Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus
We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic: each one is equipped with an additive and a scalar-multiplicati...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2014-12-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/927/pdf |
| _version_ | 1827322864267689984 |
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| author | Ali Assaf Alejandro Díaz-Caro Simon Perdrix Christine Tasson Benoî t Valiron |
| author_facet | Ali Assaf Alejandro Díaz-Caro Simon Perdrix Christine Tasson Benoî t Valiron |
| author_sort | Ali Assaf |
| collection | DOAJ |
| description | We examine the relationship between the algebraic lambda-calculus, a fragment
of the differential lambda-calculus and the linear-algebraic lambda-calculus, a
candidate lambda-calculus for quantum computation. Both calculi are algebraic:
each one is equipped with an additive and a scalar-multiplicative structure,
and their set of terms is closed under linear combinations. However, the two
languages were built using different approaches: the former is a call-by-name
language whereas the latter is call-by-value; the former considers algebraic
equalities whereas the latter approaches them through rewrite rules. In this
paper, we analyse how these different approaches relate to one another. To this
end, we propose four canonical languages based on each of the possible choices:
call-by-name versus call-by-value, algebraic equality versus algebraic
rewriting. We show that the various languages simulate one another. Due to
subtle interaction between beta-reduction and algebraic rewriting, to make the
languages consistent some additional hypotheses such as confluence or
normalisation might be required. We carefully devise the required properties
for each proof, making them general enough to be valid for any sub-language
satisfying the corresponding properties. |
| first_indexed | 2024-04-25T01:35:38Z |
| format | Article |
| id | doaj.art-7eebfdacab104701ab3f420501c2663f |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:38Z |
| publishDate | 2014-12-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-7eebfdacab104701ab3f420501c2663f2024-03-08T09:37:58ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742014-12-01Volume 10, Issue 410.2168/LMCS-10(4:8)2014927Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculusAli AssafAlejandro Díaz-Carohttps://orcid.org/0000-0002-5175-6882Simon PerdrixChristine Tassonhttps://orcid.org/0000-0001-8098-9944Benoî t ValironWe examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic: each one is equipped with an additive and a scalar-multiplicative structure, and their set of terms is closed under linear combinations. However, the two languages were built using different approaches: the former is a call-by-name language whereas the latter is call-by-value; the former considers algebraic equalities whereas the latter approaches them through rewrite rules. In this paper, we analyse how these different approaches relate to one another. To this end, we propose four canonical languages based on each of the possible choices: call-by-name versus call-by-value, algebraic equality versus algebraic rewriting. We show that the various languages simulate one another. Due to subtle interaction between beta-reduction and algebraic rewriting, to make the languages consistent some additional hypotheses such as confluence or normalisation might be required. We carefully devise the required properties for each proof, making them general enough to be valid for any sub-language satisfying the corresponding properties.https://lmcs.episciences.org/927/pdfcomputer science - logic in computer science |
| spellingShingle | Ali Assaf Alejandro Díaz-Caro Simon Perdrix Christine Tasson Benoî t Valiron Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus Logical Methods in Computer Science computer science - logic in computer science |
| title | Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus |
| title_full | Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus |
| title_fullStr | Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus |
| title_full_unstemmed | Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus |
| title_short | Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus |
| title_sort | call by value call by name and the vectorial behaviour of the algebraic lambda calculus |
| topic | computer science - logic in computer science |
| url | https://lmcs.episciences.org/927/pdf |
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