Spatial logics have been proposed to reason locally and modularly on algebraic
models of distributed systems. In this paper we define the spatial equational
logic ApiL whose models are processes of the applied pi-calculus. This
extension of the pi-calculus allows term manipulation and records
communications as active substitutions in a frame, thus augmenting the
underlying predefined equational theory. Our logic allows one to reason locally
either on frames or on processes, thanks to static and dynamic spatial
operators. We study the logical equivalences induced by various relevant
fragments of ApiL, and show in particular that the whole logic induces a
coarser equivalence than structural congruence. We give characteristic formulae
for some of these equivalences and for static equivalence. Going further into
the exploration of ApiL's expressivity, we also show that it can eliminate
standard term quantification.