4 Search Results for "Gibbons, Jeremy"

Document
DOI: 10.4230/LIPIcs.FSCD.2020.17
String Diagrams for Optics

Authors: Guillaume Boisseau

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
Optics are a data representation for compositional data access, with lenses as a popular special case. Hedges has presented a diagrammatic calculus for lenses, but in a way that does not generalize to other classes of optic. We present a calculus that works for all optics, not just lenses; this is done by embedding optics into their presheaf category, which naturally features string diagrams. We apply our calculus to the common case of lenses, extend it to effectful lenses, and explore how the laws of optics manifest in this setting.
Cite as

Guillaume Boisseau. String Diagrams for Optics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{boisseau:LIPIcs.FSCD.2020.17,
  author =	{Boisseau, Guillaume},
  title =	{{String Diagrams for Optics}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.17},
  URN =		{urn:nbn:de:0030-drops-123399},
  doi =		{10.4230/LIPIcs.FSCD.2020.17},
  annote =	{Keywords: Optic, string diagram, lens, category theory, Yoneda lemma}
}
Document
Pearl
DOI: 10.4230/LIPIcs.ECOOP.2019.25
Finally, a Polymorphic Linear Algebra Language (Pearl)

Authors: Amir Shaikhha and Lionel Parreaux

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)

Abstract
Many different data analytics tasks boil down to linear algebra primitives. In practice, for each different type of workload, data scientists use a particular specialised library. In this paper, we present Pilatus, a polymorphic iterative linear algebra language, applicable to various types of data analytics workloads. The design of this domain-specific language (DSL) is inspired by both mathematics and programming languages: its basic constructs are borrowed from abstract algebra, whereas the key technology behind its polymorphic design uses the tagless final approach (a.k.a. polymorphic embedding/object algebras). This design enables us to change the behaviour of arithmetic operations to express matrix algebra, graph algorithms, logical probabilistic programs, and differentiable programs. Crucially, the polymorphic design of Pilatus allows us to use multi-stage programming and rewrite-based optimisation to recover the performance of specialised code, supporting fixed sized matrices, algebraic optimisations, and fusion.
Cite as

Amir Shaikhha and Lionel Parreaux. Finally, a Polymorphic Linear Algebra Language (Pearl). In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 25:1-25:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{shaikhha_et_al:LIPIcs.ECOOP.2019.25,
  author =	{Shaikhha, Amir and Parreaux, Lionel},
  title =	{{Finally, a Polymorphic Linear Algebra Language}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{25:1--25:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.25},
  URN =		{urn:nbn:de:0030-drops-108172},
  doi =		{10.4230/LIPIcs.ECOOP.2019.25},
  annote =	{Keywords: Linear Algebra, Domain-Specific Languages, Tagless Final, Polymorphic Embedding, Object Algebra, Multi-Stage Programming, Graph Processing, Probabilistic Programming, Automatic Differentiation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.14
Efficient Algorithms with Asymmetric Read and Write Costs

Authors: Guy E. Blelloch, Jeremy T. Fineman, Phillip B. Gibbons, Yan Gu, and Julian Shun

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
In several emerging technologies for computer memory (main memory), the cost of reading is significantly cheaper than the cost of writing. Such asymmetry in memory costs poses a fundamentally different model from the RAM for algorithm design. In this paper we study lower and upper bounds for various problems under such asymmetric read and write costs. We consider both the case in which all but O(1) memory has asymmetric cost, and the case of a small cache of symmetric memory. We model both cases using the (M,omega)-ARAM, in which there is a small (symmetric) memory of size M and a large unbounded (asymmetric) memory, both random access, and where reading from the large memory has unit cost, but writing has cost omega >> 1. For FFT and sorting networks we show a lower bound cost of Omega(omega*n*log_{omega*M}(n)), which indicates that it is not possible to achieve asymptotic improvements with cheaper reads when omega is bounded by a polynomial in M. Moreover, there is an asymptotic gap (of min(omega,log(n)/log(omega*M)) between the cost of sorting networks and comparison sorting in the model. This contrasts with the RAM, and most other models, in which the asymptotic costs are the same. We also show a lower bound for computations on an n*n diamond DAG of Omega(omega*n^2/M) cost, which indicates no asymptotic improvement is achievable with fast reads. However, we show that for the minimum edit distance problem (and related problems), which would seem to be a diamond DAG, we can beat this lower bound with an algorithm with only O(omega*n^2/(M*min(omega^{1/3},M^{1/2}))) cost. To achieve this we make use of a "path sketch" technique that is forbidden in a strict DAG computation. Finally, we show several interesting upper bounds for shortest path problems, minimum spanning trees, and other problems. A common theme in many of the upper bounds is that they require redundant computation and a tradeoff between reads and writes.
Cite as

Guy E. Blelloch, Jeremy T. Fineman, Phillip B. Gibbons, Yan Gu, and Julian Shun. Efficient Algorithms with Asymmetric Read and Write Costs. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{blelloch_et_al:LIPIcs.ESA.2016.14,
  author =	{Blelloch, Guy E. and Fineman, Jeremy T. and Gibbons, Phillip B. and Gu, Yan and Shun, Julian},
  title =	{{Efficient Algorithms with Asymmetric Read and Write Costs}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.14},
  URN =		{urn:nbn:de:0030-drops-63656},
  doi =		{10.4230/LIPIcs.ESA.2016.14},
  annote =	{Keywords: Computational Model, Lower Bounds, Shortest-paths, Non-Volatile Memory, Sorting Networks, Fast Fourier Transform, Diamond DAG, Minimum Spanning Tree}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.290
Modules Over Monads and Their Algebras

Authors: Maciej Pirog, Nicolas Wu, and Jeremy Gibbons

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
Modules over monads (or: actions of monads on endofunctors) are structures in which a monad interacts with an endofunctor, composed either on the left or on the right. Although usually not explicitly identified as such, modules appear in many contexts in programming and semantics. In this paper, we investigate the elementary theory of modules. In particular, we identify the monad freely generated by a right module as a generalisation of Moggi's resumption monad and characterise its algebras, extending previous results by Hyland, Plotkin and Power, and by Filinski and Stovring. Moreover, we discuss a connection between modules and algebraic effects: left modules have a similar feeling to Eilenberg–Moore algebras, and can be seen as handlers that are natural in the variables, while right modules can be seen as functions that run effectful computations in an appropriate context (such as an initial state for a stateful computation).
Cite as

Maciej Pirog, Nicolas Wu, and Jeremy Gibbons. Modules Over Monads and Their Algebras. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 290-303, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{pirog_et_al:LIPIcs.CALCO.2015.290,
  author =	{Pirog, Maciej and Wu, Nicolas and Gibbons, Jeremy},
  title =	{{Modules Over Monads and Their Algebras}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{290--303},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.290},
  URN =		{urn:nbn:de:0030-drops-55404},
  doi =		{10.4230/LIPIcs.CALCO.2015.290},
  annote =	{Keywords: monad, module over monad, algebraic data types, resumptions, free object}
}
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