The vectorial λ-calculus
We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an origina...
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| Published in | Information and computation Vol. 254; no. 1; pp. 105 - 139 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.06.2017
Elsevier |
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| ISSN | 0890-5401 1090-2651 1090-2651 |
| DOI | 10.1016/j.ic.2017.04.001 |
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| Abstract | We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus. |
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| AbstractList | We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus. |
| Author | Valiron, Benoît Díaz-Caro, Alejandro Arrighi, Pablo |
| Author_xml | – sequence: 1 givenname: Pablo surname: Arrighi fullname: Arrighi, Pablo email: pablo.arrighi@univ-amu.fr organization: Aix-Marseille Université, CNRS, LIF, Marseille and IXXI, Lyon, France – sequence: 2 givenname: Alejandro surname: Díaz-Caro fullname: Díaz-Caro, Alejandro email: alejandro.diaz-caro@unq.edu.ar organization: Universidad Nacional de Quilmes & CONICET, B1876BXD Bernal, Buenos Aires, Argentina – sequence: 3 givenname: Benoît surname: Valiron fullname: Valiron, Benoît email: benoit.valiron@monoidal.net organization: LRI, CentraleSupélec, Univ. Paris Sud, CNRS, Université Paris-Saclay, 91405 Orsay Cedex, France |
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| Cites_doi | 10.1137/S0097539795293172 10.1016/j.apal.2011.09.008 10.1137/0215084 10.1051/ita/2012012 10.1016/S0304-3975(03)00392-X 10.1017/S0960129509990089 10.1017/S0956796809007369 10.3233/FI-2012-778 10.1016/0890-5401(92)90064-M 10.1006/inco.1994.1003 10.1093/logcom/exi008 10.1137/S0097539703432165 10.3233/FI-2010-324 10.1006/inco.1995.1145 10.1006/inco.1995.1086 |
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| Snippet | We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is... |
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| Title | The vectorial λ-calculus |
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