  Linearity and ramification constraints have been widely used to weaken
higher-order (primitive) recursion in such a way that the class of
representable functions equals the class of polytime functions. We show that
fine-tuning these two constraints leads to different expressive strengths, some
of them lying well beyond polynomial time. This is done by introducing a new
semantics, called algebraic context semantics. The framework stems from
Gonthier's original work and turns out to be a versatile and powerful tool for
the quantitative analysis of normalization in presence of constants and
higher-order recursion.
