A System F accounting for scalars
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 &quo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2012-02-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/846/pdf |
| _version_ | 1827322926954708992 |
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| author | Pablo Arrighi Alejandro Diaz-Caro |
| author_facet | Pablo Arrighi Alejandro Diaz-Caro |
| author_sort | Pablo Arrighi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T01:36:36Z |
| format | Article |
| id | doaj.art-683db58a03c94b6eab993a1760a68630 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:36:36Z |
| publishDate | 2012-02-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-683db58a03c94b6eab993a1760a686302024-03-08T09:27:54ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742012-02-01Volume 8, Issue 110.2168/LMCS-8(1:11)2012846A System F accounting for scalarsPablo ArrighiAlejandro Diaz-Carohttps://orcid.org/0000-0002-5175-6882The 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.https://lmcs.episciences.org/846/pdfcomputer science - logic in computer sciencecomputer science - programming languagesquantum physicsf.4.1 |
| spellingShingle | Pablo Arrighi Alejandro Diaz-Caro A System F accounting for scalars Logical Methods in Computer Science computer science - logic in computer science computer science - programming languages quantum physics f.4.1 |
| title | A System F accounting for scalars |
| title_full | A System F accounting for scalars |
| title_fullStr | A System F accounting for scalars |
| title_full_unstemmed | A System F accounting for scalars |
| title_short | A System F accounting for scalars |
| title_sort | system f accounting for scalars |
| topic | computer science - logic in computer science computer science - programming languages quantum physics f.4.1 |
| url | https://lmcs.episciences.org/846/pdf |
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