Tail calls Every call in CPS is a tail call, and the continuation is explicitly passed. Using CPS without tail call optimization (TCO) will cause not only the constructed continuation to potentially grow during recursion, but also the call stack. This is usually undesirable, but has been used in interesting ways—see the Chicken Scheme compiler. As CPS and TCO eliminate the concept of an implicit function return, their combined use can eliminate the need for a run-time stack. Several compilers and interpreters for functional programming languages use this ability in novel ways. 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 continuations but does have first-class functions and tail-call optimization. Without tail-call optimization, techniques such as 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 compilation. Functions using more than one continuation can be defined to capture various control flow paradigms, for example (in Scheme): (define (/& x y ok err) (=& y 0.0 (lambda (b) (if b (err (list "div by zero!" x y)) (ok (/ x y)))))) It is of note that CPS transform is conceptually a Yoneda embedding. It is also similar to the embedding of lambda calculus in π-calculus. Use in other fields Outside of computer science, CPS is of more general interest as an alternative to the conventional method of composing simple expressions into complex expressions. For example, within linguistic semantics, Chris Barker and his collaborators have suggested that specifying the denotations of sentences using CPS might explain certain phenomena in natural language. In mathematics, the Curry–Howard isomorphism between computer programs and mathematical proofs relates continuation-passing style translation to a variation of double-negation embeddings of classical logic into intuitionistic (constructive) logic. Unlike the regular double-negation translation, which maps atomic propositions p to ((p → ⊥) → ⊥), the continuation passing style replaces ⊥ by the type of the final expression. Accordingly, the