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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Detalles Bibliográficos
Autores: Arrighi, Pablo, Díaz Caro, Alejandro, Valiron, Benoît
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/72528
Acceso en línea:http://hdl.handle.net/11336/72528
Access Level:acceso embargado
Palabra clave:Lambda calculus
Type theory
Quantum computing
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
Descripción
Sumario: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.