A Spatial Equational Logic for the Applied pi-Calculus

Spatial logics have been proposed to reason locally andmodularly on algebraic models of distributed systems. In this paperwe define the spatial equational logic AΠL whosemodels are processes of the applied Π-calculus. Thisextension of the Π-calculus allows term manipulationand records communications as active substitutions in a frame, thusaugmenting the underlying predefined equational theory. Our logicallows one to reason locally either on frames or on processes,thanks to static and dynamic spatial operators. We study thelogical equivalences induced by various relevant fragments ofAΠL, and show in particular that the whole logicinduces a coarser equivalence than structural congruence. We givecharacteristic formulae for some of these equivalences and forstatic equivalence. Going further into the exploration ofAΠL's expressivity, we also show that it can eliminatestandard term quantification.

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