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A System F accounting for scalars

Pablo Arrighi ; Alejandro Diaz-Caro.

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&nbsp;[&hellip;]

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

Ali Assaf ; Alejandro Díaz-Caro ; Simon Perdrix ; Christine Tasson ; Benoî t Valiron.

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&nbsp;[&hellip;]

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Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model

Alejandro Díaz-Caro ; Octavio Malherbe.

In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this paper, we introduce a valid subset of typing rules, defining&nbsp;[&hellip;]

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