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As a more general class of examples, an algorithm on a tree can be decomposed into its behavior on a value and its behavior on children, and can be split up into two mutually recursive functions, one specifying the behavior on a tree, calling the forest function for the forest of children, and one specifying the behavior on a forest, calling ...
A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 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 ...
A classic example of recursion is computing the factorial, which is defined recursively by 0! := 1 and n! := n × (n - 1)!.. To recursively compute its result on a given input, a recursive function calls (a copy of) itself with a different ("smaller" in some way) input and uses the result of this call to construct its result.
The recursive program above is tail-recursive; it is equivalent to an iterative algorithm, and the computation shown above shows the steps of evaluation that would be performed by a language that eliminates tail calls. Below is a version of the same algorithm using explicit iteration, suitable for a language that does not eliminate tail calls.
A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive. The Ackermann function A(m,n) is a well-known example of a total recursive function (in fact, provable total), that is not primitive ...
In computer programming languages, a recursive data type (also known as a recursively-defined, inductively-defined or inductive data type) is a data type for values that may contain other values of the same type. Data of recursive types are usually viewed as directed graphs [citation needed].
Anonymous recursion is primarily of use in allowing recursion for anonymous functions, particularly when they form closures or are used as callbacks, to avoid having to bind the name of the function. Anonymous recursion primarily consists of calling "the current function", which results in direct recursion.
In recursive function theory, double recursion is an extension of primitive recursion which allows the definition of non-primitive recursive functions like the Ackermann function. Raphael M. Robinson called functions of two natural number variables G(n, x) double recursive with respect to given functions, if G(0, x) is a given function of x.