# Evaluation of Recursive Function Calls

Evaluating a call to a recursive function is not much different from evaluating one to a non-recursive function. Let fib be the following defined function for computing the Fibonacci numbers:

```fun fib
(n: int): int =
if n >= 2 then fib(n-1) + fib(n-2) else n
// end of [fib]
```

Suppose that we are to evaluate fib(2) under some environment ENV0. Given that 2 is already a value, we extend ENV0 to ENV1 with a binding between n and 2 and start to evaluate the body of fib under ENV1; clearly, this evaluation leads to the evaluation of fib(n-1) + fib(n-2); it is easy to see that evaluating fib(n-1) and fib(n-2) under ENV1 leads to 1 and 0, respectively, and the evaluation of fib(n-1) + fib(n-2) eventually returns 1 (as the result of 1+0); thus the evaluation of fib(2) under ENV0 yields the integer value 1.

Let us now evaluate fib(3) under ENV0; we extend ENV0 to ENV2 with a binding between n and 3, and start to evaluate the body of fib under ENV2; we then reach the evaluation of fib(n-1) + fib(n-2) under ENV2; evaluating fib(n-1) under ENV2 leads to the evaluation of fib(2) under ENV2, which eventually returns 1; evaluating fib(n-2) under ENV2 leads to the evaluation of fib(1) under ENV2, which eventually returns 1; therefore, evaluating fib(3) under ENV0 returns 2 (as the result of 1+1).