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"Recursive algorithms are particularly appropriate when the underlying problem or the data to be treated are defined in recursive terms." [27] The examples in this section illustrate what is known as "structural recursion". This term refers to the fact that the recursive procedures are acting on data that is defined recursively.
Recursion in computer programming is exemplified when a function is defined in terms of simpler, often smaller versions of itself. The solution to the problem is then devised by combining the solutions obtained from the simpler versions of the problem. One example application of recursion is in parsers for programming languages. The great ...
In terms of context-free grammar, a nonterminal is left-recursive if the leftmost symbol in one of its productions is itself (in the case of direct left recursion) or can be made itself by some sequence of substitutions (in the case of indirect left recursion).
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.
A recursive formal language is a recursive subset in the set of all possible words over the alphabet of the language. A recursive language is a formal language for which there exists a Turing machine that, when presented with any finite input string , halts and accepts if the string is in the language, and halts and rejects otherwise.
An equivalent definition states that a partial recursive function is one that can be computed by a Turing machine. A total recursive function is a partial recursive function that is defined for every input. Every primitive recursive function is total recursive, but not all total recursive functions are primitive recursive.
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 the datatypes are ...
A recursive acronym is an acronym that refers to itself, and appears most frequently in computer programming.The term was first used in print in 1979 in Douglas Hofstadter's book Gödel, Escher, Bach: An Eternal Golden Braid, in which Hofstadter invents the acronym GOD, meaning "GOD Over Djinn", to help explain infinite series, and describes it as a recursive acronym. [1]