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 in:Information and computation 2017-06, Vol.254 (1), p.105-139
Main Authors: Arrighi, Pablo, Díaz-Caro, Alejandro, Valiron, Benoît
Format: Article
Language:English
Subjects:
Computer Science
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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
DOI:10.1016/j.ic.2017.04.001