Pablo Arrighi ; Alejandro Diaz-Caro - A System F accounting for scalars

lmcs:846 - Logical Methods in Computer Science, February 27, 2012, Volume 8, Issue 1 -
A System F accounting for scalarsArticle

Authors: Pablo Arrighi ; Alejandro Diaz-Caro ORCID

    The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for the linear-algebraic lambda-calculus. We show that this "scalar" type system enjoys both the subject-reduction property and the strong-normalisation property, our main technical results. The latter yields a significant simplification of the linear-algebraic lambda-calculus itself, by removing the need for some restrictions in its reduction rules. But the more important, original feature of this scalar type system is that it keeps track of 'the amount of a type' that is present in each term. As an example of its use, we shown that it can serve as a guarantee that the normal form of a term is barycentric, i.e that its scalars are summing to one.

    Volume: Volume 8, Issue 1
    Published on: February 27, 2012
    Imported on: June 10, 2011
    Keywords: Computer Science - Logic in Computer Science,Computer Science - Programming Languages,Quantum Physics,F.4.1

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