# Tail-Call and Tail-Recursion

Suppose that a function foo makes a call in its body to a function bar, where foo and bar may be the same function. If the return value of the call to bar is also the return value of foo, then this call to bar is a tail-call. If foo and bar are the same, then this is a (recursive) self tail-call. For instance, there are two recursive calls in the body of the function f91 defined as follows:

fun f91 (n: int): int = if n >= 101 then n - 10 else f91(f91(n+11))

where the outer recursive call is a self tail-call while the inner one is not.

If each recursive call in the body of a function is a tail-call, then this function is a tail-recursive function. For instance, the following function sum_iter is tail-recursive:

fun sum_iter (n: int, res: int): int = if n > 0 then sum_iter(n-1, n+res) else (res) // end of [sum_iter]

A tail-recursive function is often referred to as an iterative function.

In ATS, the single most important optimization is probably the one that turns a self tail-call into a local jump. This optimization effectively turns every tail-recursive function into the equivalent of a loop. Although ATS provides direct syntactic support for constructing for-loops and while-loops, the preferred approach to loop construction in ATS is in general through the use of tail-recursive functions. This is the case primarily due to the fact that the syntax for writing tail-recursive functions is compatible with the syntax for other programming features in ATS while the syntax for loops is much less so.