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In computer science, corecursion is a type of operation that is dual to recursion.Whereas recursion works analytically, starting on data further from a base case and breaking it down into smaller data and repeating until one reaches a base case, corecursion works synthetically, starting from a base case and building it up, iteratively producing data further removed from a base case.
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 eval() vs. exec() built-in functions (in Python 2, exec is a statement); the former is for expressions, the latter is for statements; Statements cannot be a part of an expression—so list and other comprehensions or lambda expressions, all being expressions, cannot contain statements.
A function can be represented as a set of ordered pairs of argument and corresponding result values. For example, the set {(0,1), (4,3)} denotes a function with result 1 for argument 0, result 3 for the argument 4, and undefined otherwise. Consider for example the factorial function, which might be defined recursively as:
In this case particular lambda terms (which define functions) are considered as values. "Running" (beta reducing) the fixed-point combinator on the encoding gives a lambda term for the result which may then be interpreted as fixed-point value. Alternately, a function may be considered as a lambda term defined purely in lambda calculus.
A built-in function, or builtin function, or intrinsic function, is a function for which the compiler generates code at compile time or provides in a way other than for other functions. [23] A built-in function does not need to be defined like other functions since it is built in to the programming language. [24]
The decorator pattern is a design pattern used in statically-typed object-oriented programming languages to allow functionality to be added to objects at run time; Python decorators add functionality to functions and methods at definition time, and thus are a higher-level construct than decorator-pattern classes.
For an imperative language the overhead is to define the function, and for a functional language the overhead is to define the accumulator variable x. For example, a factorial function may be implemented iteratively in C by assigning to a loop index variable and accumulator variable, rather than by passing arguments and returning values by ...