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Recursion that contains only a single self-reference is known as single recursion, while recursion that contains multiple self-references is known as multiple recursion. Standard examples of single recursion include list traversal, such as in a linear search, or computing the factorial function, while standard examples of multiple recursion ...
The curiously recurring template pattern (CRTP) is an idiom, originally in C++, in which a class X derives from a class template instantiation using X itself as a template argument. [1] More generally it is known as F-bound polymorphism, and it is a form of F-bounded quantification.
The importance of primitive recursive functions lies in the fact that most computable functions that are studied in number theory (and more generally in mathematics) are primitive recursive. For example, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive. [1]
Fib(1) = 1 as base case 2, For all integers n > 1, Fib(n) = Fib(n − 1) + Fib(n − 2). Many mathematical axioms are based upon recursive rules. For example, the formal definition of the natural numbers by the Peano axioms can be described as: "Zero is a natural number, and each natural number has a successor, which is also a natural number ...
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 ...
Data types can also be defined by mutual recursion. The most important basic example of this is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [t[1], ..., t[k]] t: v f A forest f consists of a list of trees, while a tree t consists of a pair of a value v and a forest f (its children ...
GCC's C and C++ parsers, which are hand-coded recursive descent parsers, are both sped up by an operator-precedence parser that can quickly examine arithmetic expressions. Operator-precedence parsers are also embedded within compiler-compiler -generated parsers to noticeably speed up the recursive descent approach to expression parsing.
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...