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Start Over Author "Ali Assaf" Journal logical methods in computer science
2 results on '"Ali Assaf"'

1. Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus

Author

Ali Assaf, Alejandro Díaz-Caro, Simon Perdrix, Christine Tasson, and Benoî t Valiron

Subjects
computer science - logic in computer science, Logic, BC1-199, Electronic computers. Computer science, QA75.5-76.95
Abstract

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.

Published
2014
Full Text
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2. Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus

Author

Simon Perdrix, Alejandro Díaz-Caro, Benoît Valiron, Christine Tasson, Ali Assaf, École polytechnique (X), Deduction modulo, interopérabilité et démonstration automatique (DEDUCTEAM), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Universidad Nacional de Quilmes (UNQ), Theoretical adverse computations, and safety (CARTE), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Formal Methods (LORIA - FM), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Preuves, Programmes et Systèmes (PPS), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), and ANR-10-BLAN-0213,LOGOI,Logique et géometrie de l'interaction(2010)

Subjects
Computer Science - Logic in Computer Science, ACM: F.: Theory of Computation/F.1: COMPUTATION BY ABSTRACT DEVICES/F.1.1: Models of Computation, General Computer Science, Structure (category theory), [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Theoretical Computer Science, Set (abstract data type), linear-algebraic lambda-calculus, Fragment (logic), CPS simulation, Computer Science::Logic in Computer Science, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Calculus, Algebraic lambda-calculus, Algebraic number, Linear combination, Mathematics, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], 16. Peace & justice, ACM: F.: Theory of Computation/F.4: MATHEMATICAL LOGIC AND FORMAL LANGUAGES/F.4.1: Mathematical Logic/F.4.1.2: Lambda calculus and related systems, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, TheoryofComputation_LOGICSANDMEANINGSOFPROGRAMS, Confluence, Computer Science::Programming Languages, Rewriting, Differential (mathematics)
Abstract

International audience; 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.

Published
2014
Full Text
View/download PDF

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