  Boolean calculus has been studied extensively in the past in the context of
switching circuits, error-correcting codes etc. This work generalizes several
approaches to defining a differential calculus for Boolean functions. A unified
theory of Boolean calculus, complete with k-forms and integration, is presented
through the use of Zhegalkin algebras (i.e., algebraic normal forms),
culminating in a Stokes-like theorem for Boolean functions.

Rings and Algebras