In computer science, a tail call is a subroutine call performed as the final action of a procedure. If the target of a tail is the same subroutine, the subroutine is said to be tail recursive, which is a special case of direct recursion. Tail recursion (or tail-end recursion) is particularly useful, and is often easy to optimize in implementations. Tail calls can be implemented without adding a new stack frame to the call stack. Most of the frame of the current procedure is no longer needed, and can be replaced by the frame of the tail call, modified as appropriate (similar to overlay for processes, but for function calls). The program can then jump to the called subroutine. Producing such code instead of a standard call sequence is called tail-call elimination or tail-call optimization. Tail-call elimination allows procedure calls in tail position to be implemented as efficiently as goto statements, thus allowing efficient structured programming. In the words of Guy L. Steele, "in general, procedure calls may be usefully thought of as GOTO statements which also pass parameters, and can be uniformly coded as [machine code] JUMP instructions". Not all programming languages require tail-call elimination. However, in functional programming languages, tail-call elimination is often guaranteed by the language standard, allowing tail recursion to use a similar amount of memory as an equivalent loop. The special case of tail-recursive calls, when a function calls itself, may be more amenable to call elimination than general tail calls. When the language semantics do not explicitly support general tail calls, a compiler can often still optimize sibling calls, or tail calls to functions which take and return the same types as the caller.
Description When a function is called, the computer must "remember" the place it was called from, the return address, so that it can return to that location with the result once the call is complete. Typically, this information is saved on the call stack, a list of return locations in the order that the call locations were reached. In addition, compilers allocate memory for local variables of the called function and push register content (if any and/or relevant) onto the stack. Typically, it is done by allocating a stack frame including saved registers, space allocated for non-register local variables, return address and call parameters (unless they are passed in registers). For tail calls, there is no need to remember the caller or preserve content of registers – instead, tail-call elimination avoids allocation of new stack frames and makes only the minimum necessary changes to the existing stack frame before passing it on, and the tail-called function will return directly to the original caller. This, however, leads to complete loss of the caller's stack frame, which is sometimes considered as a hindrance in debugging. The tail call doesn't have to appear lexically after all other statements in the source code; it is only important that the calling function return immediately after the tail call, returning the tail call's result if any, since the calling function is bypassed when the optimization is performed. For non-recursive function calls, this is usually an optimization that saves only a little time and space, since there are not that many different functions available to call. When dealing with recursive or mutually recursive functions where recursion happens through tail calls, however, the stack space and the number of returns saved can grow to be very significant, since a function can call itself, directly or indirectly, creating a new call stack frame each time. Tail-call elimination often reduces asymptotic stack space requirements from linear, or O(n), to constant, or O(1). Tail-call elimination is thus required by the standard definitions of some programming languages, such as Scheme, and languages in the ML family among others. The Scheme language definition formalizes the intuitive notion of tail position exactly, by specifying which syntactic forms allow having results in tail context. Implementations allowing an unlimited number of tail calls to be active at the same moment, thanks to tail-call elimination, can also be called "properly tail recursive". Besides space and execution efficiency, tail-call elimination is important in the functional programming idiom known as continuation-passing style (CPS), which would otherwise quickly run out of stack space.
Syntactic form A tail call can be located just before the syntactical end of a function.
Here, both a(data) and b(data) are calls, but b is the last thing the procedure executes before returning and is thus in tail position. However, not all tail calls are necessarily located at the syntactical end of a subroutine:
Here, both calls to b and c are in tail position. This is because each of them lies in the end of if-branch respectively, even though the first one is not syntactically at the end of bar's body. Consider this example:
The call to a(data) is in tail position in foo2, but it is not in tail position either in foo1 or in foo3, because control must return to the caller to allow it to inspect or modify the return value before returning it.
Example programs The following program is an example in Scheme:
This is not written in a tail-recursive style, because the multiplication function ("*") is in the tail position. This can be compared to:
This program assumes applicative-order evaluation. The inner procedure fact-iter calls itself last in the control flow. This allows an interpreter or compiler to reorganize the execution which would ordinarily look like this:
call factorial (4) call fact-iter (1 4) call fact-iter (4 3) call fact-iter (12 2) call fact-iter (24 1) return 24 return 24 return 24 return 24 return 24
into the more efficient variant, in terms of both space and time:
call factorial (4) call fact-iter (1 4) replace arguments with (4 3) replace arguments with (12 2) replace arguments with (24 1) return 24 return 24
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