Malicious attacks on systems are a threat to business, government, and defense. Many attacks exploit system behavior unknown to the developers who created it. In today?s state of art, software engineers have no practical means to determine how a sizable program will behave in all circumstances of use. This sobering reality lies at the heart of many problems in security and survivability. If full behavior is unknown, so too are embedded errors, vulnerabilities, and malicious code. This paper describes function-theoretic foundations for automated calculation of full program behavior. These foundations treat program control structures as mathematical functions or relations. The function, or behavior, of control structures can be abstracted in a stepwise process into procedure-free expressions that specify their net functional effects. Problems of computability and complexities of language semantics appear to have engineering solutions. Automated behavior calculation will add rigor to security and survivability engineering.