Talk:Primitive recursive function: Difference between revisions

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:Moreover, these sections are not sourced. This could be a reason for removing them as [[WP:OR]].

:So, I have reverted your tag removals. Please do not remove them again without addressing the issues of these sections. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 10:08, 28 February 2024 (UTC)

:: According to [[Second-order_arithmetic]] there is more than one PA. Which might be contextually relevant, since the principia used higher order logic, as noted by Gödel 2.1 Definitions https://hirzels.com/martin/papers/canon00-goedel.pdf

:: [[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 12:33, 28 February 2024 (UTC)

:: Nobody uses the terminology "multivariate" in recursion theory. The term n-ary means a function with n-arguments. The Cantor [[Pairing_function]] can be used to encode two or more arguments in one argument, and its also possible to reverse the process. The function is itself primitive recursive, so are its projections.

:: To reduce complexity of the article I would split off Gödel, and I would also

:: [[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 1323:2602, 28 February 2024 (UTC)

split LOOP/WHILE.

:: [[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 13:26, 28 February 2024 (UTC)

About the used references in the article. Instead of Rose as reference for Elimination of Parameters, its seems you could also use Moschovakis 1994, ch. 5.

Or as SEP has put it, they show the other way around from h, to h2 and then to h1, but then have the following remark:

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[[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 11:44, 28 February 2024 (UTC)

:You do not adress the main issue of these sections. Wikipedia is not for summarizing some specific articles, relying on these articles to know author's definitions of the technical terms. The aim of an encyclopedy is to present the most important results in a language that is compatible with the most common terminology, and is accessible to (in the case of this article) a undergraduate student in mathematics. It must also be clear why a result is important enough to belong to the article (per [[WP:UNDUE]]). Neither the sections under discussion nor your above comments satisfy these requisites. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 14:12, 28 February 2024 (UTC)

== Split off LOOP / WHILE [LOOP Isomorphism] ==

::To reduce complexity of the article I would split off Gödel, and I would also split off LOOP/WHILE. Devote separate articles to the two, would make the primitive recursive article more readable and less cluttered with applications of the notion primitive recursive in Gödels theorem and computational devices such as LOOP, that show primitive recursive behaviour.

The notion primitive recursive pays tribute to Dedekinds 1888 Recursion Theorem.

::[[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 22:41, 28 February 2024 (UTC)

Its housed more in mathematics and less in computer science. Whereby Dedekind

was interested whether primitive recursive functions are uniquely defined. One

could experiment to make an extra Wikipedia article that relates

primitive recursive with LOOPS, and not throw LOOPs into the primitive

recursive article.

Its still a step more to show that LOOPS are primitive recursive, if

you want to do it properly you would use something like Hoare triples,

etc.. For example WHILE is defined here:

I have deleted the first disputed section,

http://www.concrete-semantics.org/

and move the second disputed section to here:

[[Gödel's β function]]

They say LOOP is syntactic sugar. Well there is more to it. I think

your primitive recursive article refers already to results about LOOP.

There I would also like to add a reference to this:

But why not make it a separate article. Most likely Dedekind hardly had

same idea of LOOP, there was no BASIC programming language with a FOR

NEXT statements at his time. Unfortuntaley I cannot help with a title for

this separate article. By what name goes the LOOP Isomorphism?

PRIMITIVE RECURSIVE FUNCTIONS by<br>

== Split off Gödel stuff ==

Zéev Rosenfeld - March 1959<br>

Given Dedekinds 1888 Recursion Theorem, I guess Gödel is not

Department of Mathematics McGill University Montreal.

the father of primitive recursive. The history has landmarks such

as Daiv Hilbert believe primitive recursive is the only notion

But I don't know how to edit and add a reference.

of computable functions, until Ackerman proved contrary in 1926

with the function named after him. An Ackerman function cannot be

written with a LOOP program, only WHILE programs suffice.

[[User:Janburse|Jan Burse]] ([[User talk:Janburse|talk]]) 22:51, 28 February 2024 (UTC)

So why not devote a separte article to Gödels use of the notion

primitive recursive.