Abstract

Boolean algebra has made an indispensable contribution to the design of computer hardware. I suggest an algebra of programs, supported by mechanised tools, may be important in the engineering of software. The algebraic laws that govern program constructions are extremely familiar (e.g. associativity, commutativity), but with a couple of novel extensions to treat concurrency, and they apply to program specifications and designs as well. The laws justify algebraic proofs of a collection of useful programming calculi, including both deductive rules (e.g. Hoare Logic) and operational semantics (e.g. Milner transitions). Surprisingly, the algebra is simpler than each of these calculi individually, and as strong as all of them in combination.