Hyperbolic space: Difference between revisions

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en>David Eppstein
See also: Murakami–Yano formula
en>BD2412
m minor fixes, mostly disambig links using AWB
 
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{{Unreferenced|date=December 2009}}
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A '''strict function''' in the [[denotational semantics]] of [[programming language]]s is a [[function (mathematics)|function]] ''f'' where <math>f\left(\perp\right) = \perp</math>. The entity <math>\perp</math>, called ''[[Bottom element|bottom]]'', denotes an expression which does not return a normal value, either because it loops endlessly or because it aborts due to an error such as division by zero. A function which is not strict is called '''non-strict'''. A [[strict programming language]] is one in which user-defined functions are always strict.


Intuitively, non-strict functions correspond to [[control structure]]s. Operationally, a strict function is one which always [[evaluate]]s its [[parameter|argument]]; a non-strict function is one which may not evaluate some of its arguments. Functions having more than one parameter may be strict or non-strict in each parameter independently, as well as ''jointly strict'' in several parameters simultaneously.
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As an example, the <tt>if-then-else</tt> expression of many programming languages may be thought of as a function of three parameters. This function is strict in its first parameter, since the function must know whether its first argument evaluates to true or to false before it can return; but it is non-strict in its second parameter, because (for example) <tt>if(false,<math>\perp</math>,1) = 1</tt>, as well as non-strict in its third parameter, because (for example) <tt>if(true,2,<math>\perp</math>) = 2</tt>. However, it is jointly strict in its second and third parameters, since <tt>if(true,<math>\perp</math>,<math>\perp</math>) = <math>\perp</math></tt> and <tt>if(false,<math>\perp</math>,<math>\perp</math>) = <math>\perp</math></tt>.
 
In a [[non-strict programming language|non-strict]] [[functional programming]] language, [[strictness analysis]] refers to any algorithm used to prove the strictness of a function with respect to one or more of its arguments. Such functions can be [[compilation (programming)|compiled]] to use a more efficient [[calling convention]] without changing the meaning of the enclosing program.
 
{{DEFAULTSORT:Strict Function}}
[[Category:Formal methods]]
[[Category:Denotational semantics]]
[[Category:Evaluation strategy]]

Latest revision as of 18:03, 6 January 2015

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