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Structured program theorem

Theorem that a class of control flow graphs can compute any computable function if it combines subprograms only through sequence, selection, and iteration

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In programming language theory, the structured program theorem, generally called the Böhm–Jacopini theorem, states that a class of control-flow graphs (historically called flowcharts in this context) can compute any computable function using only the following three control structures to combine subprograms (statements and blocks): Sequence Executing one subprogram, and then another subprogram Selection Executing one of two subprograms according to the value of a boolean expression Iteration Repeatedly executing a subprogram as long as a boolean expression is true More precise definitions are listed in the next section. The structured chart subject to these constraints, particularly the loop constraint implying a single exit (as described later in this article), may however use additional variables in the form of bits (stored in an extra integer variable in the original proof) in order to keep track of information that the original program represents by the program location. The construction was based on Böhm's programming language P′′. The theorem forms the basis of structured programming, a programming paradigm which eschews the goto statement, exclusively using other control semantics for selection and iteration.

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