Structured program theorem

The structured program theorem, also called the Böhm–Jacopini theorem, is a result in <a href="/facts/Programming_language_theory/MfecfTFI">programming language theory</a>. It states that a class of <a href="/facts/Control-flow_graph/BLsvNzcP">control-flow graphs</a> (historically called <a href="/facts/Flowchart/BtNXBfUG">flowcharts</a> in this context) can compute any <a href="/facts/Computable_function/dzwBlLGn">computable function</a> if it combines subprograms in only three specific ways (<a href="/facts/Control_structure/2XTDfErC">control structures</a>). These are

<ol><li>Executing one subprogram, and then another subprogram (sequence)</li>
<li>Executing one of two subprograms according to the value of a <a href="/facts/Boolean_data_type/0GWYLDoC">boolean</a> expression (selection)</li>
<li>Repeatedly executing a subprogram as long as a boolean expression is true (iteration)</li></ol>
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 <a href="/facts/Bit/S972NSaD">bits</a> (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 <a href="/facts/P%25E2%2580%25B2%25E2%2580%25B2/IBjep8Dj">P′′</a>.

The theorem forms the basis of <a href="/facts/Structured_programming/zA8b8dP1">structured programming</a>, a programming paradigm which eschews <a href="/facts/Goto/kWdNKT2M">goto commands</a> and exclusively uses subroutines, sequences, selection and iteration.

Structured program theorem open-in-new

Structured program theorem