Type inference for array programming with dimensioned vector spaces

Griffioen, Paul

doi:10.1145/2897336.2897341

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…Recent analytical frameworks also include type safety. For example, type systems for linear algebra are proposed by Griffioen [6] and by Muranushi et al [12]. The Spark framework [15] provides advanced structures like Datasets that add type safety guarantees over DataFrames.…”

Section: Related Workmentioning

confidence: 99%

Preventing Technical Errors in Data Lake Analyses with Type Theory

Guyot

Leclercq

Gillet

et al. 2023

Lecture Notes in Computer Science

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Related Workmentioning

confidence: 99%

Preventing Technical Errors in Data Lake Analyses with Type Theory

Guyot

Leclercq

Gillet

et al. 2023

Lecture Notes in Computer Science

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“…The works of Muranushi et al [29] and Griffioen [16] propose a typed linear algebra system, that leads to a more functional and index-free matrix and allows to infer the type of any linear algebra expression. Their implementation in Haskell can detect typing error at compile time.…”

Section: Related Workmentioning

confidence: 99%

Empowering big data analytics with polystore and strongly typed functional queries

Gillet¹,

Leclercq²,

Savonnet³

et al. 2020

Proceedings of the 24th Symposium on International Database Engineering &Amp; Applications

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Polystores are of primary importance to tackle the diversity and the volume of Big Data, as they propose to store data according to specific use cases. Nevertheless, analytics frameworks often lack a uniform interface allowing to fully access and take advantage of the various models offered by the polystore.It also should be ensured that the typing of the algebraic expressions built with data manipulation operators can be checked and that schema can be inferred before starting to execute the operators (type-safe).Tensors are good candidates for supporting a pivot data model. They are powerful abstract mathematical objects which can embed complex relationships between entities and that are used in major analytics frameworks. However, they are far away from data models, and lack high level operators to manipulate their content, resulting in bad coding habits and less maintainability, and sometimes poor performances.With TDM (Tensor Data Model), we propose to join the best of both worlds, to take advantage of modeling capabilities of tensors by adding schema and data manipulation operators to them. We developed an implementation in Scala using Spark, providing users with a type-safe and schema inference mechanism that guarantees the technical and functional correctness of composed expressions on tensors at compile time. We show that this extension does not induce overhead and allows to outperform Spark query optimizer using bind join.

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“…[Eaton 2006] implemented a typed linear algebra system in Haskell where dimension sizes are encoded in the type system. [Grioen 2015] proposed dimensioned matrices/tensors in which each axis is dimensioned with a unit of measurement, and by this the unit of measurements of each dimension of tensors can be determined at compile time. [Muranushi and Eisenberg 2014] extends this idea to be used in astrophysics research and typed the length of each dimension by using type-level integers.…”

Section: Related Workmentioning

confidence: 99%

Typesafe abstractions for tensor operations (short paper)

Chen

2017

Proceedings of the 8th ACM SIGPLAN International Symposium on Scala

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We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM. CCS Concepts • Software and its engineering → Software libraries and repositories;We propose a typesafe tensor abstraction, in which the axes are encoded by a heterogeneous list (HList) type parameter. trait Tensor[D, A <: HList]D is the type of the elements this tensor holds (e.g. Float, Double, etc.), whereas types in the HList type parameter A are phantom types, i.e., they only serve as labels.Basic constructs such as scalars, vectors and matrices could be represented as follows (types A, B etc. are labels / names to axes). type Scalar = Tensor[Float, HNil] type Vector[A] = Tensor[Float, A :: HNil] type Matrix[A, B] = Tensor[Float, A :: B :: HNil]Looking at more concrete examples from deep learning applications, images in computer vision, or sentences in which each word is mapped to a word embedding (i.e. vector representation of that word in R d space) in natural language processing could be encoded as follows. (See Fig. 1) type Image = Tensor[Float, Width :: Height :: Channel :: HNil] type EmbeddedSentence = Tensor[Float, Word :: Embedding :: HNil]By encoding the meaning of each axis into the type, our system guarantees that all operations on tensors are allowed 3 github.com/milessabin/shapeless. 4 github.com/ctongfei/nexus.

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Type inference for array programming with dimensioned vector spaces

Cited by 4 publications

References 16 publications

Preventing Technical Errors in Data Lake Analyses with Type Theory

Preventing Technical Errors in Data Lake Analyses with Type Theory

Empowering big data analytics with polystore and strongly typed functional queries

Typesafe abstractions for tensor operations (short paper)

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