In mathematical logic, the primitive recursive functionals are a generalization of primitive recursive functions into higher type theory. They consist...

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all...

Recursion (in general) Sierpiński curve McCarthy 91 function μ-recursive functions Primitive recursive functions Tak (function) Logic programming Graham, Ronald;...

references can occur. A process that exhibits recursion is recursive. Video feedback displays recursive images, as does an infinity mirror. In mathematics and...

Primitive recursive arithmetic (PRA) is a quantifier-free formalization of the natural numbers. It was first proposed by Norwegian mathematician Skolem...

common in functional programming and in some problem domains, such as recursive descent parsers, where the datatypes are naturally mutually recursive. The...

List of pioneers in computer science Mathematical Platonism Primitive recursive functional Strange loop Tarski's undefinability theorem World Logic Day...

called 'properly tail recursive'. Besides space and execution efficiency, tail-call elimination is important in the functional programming idiom known...

a more natural style of expressing computation than simply using primitive recursive functions. Since the halting problem cannot be solved in general...

24 Every recursively defined function can be seen as a fixed point of some suitably defined higher order function (also known as functional) closing over...

been developed in a number of recursive and non-recursive varieties. More complex patterns can be built from the primitive ones of the previous section...

intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel...

factorial, which is defined recursively by 0! := 1 and n! := n × (n - 1)!. To recursively compute its result on a given input, a recursive function calls (a copy...

mathematics, the Riemann hypothesis. In computability theory, a general recursive function is a partial function from the integers to the integers whose...

contain any contradictions either. This other system, today called "primitive recursive arithmetic with the additional principle of quantifier-free transfinite...

function can be chosen to be injective. The set S is the range of a primitive recursive function or empty. Even if S is infinite, repetition of values may...

for a 1-ary primitive recursive function g the value of g(n+1) is computed only from g(n) and n. The factorial function n! is recursively defined by the...

tree model External memory model Functional models include: Abstract rewriting systems Combinatory logic General recursive functions Lambda calculus Concurrent...

these is the primitive recursive functions. Another example is the Ackermann function, which is recursively defined but not primitive recursive. For definitions...

LOOP is a simple register language that precisely captures the primitive recursive functions. The language is derived from the counter-machine model....

with Jacques Herbrand, formalized the definition of the class of general recursive functions: the smallest class of functions (with arbitrarily many arguments)...

unit f In addition to being constructed from primitives by functionals, a function may be defined recursively by an equation, the simplest kind being: f...

computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of every natural...

Leopold Kronecker formulated notions of computability, defining primitive recursive functions. These functions can be calculated by rote computation...

The initials "RCA" stand for "recursive comprehension axiom", where "recursive" means "computable", as in recursive function. This name is used because...

natural class of functions, such as the primitive recursive or polynomial-time computable functions. Functional interpretations have also been used to...

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 ...

Erlang (/ˈɜːrlæŋ/ UR-lang) is a general-purpose, concurrent, functional high-level programming language, and a garbage-collected runtime system. The term...

reverse mathematics (Simpson 2009). Elementary recursive arithmetic (ERA) is a subsystem of primitive recursive arithmetic (PRA) in which recursion is restricted...

programming, functional programming places little emphasis on explicit sequencing. Instead, computations are characterised by various kinds of recursive higher-order...