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  • 标题:A System F accounting for scalars
  • 本地全文:下载
  • 作者:Pablo Arrighi ; Alejandro Díaz-Caro
  • 期刊名称:Logical Methods in Computer Science
  • 印刷版ISSN:1860-5974
  • 电子版ISSN:1860-5974
  • 出版年度:2012
  • 卷号:8
  • 期号:1
  • 页码:1
  • DOI:10.2168/LMCS-8(1:11)2012
  • 出版社:Technical University of Braunschweig
  • 摘要: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.
  • 其他关键词:linear-algebraic λ-calculus; type theory; barycentric calculus.
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