gives substantial vector speedups for a range of programs written in a natural programming style. We compare performance with that of programs compiled by the Glasgow Haskell Compiler.
{"title":"Automatic SIMD vectorization for Haskell","authors":"Leaf Petersen, Dominic A. Orchard, Neal Glew","doi":"10.1145/2500365.2500605","DOIUrl":"https://doi.org/10.1145/2500365.2500605","url":null,"abstract":"Expressing algorithms using immutable arrays greatly simplifies the challenges of automatic SIMD vectorization, since several important classes of dependency violations cannot occur. The Haskell programming language provides libraries for programming with immutable arrays, and compiler support for optimizing them to eliminate the overhead of intermediate temporary arrays. We describe an implementation of automatic SIMD vectorization in a Haskell compiler which gives substantial vector speedups for a range of programs written in a natural programming style. We compare performance with that of programs compiled by the Glasgow Haskell Compiler.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86912418","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}
Continuations are programming abstractions that allow for manipulating the "future" of a computation. Amongst their many applications, they enable implementing unstructured program flow through higher-order control operators such as callcc. In this paper we develop a Hoare-style logic for the verification of programs with higher-order control, in the presence of dynamic state. This is done by designing a dependent type theory with first class callcc and abort operators, where pre- and postconditions of programs are tracked through types. Our operators are algebraic in the sense of Plotkin and Power, and Jaskelioff, to reduce the annotation burden and enable verification by symbolic evaluation. We illustrate working with the logic by verifying a number of characteristic examples.
{"title":"Hoare-style reasoning with (algebraic) continuations","authors":"G. Delbianco, Aleksandar Nanevski","doi":"10.1145/2500365.2500593","DOIUrl":"https://doi.org/10.1145/2500365.2500593","url":null,"abstract":"Continuations are programming abstractions that allow for manipulating the \"future\" of a computation. Amongst their many applications, they enable implementing unstructured program flow through higher-order control operators such as callcc. In this paper we develop a Hoare-style logic for the verification of programs with higher-order control, in the presence of dynamic state. This is done by designing a dependent type theory with first class callcc and abort operators, where pre- and postconditions of programs are tracked through types. Our operators are algebraic in the sense of Plotkin and Power, and Jaskelioff, to reduce the annotation burden and enable verification by symbolic evaluation. We illustrate working with the logic by verifying a number of characteristic examples.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89145164","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}
Benjamin Delaware, Steven Keuchel, T. Schrijvers, B. C. D. S. Oliveira
This paper presents 3MT, a framework for modular mechanized meta-theory of languages with effects. Using 3MT, individual language features and their corresponding definitions -- semantic functions, theorem statements and proofs-- can be built separately and then reused to create different languages with fully mechanized meta-theory. 3MT combines modular datatypes and monads to define denotational semantics with effects on a per-feature basis, without fixing the particular set of effects or language constructs. One well-established problem with type soundness proofs for denotational semantics is that they are notoriously brittle with respect to the addition of new effects. The statement of type soundness for a language depends intimately on the effects it uses, making it particularly challenging to achieve modularity. 3MT solves this long-standing problem by splitting these theorems into two separate and reusable parts: a feature theorem that captures the well-typing of denotations produced by the semantic function of an individual feature with respect to only the effects used, and an effect theorem that adapts well-typings of denotations to a fixed superset of effects. The proof of type soundness for a particular language simply combines these theorems for its features and the combination of their effects. To establish both theorems, 3MT uses two key reasoning techniques: modular induction and algebraic laws about effects. Several effectful language features, including references and errors, illustrate the capabilities of 3MT. A case study reuses these features to build fully mechanized definitions and proofs for 28 languages, including several versions of mini-ML with effects.
{"title":"Modular monadic meta-theory","authors":"Benjamin Delaware, Steven Keuchel, T. Schrijvers, B. C. D. S. Oliveira","doi":"10.1145/2500365.2500587","DOIUrl":"https://doi.org/10.1145/2500365.2500587","url":null,"abstract":"This paper presents 3MT, a framework for modular mechanized meta-theory of languages with effects. Using 3MT, individual language features and their corresponding definitions -- semantic functions, theorem statements and proofs-- can be built separately and then reused to create different languages with fully mechanized meta-theory. 3MT combines modular datatypes and monads to define denotational semantics with effects on a per-feature basis, without fixing the particular set of effects or language constructs. One well-established problem with type soundness proofs for denotational semantics is that they are notoriously brittle with respect to the addition of new effects. The statement of type soundness for a language depends intimately on the effects it uses, making it particularly challenging to achieve modularity. 3MT solves this long-standing problem by splitting these theorems into two separate and reusable parts: a feature theorem that captures the well-typing of denotations produced by the semantic function of an individual feature with respect to only the effects used, and an effect theorem that adapts well-typings of denotations to a fixed superset of effects. The proof of type soundness for a particular language simply combines these theorems for its features and the combination of their effects. To establish both theorems, 3MT uses two key reasoning techniques: modular induction and algebraic laws about effects. Several effectful language features, including references and errors, illustrate the capabilities of 3MT. A case study reuses these features to build fully mechanized definitions and proofs for 28 languages, including several versions of mini-ML with effects.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79486419","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}
Neil Sculthorpe, J. Bracker, George Giorgidze, Andy Gill
In Haskell, there are many data types that would form monads were it not for the presence of type-class constraints on the operations on that data type. This is a frustrating problem in practice, because there is a considerable amount of support and infrastructure for monads that these data types cannot use. Using several examples, we show that a monadic computation can be restructured into a normal form such that the standard monad class can be used. The technique is not specific to monads, and we show how it can also be applied to other structures, such as applicative functors. One significant use case for this technique is domain-specific languages, where it is often desirable to compile a deep embedding of a computation to some other language, which requires restricting the types that can appear in that computation.
{"title":"The constrained-monad problem","authors":"Neil Sculthorpe, J. Bracker, George Giorgidze, Andy Gill","doi":"10.1145/2500365.2500602","DOIUrl":"https://doi.org/10.1145/2500365.2500602","url":null,"abstract":"In Haskell, there are many data types that would form monads were it not for the presence of type-class constraints on the operations on that data type. This is a frustrating problem in practice, because there is a considerable amount of support and infrastructure for monads that these data types cannot use. Using several examples, we show that a monadic computation can be restructured into a normal form such that the standard monad class can be used. The technique is not specific to monads, and we show how it can also be applied to other structures, such as applicative functors. One significant use case for this technique is domain-specific languages, where it is often desirable to compile a deep embedding of a computation to some other language, which requires restricting the types that can appear in that computation.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88729442","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}
Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent such unifications are the 'recursion schemes from comonads' of Uustalu, Vene and Pardo, and our own 'adjoint folds'. Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads. The proof of this claim involves standard constructions in category theory that are nevertheless not well known in functional programming: Eilenberg-Moore categories and bialgebras.
{"title":"Unifying structured recursion schemes","authors":"Ralf Hinze, Nicolas Wu, Jeremy Gibbons","doi":"10.1145/2500365.2500578","DOIUrl":"https://doi.org/10.1145/2500365.2500578","url":null,"abstract":"Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent such unifications are the 'recursion schemes from comonads' of Uustalu, Vene and Pardo, and our own 'adjoint folds'. Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads. The proof of this claim involves standard constructions in category theory that are nevertheless not well known in functional programming: Eilenberg-Moore categories and bialgebras.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87446069","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}
In this paper we investigate laziness and optimal evaluation strategies for functional programming languages. We consider the weak lambda-calculus as a basis of functional programming languages, and we adapt to this setting the concepts of optimal reductions that were defined for the full lambda-calculus. We prove that the usual implementation of call-by-need using sharing is optimal, that is, normalizing any lambda-term with call-by-need requires exactly the same number of reduction steps as the shortest reduction sequence in the weak lambda-calculus without sharing. Furthermore, we prove that optimal reduction sequences without sharing are not computable. Hence sharing is the only computable means to reach weak optimality.
{"title":"Weak optimality, and the meaning of sharing","authors":"Thibaut Balabonski","doi":"10.1145/2500365.2500606","DOIUrl":"https://doi.org/10.1145/2500365.2500606","url":null,"abstract":"In this paper we investigate laziness and optimal evaluation strategies for functional programming languages. We consider the weak lambda-calculus as a basis of functional programming languages, and we adapt to this setting the concepts of optimal reductions that were defined for the full lambda-calculus. We prove that the usual implementation of call-by-need using sharing is optimal, that is, normalizing any lambda-term with call-by-need requires exactly the same number of reduction steps as the shortest reduction sequence in the weak lambda-calculus without sharing. Furthermore, we prove that optimal reduction sequences without sharing are not computable. Hence sharing is the only computable means to reach weak optimality.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89547065","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}
In this paper, we study strong normalization of a core language based on System F-omega which supports programming with finite and infinite structures. Building on our prior work, finite data such as finite lists and trees are defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. In this work, we take a type-based approach to strong normalization by tracking size information about finite and infinite data in the type. This guarantees compositionality. More importantly, the duality of pattern and copatterns provide a unifying semantic concept which allows us for the first time to elegantly and uniformly support both well-founded induction and coinduction by mere rewriting. The strong normalization proof is structured around Girard's reducibility candidates. As such our system allows for non-determinism and does not rely on coverage. Since System F-omega is general enough that it can be the target of compilation for the Calculus of Constructions, this work is a significant step towards representing observation-centric infinite data in proof assistants such as Coq and Agda.
{"title":"Wellfounded recursion with copatterns: a unified approach to termination and productivity","authors":"Andreas Abel, B. Pientka","doi":"10.1145/2500365.2500591","DOIUrl":"https://doi.org/10.1145/2500365.2500591","url":null,"abstract":"In this paper, we study strong normalization of a core language based on System F-omega which supports programming with finite and infinite structures. Building on our prior work, finite data such as finite lists and trees are defined via constructors and manipulated via pattern matching, while infinite data such as streams and infinite trees is defined by observations and synthesized via copattern matching. In this work, we take a type-based approach to strong normalization by tracking size information about finite and infinite data in the type. This guarantees compositionality. More importantly, the duality of pattern and copatterns provide a unifying semantic concept which allows us for the first time to elegantly and uniformly support both well-founded induction and coinduction by mere rewriting. The strong normalization proof is structured around Girard's reducibility candidates. As such our system allows for non-determinism and does not rely on coverage. Since System F-omega is general enough that it can be the target of compilation for the Calculus of Constructions, this work is a significant step towards representing observation-centric infinite data in proof assistants such as Coq and Agda.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"92 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73080731","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}
Computer science is one of the richest, most exciting disciplines on the planet, yet any teenager will tell you that ICT (as it is called in UK schools --- "information and communication technology") is focused almost entirely on the use and application of computers, and in practice covers nothing about how computers work, nor programming, nor anything of the discipline of computer science as we understand it. Over the last two decades, computing at school has drifted from writing adventure games on the BBC Micro to writing business plans in Excel. This is bad for our young people's education, and it is bad for our economy. Nor is this phenomenon restricted to the UK: many countries are struggling with the same issues. Our young people should be educated not only in the application and use of digital technology, but also in how it works, and its foundational principles. Lacking such knowledge renders them powerless in the face of complex and opaque technology, disenfranchises them from making informed decisions about the digital society, and deprives our nations of a well-qualified stream of students enthusiastic and able to envision and design new digital systems. Can anything be done, given the enormous inertia of our various countries' educational systems? Sometimes, yes. After a decade of stasis, change has come to the UK. Over the last 18 months, there has been a wholesale reform of the English school computing curriculum, and substantial movement in Scotland and Wales. It now seems likely that computer science will, for the first time, become part of every child's education. This change has been driven not by institutions or by the government, but by a grass-roots movement of parents, teachers, university academics, software developers, and others. A key agent in this grass-roots movement---although not the only one---is the Computing At School Working Group (CAS). In this talk I will describe how CAS was born and developed, and the radical changes that have taken place since in the UK. I hope that this may be encouraging for those pushing water uphill in other parts of the world, and I will also try to draw out some lessons from our experience that may be useful to others.
{"title":"Computer science as a school subject","authors":"S. Jones","doi":"10.1145/2544174.2500609","DOIUrl":"https://doi.org/10.1145/2544174.2500609","url":null,"abstract":"Computer science is one of the richest, most exciting disciplines on the planet, yet any teenager will tell you that ICT (as it is called in UK schools --- \"information and communication technology\") is focused almost entirely on the use and application of computers, and in practice covers nothing about how computers work, nor programming, nor anything of the discipline of computer science as we understand it. Over the last two decades, computing at school has drifted from writing adventure games on the BBC Micro to writing business plans in Excel. This is bad for our young people's education, and it is bad for our economy. Nor is this phenomenon restricted to the UK: many countries are struggling with the same issues. Our young people should be educated not only in the application and use of digital technology, but also in how it works, and its foundational principles. Lacking such knowledge renders them powerless in the face of complex and opaque technology, disenfranchises them from making informed decisions about the digital society, and deprives our nations of a well-qualified stream of students enthusiastic and able to envision and design new digital systems. Can anything be done, given the enormous inertia of our various countries' educational systems? Sometimes, yes. After a decade of stasis, change has come to the UK. Over the last 18 months, there has been a wholesale reform of the English school computing curriculum, and substantial movement in Scotland and Wales. It now seems likely that computer science will, for the first time, become part of every child's education. This change has been driven not by institutions or by the government, but by a grass-roots movement of parents, teachers, university academics, software developers, and others. A key agent in this grass-roots movement---although not the only one---is the Computing At School Working Group (CAS). In this talk I will describe how CAS was born and developed, and the radical changes that have taken place since in the UK. I hope that this may be encouraging for those pushing water uphill in other parts of the world, and I will also try to draw out some lessons from our experience that may be useful to others.","PeriodicalId":20504,"journal":{"name":"Proceedings of the 18th ACM SIGPLAN international conference on Functional programming","volume":"8 1","pages":"159-160"},"PeriodicalIF":0.0,"publicationDate":"2013-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81972199","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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