## 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.