## Fibonacci Numbers

 FP  Lambda   Introduction   Examples    Fibonacci     Fib'memo-tree

Another circular program - the list nums is defined in terms of itself:

 ```let rec first = lambda n. lambda L. if n = 0 then nil else (hd L)::(first (n-1) tl L), nums = 1::(1::(F nums)), F = lambda L. (hd L + hd tl L)::(F tl L) in first 5 nums {\fB Fibonacci List \fP} ```

F adds the first two numbers on its input L to form the first element of its output, which in turn becomes part of the input. Note that first and F are quite ordinary functions and could be applied to many other lists.

 let rec first = lambda n. lambda L. if n = 0 then nil else (hd L)::(first (n-1) tl L), nums = 1::(1::(F nums)), F = lambda L. (hd L + hd tl L)::(F tl L) in first 5 nums {\fB Fibonacci List \fP}
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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, 22-Oct-2016 08:55:44 EST.