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Concept
Switch statement
Summary
In computer programming languages, a switch statement is a type of selection control mechanism used to allow the value of a variable or expression to change the control flow of program execution via search and map.
Switch statements function somewhat similarly to the if statement used in programming languages like C/C++, C#, Visual Basic .NET, Java and exists in most high-level imperative programming languages such as Pascal, Ada, C/C++, C#, Visual Basic .NET, Java, and in many other types of language, using such keywords as switch, case, select or inspect.
Switch statements come in two main variants: a structured switch, as in Pascal, which takes exactly one branch, and an unstructured switch, as in C, which functions as a type of goto. The main reasons for using a switch include improving clarity, by reducing otherwise repetitive coding, and (if the heuristics permit) also offering the potential for faster execution through easier compiler optimization in many cases.
In his 1952 text Introduction to Metamathematics, Stephen Kleene formally proved that the CASE function (the IF-THEN-ELSE function being its simplest form) is a primitive recursive function, where he defines the notion definition by cases in the following manner:
"#F. The function φ defined thus
φ(x1 , ... , xn ) =
φ1(x1 , ... , xn ) if Q1(x1 , ... , xn ),
. . . . . . . . . . .
φm(x1 , ... , xn ) if Qm(x1 , ... , xn ),
φm+1(x1 , ... , xn ) otherwise,
where Q1 , ... , Qm are mutually exclusive predicates (or φ(x1 , ... , xn) shall have the value given by the first clause which applies) is primitive recursive in φ1, ..., φm+1, Q1, ..., Qm+1.
Kleene provides a proof of this in terms of the Boolean-like recursive functions "sign-of" sg( ) and "not sign of" ~sg( ) (Kleene 1952:222-223); the first returns 1 if its input is positive and −1 if its input is negative.
Boolos-Burgess-Jeffrey make the additional observation that "definition by cases" must be both mutually exclusive and collectively exhaustive.
Official source
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