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  2. Primitive recursive function - Wikipedia

    en.wikipedia.org/wiki/Primitive_recursive_function

    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 can be determined before entering the loop). Primitive recursive functions form a strict subset of those general ...

  3. General recursive function - Wikipedia

    en.wikipedia.org/wiki/General_recursive_function

    General recursive function. In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total ...

  4. Recursion (computer science) - Wikipedia

    en.wikipedia.org/wiki/Recursion_(computer_science)

    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. [1] [2] Recursion solves such recursive problems by using functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion ...

  5. Mutual recursion - Wikipedia

    en.wikipedia.org/wiki/Mutual_recursion

    Mutual recursion. In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes, are defined in terms of each other. [1] Mutual recursion is very common in functional programming and in some problem domains, such as recursive descent parsers, where ...

  6. Recursion - Wikipedia

    en.wikipedia.org/wiki/Recursion

    A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor. One's ancestor is either: One's parent (base case), or; One's parent's ancestor (recursive step). The Fibonacci sequence is another classic example of recursion: Fib(0) = 0 as ...

  7. Course-of-values recursion - Wikipedia

    en.wikipedia.org/wiki/Course-of-values_recursion

    In computability theory, course-of-values recursion is a technique for defining number-theoretic functions by recursion. In a definition of a function f by course-of-values recursion, the value of f ( n) is computed from the sequence . The fact that such definitions can be converted into definitions using a simpler form of recursion is often ...

  8. Elementary function arithmetic - Wikipedia

    en.wikipedia.org/wiki/Elementary_function_arithmetic

    Elementary recursive arithmetic (ERA) is a subsystem of primitive recursive arithmetic (PRA) in which recursion is restricted to bounded sums and products. This also has the same Π 2 0 {\displaystyle \Pi _{2}^{0}} sentences as EFA, in the sense that whenever EFA proves ∀x∃y P ( x , y ), with P quantifier-free, ERA proves the open formula P ...

  9. Grzegorczyk hierarchy - Wikipedia

    en.wikipedia.org/wiki/Grzegorczyk_hierarchy

    The Grzegorczyk hierarchy ( / ɡrɛˈɡɔːrtʃək /, Polish pronunciation: [ɡʐɛˈɡɔrt͡ʂɨk] ), named after the Polish logician Andrzej Grzegorczyk, is a hierarchy of functions used in computability theory. [1] Every function in the Grzegorczyk hierarchy is a primitive recursive function, and every primitive recursive function appears in ...

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