  Contextuality is a non-classical behaviour that can be exhibited by quantum
systems. It is increasingly studied for its relationship to
quantum-over-classical advantages in informatic tasks. To date, it has largely
been studied in discrete-variable scenarios, where observables take values in
discrete and usually finite sets. Practically, on the other hand,
continuous-variable scenarios offer some of the most promising candidates for
implementing quantum computations and informatic protocols. Here we set out a
framework for treating contextuality in continuous-variable scenarios. It is
shown that the Fine--Abramsky--Brandenburger theorem extends to this setting,
an important consequence of which is that Bell nonlocality can be viewed as a
special case of contextuality, as in the discrete case. The contextual
fraction, a quantifiable measure of contextuality that bears a precise
relationship to Bell inequality violations and quantum advantages, is also
defined in this setting. It is shown to be a non-increasing monotone with
respect to classical operations that include binning to discretise data.
Finally, we consider how the contextual fraction can be formulated as an
infinite linear program. Through Lasserre relaxations, we are able to express
this infinite linear program as a hierarchy of semi-definite programs that
allow to calculate the contextual fraction with increasing accuracy.
