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Recursive drawing of a sierpiński triangle through turtle graphics in computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem See application to quines below [1][2] recursion solves such recursive problems by using functions that call themselves from within their own code.
In mathematics and computer science, mutual recursion is a form of recursion where two or more mathematical or computational objects, such as functions or datatypes, are defined in terms of each other Kleene's second recursion theorem the second recursion theorem is a generalization of rogers's theorem with a second input in the function [1] mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, where the datatypes are naturally mutually recursive.
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and turing degrees.
In computer programming, a recursive data type is a data type whose definition contains values of the same type It is also known as a recursively defined, inductively defined or inductive data type Data of recursive types are usually viewed as directed graphs [citation needed] an important application of recursion in computer science is in defining dynamic data structures such as lists and.
In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all for loops (that is, an upper bound of the number of iterations of every loop is fixed before entering the loop) Primitive recursive functions form a strict subset of those general recursive functions that are also total functions Left recursion in the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by the fact that it decomposes into a string from that same language (on the left) and a suffix (on the right). The formal criteria for what constitutes a valid recursive definition are more complex for the general case
An outline of the general proof and the criteria can be found in james munkres.
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