Categories as Type Classes in the Scala Algebra System

Jolly, Raphael

doi:10.1007/978-3-319-02297-0_18

Cited by 3 publications

(2 citation statements)

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“…In this section, we will see how the progressive type-level functionalities of GHC can be exploited to construct a safe, composable and flexible type-system for a computer algebra system. There are several existing works on type-systems for computer algebra, such as in Java and Scala [18,15], and DoCon. However, none of them achieves the same level of safety and composability as our approach, which utilises the power of dependent types and type-level functions.…”

Section: Type System For Safety and Composabilitymentioning

confidence: 99%

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A Purely Functional Computer Algebra System Embedded in Haskell

Ishii

2018

Developments in Language Theory

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We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-ofconcept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded domain-specific language in Haskell, a purely functional programming language. Utilising methods in functional programming and prominent features of Haskell, this library achieves safety, composability, and correctness at the same time. To demonstrate the advantages of our approach, we have implemented advanced Gröbner basis algorithms, such as Faugère's F4 and F5, in a composable way.

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Section: Type System For Safety and Composabilitymentioning

confidence: 99%

“…Mechveliani [23] or Jolly [15]), and we build our system on top of the existing algebra package [17], which provides a fine-grained abstract algebraic hierarchy. Code 1 illustrates a simplified version of the algebraic hierarchy up to Group provided by the algebra package.…”

Section: Type Classes To Encode Algebraic Hierarchymentioning

confidence: 99%