The vectorial λ-calculus

We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an origina...

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Bibliographic Details
Published inInformation and computation Vol. 254; no. 1; pp. 105 - 139
Main Authors Arrighi, Pablo, Díaz-Caro, Alejandro, Valiron, Benoît
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2017
Elsevier
Subjects
Computer Science
Online AccessGet full text
ISSN0890-5401
1090-2651
1090-2651
DOI10.1016/j.ic.2017.04.001

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Summary:We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.
ISSN:0890-5401
1090-2651
1090-2651
DOI:10.1016/j.ic.2017.04.001