Overall Objectives
Application Domains
Partnerships and Cooperations
Bibliography
Inria | Raweb 2014 | Exploratory Action
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## Section: New Results

### Algebraic $\lambda$-calculus

Ali Assaf, Alejandro Díaz-Caro, Simon Perdrix, Christine Tasson, and Benoit Valiron completed a journal paper covering results on different algebraic extensions of the $\lambda$-calculus [12] . These extensions equip the calculus with an additive and a scalar-multiplicative structure, and their set of terms is closed under linear combinations. Two such extensions, the algebraic $\lambda$-calculus and the linear-algebraic $\lambda$-calculus arise independently in different contexts – the former is a fragment of the differential $\lambda$-calculus, the latter is a candidate $\lambda$-calculus for quantum computation – and have different operational semantics. In this paper, the authors showed how the two approaches relate to each other. They showed that the the first calculus follows a call-by-name strategy while the second follows a call-by-value strategy. They proved that the two can simulate each other using algebraic extensions of continuation passing style (CPS) translations that are sound and complete.