Below you will find example sentences with "recursive functions". The examples show how this phrase is used in natural context and which words often surround it.

Recursive Functions in a sentence

Corpus data

  • Displayed example sentences: 20
  • Discovered as a combination around: functions
  • Corpus frequency in the collocation scan: 17
  • Phrase length: 2 words
  • Average sentence length: 22.1 words

Words in this phrase

recursive functions

Meanings of words in this phrase

  • recursive can mean: drawing upon itself, referring back. Less frequent word
  • functions can mean: plural of function Frequent word

Sentence profile

  • Phrase position: 7 start, 8 middle, 5 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

all primitive recursive functions are total 1× all primitive recursive functions halt 1× all total recursive functions which is 1× ary primitive recursive functions then is 1× basic primitive recursive functions are given 1× caching and recursive functions in a 1× complex primitive recursive functions can be 1× computability and recursive functions to the 1×

Sentence openings and endings

Common sentence openings:

a sketch of 1× all primitive recursive 1× certainly the initial 1× during this year 1× effectively this in 1× for example certain 1×

Common sentence endings:

also primitive recursive 1× also very straightforward 1× are primitive recursive 1× axioms ordered example 1× by recursive functions 1× concept of truth 1×

Context words

These words often appear near this phrase in the example sentences:

primitive 20× function 7× total 6× given 4× ackermann 3× computable 3× set 3× basic 3× operations 3× example 3× follows 2× recursively 2×

Related phrases

continuous functions hash functions

Phrases around this combination

Other phrases discovered around functions:

hash functions 12×

Just before it in the phrase index:

recreational marijuana recovery routine recovery process recovered cases records act recording studio

Just after it in the phrase index:

red blood red bull red card red carpet red crescent red cross

Other phrases with the same pattern

Same ending:

continuous functions hash functions

Corpus analysis

  • The phrase "recursive functions" has 2 words and usually appears in the middle in these examples. The average sentence has 22.1 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as all primitive recursive functions are total, all primitive recursive functions halt, primitive, function and total stand out.
  • In the phrase index, this combination connects with continuous functions, hash functions and hash functions, linking the page to nearby combinations.

Example types with recursive functions

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

However, all primitive recursive functions halt. (6 words)

Primitive recursive functions are a defined subclass of the recursive functions. (11 words)

Fractals can be computed (up to a given resolution) by recursive functions. (12 words)

Longer example sentences

This follows from the facts that the functions of this form are the most quickly growing primitive recursive functions, and that a function is primitive recursive if and only if its time complexity is bounded by a primitive recursive function. (40 words)

For the latter, see citation An important property of the primitive recursive functions is that they are a recursively enumerable subset of the set of all total recursive functions (which is not itself recursively enumerable). (35 words)

During this year, Gödel also developed the ideas of computability and recursive functions to the point where he was able to present a lecture on general recursive functions and the concept of truth. (33 words)

Example sentences (20)

Other examples of total recursive but not primitive recursive functions are known: *The function that takes m to Ackermann (m,m) is a unary total recursive function that is not primitive recursive.

This follows from the facts that the functions of this form are the most quickly growing primitive recursive functions, and that a function is primitive recursive if and only if its time complexity is bounded by a primitive recursive function.

All primitive recursive functions are total and computable, but the Ackermann function illustrates that not all total computable functions are primitive recursive.

During this year, Gödel also developed the ideas of computability and recursive functions to the point where he was able to present a lecture on general recursive functions and the concept of truth.

For the latter, see citation An important property of the primitive recursive functions is that they are a recursively enumerable subset of the set of all total recursive functions (which is not itself recursively enumerable).

Primitive recursive functions are a defined subclass of the recursive functions.

The basic primitive recursive functions are given by these axioms : ordered More complex primitive recursive functions can be obtained by applying the operations given by these axioms: ordered Example.

There is a characterization of the primitive recursive functions as a subset of the total recursive functions using the Ackermann function.

Advertentie

For example, if g and h are 2-ary primitive recursive functions then : is also primitive recursive.

Given primitive recursive functions e, f, g, and h, a function that returns the value of g when e≤f and the value of h otherwise is primitive recursive.

In functional languages, the recursive definition is often implemented directly to illustrate recursive functions.

The primitive recursive functions are the basic functions and those obtained from the basic functions by applying these operations a finite number of times.

Certainly the initial functions are intuitively computable (in their very simplicity), and the two operations by which one can create new primitive recursive functions are also very straightforward.

Similarly a set of three or more functions that call each other can be called a set of mutually recursive functions.

The combination of DNS caching and recursive functions in a name server is not mandatory; the functions can be implemented independently in servers for special purposes.

A sketch of the proof is as follows: :The primitive recursive functions of one argument (i.

Effectively, this, in combination with the order, allows the definition of recursive functions.

For example, certain recursive functions called on inductive types are guaranteed to terminate.

Fractals can be computed (up to a given resolution) by recursive functions.

However, all primitive recursive functions halt.

Advertentie