Editing Short-circuit evaluation (section)

== Definition ==
In any programming language that implements short-circuit evaluation, the expression <code>''x'' and ''y''</code> is equivalent to the [[Conditional (programming)|conditional expression]] <code>if ''x'' then ''y'' else ''x''</code>, and the expression <code>''x'' or ''y''</code> is equivalent to <code>if ''x'' then ''x'' else ''y''</code>. In either case, ''x'' is only evaluated once.

The generalized definition above accommodates loosely typed languages that have more than the two [[truth-value]]s <code>True</code> and <code>False</code>, where short-circuit operators may return the last evaluated subexpression. This is called "last value" in the table below. For a strictly-typed language, the expression is simplified to <code>if ''x'' then ''y'' else '''false'''</code> and <code>if ''x'' then '''true''' else ''y''</code> respectively for the boolean case.

=== Precedence ===
Although {{code|AND}} takes [[operator precedence|precedence]] over {{code|OR}} in many languages, this is not a universal property of short-circuit evaluation. An example of the two operators taking the same precedence and being [[left-associative]] with each other is [[POSIX shell]]'s command-list syntax.<ref>{{cite web |title=Shell Command Language |url=https://pubs.opengroup.org/onlinepubs/009695399/utilities/xcu_chap02.html |website=pubs.opengroup.org}}</ref>{{rp|at=§2.9.3}}

The following simple left-to-right evaluator enforces a precedence of {{code|AND}} over {{code|OR}} by a {{code|continue}}:

 '''function''' short-circuit-eval (''operators'', ''values'')
     '''let''' ''result'' := True
     '''for each''' (''op'', ''val'') in (''operators'', ''values''):
         '''if''' ''op'' = "AND" && ''result'' = False
             '''continue'''
         '''else if''' ''op'' = "OR" && ''result'' = True
             '''return''' ''result''
         '''else'''
             ''result'' := ''val''
     '''return''' ''result''

=== Formalization ===
Short-circuit logic, with or without side-effects, have been formalized based on [[Hoare logic#Conditional rule|Hoare's conditional]]. A result is that non-short-circuiting operators can be defined out of short-circuit logic to have the same sequence of evaluation.<ref>{{cite arXiv |last1=Bergstra |first1=Jan A. |last2=Ponse |first2=A. |last3=Staudt |first3=D.J.C. |date=2010 |title=Short-circuit logic |eprint=1010.3674|class=cs.LO}}</ref>