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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.
Recursion that contains only a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. Standard examples of single recursion include list traversal, such as in a linear search, or computing the factorial function, while standard examples of multiple recursion ...
As with direct recursion, tail call optimization is necessary if the recursion depth is large or unbounded, such as using mutual recursion for multitasking. Note that tail call optimization in general (when the function called is not the same as the original function, as in tail-recursive calls) may be more difficult to implement than the ...
Every call in CPS is a tail call, and the continuation is explicitly passed. Using CPS without tail call optimization (TCO) will cause not only the constructed continuation to potentially grow during recursion, but also the call stack. This is usually undesirable, but has been used in interesting ways—see the Chicken Scheme compiler. As CPS ...
The Scheme language standard requires implementations to support proper tail recursion, meaning they must allow an unbounded number of active tail calls. [ 60 ] [ 61 ] Proper tail recursion is not simply an optimization; it is a language feature that assures users that they can use recursion to express a loop and doing so would be safe-for ...
The good news is that it’s easy to make flavorful, rich desserts without dairy or eggs. Give one of these vegan-friendly desserts a spin: Vegan Flourless Chocolate Cake , Apple Crisp with ...
“This is care that people’s doctors recommend for them, and some of this care can be frightening,” Sara Collins, senior scholar at The Commonwealth Fund, a health policy foundation, told CNN ...
As one of the examples used to demonstrate such reasoning, Manna's book includes a tail-recursive algorithm equivalent to the nested-recursive 91 function. Many of the papers that report an "automated verification" (or termination proof ) of the 91 function only handle the tail-recursive version.