Primitive recursive functional information

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...

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

that exhibits recursion is recursive. In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined...

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

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...

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

In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining...

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

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...

computability theory, a set of natural numbers is called computable, recursive, or decidable if there is an algorithm which takes a number as input,...

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

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

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

f; this means a recursive function definition cannot be used as the N with let. The letrec construction would allow writing recursive function definitions...

context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms Σ {\displaystyle \Sigma } of the...

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

proposition to hold for all x.) A structurally recursive function uses the same idea to define a recursive function: "base cases" handle each minimal structure...

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...

theory specifies the rules of syntax (rules of grammar) usually as a recursive definition that starts with "0" and specifies how to build acceptable...

computing power as Turing machines; for example the μ-recursive functions obtained from primitive recursion and the μ operator. The terminology for computable...

In mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent,...

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