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Chains of three or more functions are possible; for example, function 1 calls function 2, function 2 calls function 3, and function 3 calls function 1 again. Indirect recursion is also called mutual recursion, which is a more symmetric term, though this is simply a difference of emphasis, not a different notion.
The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n, until reaching the base case, analogously to the mathematical definition of factorial. Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of ...
Mutual recursion is also known as indirect recursion, by contrast with direct recursion, where a single function calls itself directly. This is simply a difference of emphasis, not a different notion: "indirect recursion" emphasises an individual function, while "mutual recursion" emphasises the set of functions, and does not single out an ...
Anonymous recursion can also be used for named functions, rather that calling them by name, say to specify that one is recursing on the current function, or to allow one to rename the function without needing to change the name where it calls itself. However, as a matter of programming style this is generally not done.
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. [3]
When a function calls itself recursively, a return address needs to be stored for each activation of the function so that it can later be used to return from the function activation. Stack structures provide this capability automatically.
The Ackermann function grows faster than any primitive recursive function and therefore is not itself primitive recursive. The sketch of the proof is this: a primitive recursive function defined using up to k recursions must grow slower than f k + 1 ( n ) {\displaystyle f_{k+1}(n)} , the (k+1)-th function in the fast-growing hierarchy, but the ...
Most modern implementations of a function call use a call stack, a special case of the stack data structure, to implement function calls and returns. Each procedure call creates a new entry, called a stack frame , at the top of the stack; when the procedure returns, its stack frame is deleted from the stack, and its space may be used for other ...