## Lambda Calculus Fixed Point Operator Y (strict)

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FP
Lambda
Introduction
Examples
Y (lazy)
Y (strict)

The strict version of Y works with the strict interpreter (the lazy one will not). You can program this Y in many conventional languages such as [Algol-68].

 ```let F = lambda f. lambda n. if n=0 then 1 else n*f(n-1), Y = lambda G. let Ggg = lambda g. lambda n. G(g g)n in Ggg Ggg in Y F 10 {\fB Strict Version of Y. \fP} ``` let F = lambda f. lambda n. if n=0 then 1 else n*f(n-1), Y = lambda G. let Ggg = lambda g. lambda n. G(g g)n in Ggg Ggg in Y F 10 {\fB Strict Version of Y. \fP}
 Coding Ockham's Razor, L. Allison, Springer A Practical Introduction to Denotational Semantics, L. Allison, CUP

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λ ...
 :: list cons nil the [ ] list null predicate hd head (1st) tl tail (rest)

 © L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated), Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University, was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.) Created with "vi (Linux + Solaris)",  charset=iso-8859-1,  fetched Saturday, 09-Dec-2023 18:46:31 AEDT.