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Even without mechanisms to refer to the current function or calling function, anonymous recursion is possible in a language that allows functions as arguments. This is done by adding another parameter to the basic recursive function and using this parameter as the function for the recursive call.
The Y combinator allows recursion to be defined as a set of rewrite rules, [21] without requiring native recursion support in the language. [22] In programming languages that support anonymous functions, fixed-point combinators allow the definition and use of anonymous recursive functions, i.e. without having to bind such functions to identifiers.
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 ...
As an example, the function argument in the recursive expression for the factorial function below will always decrease by 1; by the well-ordering property of natural numbers, the argument will eventually reach 1 and the recursion will terminate. function factorial (argument as natural number) if argument = 0 or argument = 1 return 1 otherwise ...
Methods on objects are functions attached to the object's class; the syntax instance. method (argument) is, for normal methods and functions, syntactic sugar for Class. method (instance, argument). Python methods have an explicit self parameter to access instance data , in contrast to the implicit self (or this ) in some other object-oriented ...
The direct-style factorial takes, as might be expected, a single argument; the CPS factorial& takes two: the argument and a continuation. Any function calling a CPS-ed function must either provide a new continuation or pass its own; any calls from a CPS-ed function to a non-CPS function will use implicit continuations.
The factorial function is a common feature in scientific calculators. [73] It is also included in scientific programming libraries such as the Python mathematical functions module [74] and the Boost C++ library. [75]
The dispatch semantics of this, namely that method calls on this are dynamically dispatched, is known as open recursion, and means that these methods can be overridden by derived classes or objects. By contrast, direct named recursion or anonymous recursion of a function uses closed recursion, with static dispatch.