10.2168/LMCS-8(1:11)2012
Arrighi, Pablo
Pablo
Arrighi
Diaz-Caro, Alejandro
Alejandro
Diaz-Caro
A System F accounting for scalars
episciences.org
2012
Computer Science - Logic in Computer Science
Computer Science - Programming Languages
Quantum Physics
F.4.1
contact@episciences.org
episciences.org
2011-06-10T00:00:00+02:00
2016-11-21T15:29:03+01:00
2012-02-27
eng
Journal article
https://lmcs.episciences.org/846
arXiv:0903.3741
1860-5974
PDF
1
Logical Methods in Computer Science ; Volume 8, Issue 1 ; 1860-5974
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.