Fibonacci numbers in APL

Example for versions Dyalog APL 13.1

This example uses Binet’s formula implemented via an anonymous D-function. is expression separator, so the function consists of two expressions evaluated in left-to-right order. The first one calculates golden ration and binds it to name phi. The second one calculates the value of the function (Fibonacci number) based on its right argument (the index of the number). rounds the number up.

Since the function is unary and is defined using scalar functions only, it can be applied to an array — in this case to an array of indices between 1 and 16, inclusive. This will result in an array of Fibonacci numbers:

1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987

{phi(1+5*0.5)÷2  ((phi*) - (1-phi)*)÷5*0.5} 1+16