### Some articles on *recursive functions, functions, primitive, function, recursive, primitive recursive functions*:

... The μ-

**recursive functions**(or partial μ-

**recursive functions**) are partial

**functions**that take finite tuples of natural numbers and return a single natural number ... They are the smallest class of partial

**functions**that includes the initial

**functions**and is closed under composition,

**primitive**recursion, and the μ operator ... The smallest class of

**functions**including the initial

**functions**and closed under composition and

**primitive**recursion (i.e ...

... Every effectively calculable

**function**(effectively decidable predicate) is general

**recursive**" (First stated by Kleene in 1943 (reprinted page 274 in Davis, ed ... in Kleene (1952) p.300) In a nutshell to calculate any

**function**the only operations a person needs (technically, formally) are the 6

**primitive**operators of "general" recursion (nowadays called the operators of ... calculation (decision) procedure or algorithm, for the case of a

**function**(predicate) of natural numbers" (p ...

**Primitive Recursive Functions**

... The definition of is the same as that of the

**primitive recursive functions**, RP, except that recursion is limited ( for some j in ) and the

**functions**are explicitly included in ... the Grzegorczyk hierarchy can be seen as a way to limit the power of

**primitive**recursion to different levels ... It is clear from this fact that all

**functions**in any level of the Grzegorczyk hierarchy are

**primitive recursive functions**(i.e ...

... The

**primitive recursive functions**are defined using

**primitive**recursion and composition as central operations and are a strict subset of the total µ-

**recursive functions**... In computability theory,

**primitive recursive functions**are a class of

**functions**that form an important building block on the way to a full formalization of ... These

**functions**are also important in proof theory ...

... Because

**primitive recursive functions**use natural numbers rather than integers, and the natural numbers are not closed under subtraction, a limited subtraction

**function**is studied ... This limited subtraction

**function**sub(a,b) returns if this is nonnegative and returns 0 otherwise ... The predecessor

**function**acts as the opposite of the successor

**function**and is recursively defined by the rules pred(0)=0, pred(n+1)=n ...

### Famous quotes containing the words functions and/or primitive:

“In today’s world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the *functions* of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.”

—Urie Bronfenbrenner (b. 1917)

“The *primitive* wood is always and everywhere damp and mossy, so that I traveled constantly with the impression that I was in a swamp; and only when it was remarked that this or that tract, judging from the quality of the timber on it, would make a profitable clearing, was I reminded, that if the sun were let in it would make a dry field, like the few I had seen, at once.”

—Henry David Thoreau (1817–1862)