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In programming language theory, lazy evaluation, or call-by-need, [1] is an evaluation strategy which delays the evaluation of an expression until its value is needed (non-strict evaluation) and which avoids repeated evaluations (by the use of sharing). [2] [3] The benefits of lazy evaluation include:
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 ...
A recursive function named foo, which is passed a single parameter, x, and if the parameter is 0 will call a different function named bar and otherwise will call baz, passing x, and also call itself recursively, passing x-1 as the parameter, could be implemented like this in Python:
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.
This is done by adding another parameter to the basic recursive function and using this parameter as the function for the recursive call. This creates a higher-order function, and passing this higher function itself allows anonymous recursion within the actual recursive function. This can be done purely anonymously by applying a fixed-point ...
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]
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 ...
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 ...