Editing Continuation-passing style (section)

==Use and implementation==
Continuation passing style can be used to implement continuations and control flow operators in a functional language that does not feature first-class [[continuation]]s but does have [[first-class function]]s and [[tail-call optimization]]. Without tail-call optimization, techniques such as [[trampoline (computers)|trampolining]], i.e., using a loop that iteratively invokes [[thunk]]-returning functions, can be used; without first-class functions, it is even possible to convert tail calls into just gotos in such a loop.

Writing code in CPS, while not impossible, is often error-prone. There are various translations, usually defined as one- or two-pass conversions of pure [[lambda calculus]], which convert direct style expressions into CPS expressions. Writing in trampolined style, however, is extremely difficult; when used, it is usually the target of some sort of transformation, such as [[compiler|compilation]].

Functions using more than one continuation can be defined to capture various control flow paradigms, for example (in [[Scheme (programming language)|Scheme]]):
<syntaxhighlight lang=scheme>
(define (/& x y ok err)
 (=& y 0.0 (lambda (b)
            (if b
                (err (list "div by zero!" x y))
                (ok (/ x y))))))
</syntaxhighlight>

A CPS transform is conceptually a [[Yoneda embedding]].<ref>{{cite report |last1=Stay |first1=Mike |url=http://golem.ph.utexas.edu/category/2008/01/the_continuation_passing_trans.html |title=The Continuation Passing Transform and the Yoneda Embedding}}</ref> It is also similar to the embedding of [[lambda calculus]] in [[π-calculus]].<ref>Mike Stay, [http://golem.ph.utexas.edu/category/2009/09/the_pi_calculus_ii.html "The Pi Calculus II"]</ref><ref>{{cite CiteSeerX |first1=Gérard |last1=Boudol |year=1997 |citeseerx=10.1.1.52.6034 |title=The π-Calculus in Direct Style}}</ref>