Uncommon · Knowledge
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
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 boolea...
From Wikipedia
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.
Text: Wikipédia, CC BY-SA 4.0. ·
Related cards
-
★★
Structured text
One of the five languages supported by the IEC 61131-3 standard, designed for programmable logic controllers (PLCs)
-
★★★★
Congruence (integers)
Relation between two elements differing from a multiple of an element called modulus
-
★★★
Material conditional
Logical connective between two assertions, frequently symbolized by a (most often double) arrow to the right
-
★★★
Mean value theorem
On the existence of a tangent to an arc parallel to the line through its endpoints
-
★★
Theory of planned behavior
In psychology, a theory that links one's beliefs and behavior
-
★★
Five circles theorem
-
T★★★
Turing completeness
Ability of a computing system to simulate Turing machines
-
★★★
Structure
Arrangement and organization of interrelated elements in an object or system, or the object or system so organized
-
S★
Spectral theory
Field of mathematics about eigenvalues and eigenvectors of linear operators
-
M★
Modus ponendo tollens
If X and Y can't both be true, and X is true, then Y isn't true
-
B★
Barker code
Mathematical number sequence
-
T★
Teorema de Carathéodory
-
★
Gauss–Markov theorem
Statistics theorem that ordinary least squares is the best linear unbiased estimator under certain conditions
-
T★★
True quantified Boolean formula
Problem of deciding the satisfiability of a true quantified Boolean formula
-
★★★★
Gödel's incompleteness theorems
Theorem that a wide class of logical systems cannot be both consistent and complete
-
★
Maschke's theorem
Theorem that a representation of a finite group over a field with characteristic not dividing the order of the group decomposes as a direct sum of irreducible representations
-
★
Lazy caterer's sequence
Sequence of integers
-
O★
Order topology
Certain topology on totally ordered sets