Editing Fixed-point combinator (section)

===<span class="anchor" id="Z combinator"></span>Strict fixed-point combinator===

In a [[strict programming language]] the Y combinator will expand until [[stack overflow]], or never halt in case of [[tail call optimization]].<ref>{{cite web |last1=Bene |first1=Adam |date=17 August 2017 |title=Fixed-Point Combinators in JavaScript |url=https://blog.benestudio.co/fixed-point-combinators-in-javascript-c214c15ff2f6 |website=Bene Studio |publisher=Medium |access-date=2 August 2020 |language=en}}</ref> The Z combinator will work in [[Strict programming language|strict languages]] (also called eager languages, where applicative evaluation order is applied). The Z combinator has the next argument defined explicitly, preventing the expansion of <math>Z g</math> in the right-hand side of the definition:<ref>{{cite web |title=CS 6110 S17 Lecture 5. Recursion and Fixed-Point Combinators |url=https://www.cs.cornell.edu/courses/cs6110/2017sp/lectures/lec05.pdf |website=Cornell University |at=4.1 A CBV Fixed-Point Combinator}}</ref>
: <math>Z g v = g (Z g) v\ .</math>

and in lambda calculus it is an [[Eta expansion|eta-expansion]] of the ''Y'' combinator:
: <math>Z = \lambda f.(\lambda x.f (\lambda v.x x v)) \ (\lambda x.f (\lambda v.x x v))\ .</math>