Section:
New Results
Algebraic -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 -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
-calculus and the linear-algebraic -calculus arise
independently in different contexts – the former is a fragment of the
differential -calculus, the latter is a candidate -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.