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{{summary in|Lambda calculus}}
{{WikiProject
{{WikiProject Computer science|importance=Mid}}
{{WikiProject Mathematics|priority=low}}
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: and then you can define your f as
f' x = (fix plus') x 1
:[[User:jbolden1517|jbolden1517]]
Hmmmm. So, if I read you right, you're basically saying what I was figuring at first: that fix (by which I assume you mean Y) can only be defined on functions like plus' which are specially written in such a way as to receive a (fix whatever) function as a first argument? And not on functions like plus which are not?
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[[Fixed point combinator]] → {{no redirect|1=Fixed-point combinator}} –
Per WP:HYPHEN and a good proportion of sources.
*'''Support''' in accord with Wikipedia's style guidelines – the appropriate point of reference for, um, ... points of style on Wikipedia. <
*'''<s>Meh</s>''' '''Weak support''' In my experience "fixed point combinator" is more common than "fixed-point combinator". Google Scholar seems to confirm this [http://scholar.google.com/scholar?hl=en&q=%22fixed-point+combinator%22&btnG=Search&as_sdt=0%2C5&as_ylo=&as_vis=0], although the margins are not very wide. I would have to consult a few standard references first to form a strong opinion, as those would carry more weight. English is not my native language, but isn't there are rule for (not) using a hyphen for words of the form "(''adjective'' ''noun'') ''noun''" where (''adjective'' ''noun'') is used as an adjective? —''[[User:Ruud Koot|Ruud]]'' 12:07, 20 October 2011 (UTC)
**Your opinion is no less valid as a second-language speaker, Ruud. Where minority usage out there accords with WP's in-house style, we usually go with it, favouring internal consistency over inconsistency with ''some'' external sources. Here, there's a good reason to hyphenate, especially for non-experts: is it a point combinator that is fixed? And it's a compound adjective, isn't it, qualifying "combinator" the noun? "Point" might be a noun on the second "rank", but that's within the compound adjective.
*** I checked the indexes of a few of the books on my shelf and found one instance of "fixed-point combinator" and two of "[[fixed point theorem]]". The hyphenated could possibly be less ambiguous for some people. You might want to check with [[Wikipedia:WikiProject Mathematics]] before (or after ;) moving all the theorems, though. Common spellings of obscure names don't always agree with common sense. —''[[User:Ruud Koot|Ruud]]'' 19:54, 20 October 2011 (UTC)
****Most of the articles are already correctly punctuated. I updated [[Fixed-point theorem]] to reflect that. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 20:59, 20 October 2011 (UTC)
* '''Support''' – when the hyphen is grammatically correct and useful, it is WP style to use it, other styles notwithstanding. [[User:Dicklyon|Dicklyon]] ([[User talk:Dicklyon|talk]]) 20:34, 20 October 2011 (UTC)
* '''Support''' It's not a "point combinator" that happens to be fixed; it's a combinator that has something to do with fixed points. A hyphen leaves no ambiguity. It is true that present-day usage often omits it, and I actually suspect that's because they've stopped teaching it. But it's still in standard use in many media. I'd normally use a hyphen for something like this. [[User:Michael Hardy|Michael Hardy]] ([[User talk:Michael Hardy|talk]]) 14:08, 21 October 2011 (UTC)
:''The above discussion is preserved as an archive of a [[WP:RM|requested move]]. <span style="color:red">'''Please do not modify it.'''</span> Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.''</div><!-- Template:RM bottom -->
== Can we set out the field at the beginning? ==
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Cheers.—[[User:InternetArchiveBot|'''<span style="color:darkgrey;font-family:monospace">InternetArchiveBot</span>''']] <span style="color:green;font-family:Rockwell">([[User talk:InternetArchiveBot|Report bug]])</span> 23:08, 21 January 2018 (UTC)
== Confusing/contradictory claims about lambda calculus semantics ==
This is mostly about the "values and domains" section, but there are also various other comments scattered throughout the article that I think need clearing up.
I'm not an expert, but it seems to me that there are at least two ways to think about the semantics of untyped lambda calculus. One is the "___domain" approach, explained (though not very clearly) in the linked [[Deductive lambda calculus]] article. In this interpretation every lambda expression has a value, even the non-halting ones. But there is also the more obvious semantics where each lambda expression is a partial function. It has a value if it beta reduces to a normal form, but otherwise it doesn't have a value. I believe that both of these are consistent and it's really a matter of choice which one to use.
The issue is that the article sometimes talks in terms of one and sometimes in terms of the other. For example, in the lede it states
: a fixed-point combinator (or fixpoint combinator) is a higher-order function that returns some fixed point of its argument function, if one exists.
This sounds like it's taking the partial function view: the argument function might not have a fixed point, and in that case the fixed-point combinator doesn't return a value.
(Though now I come to think of it, this statement is not actually correct. Consider the Y combinator applied to the identity function. It's easy to see that no value is returned in this case, even though any lambda term at all is a fixed point of the identity function. I guess the correct statement would be that it returns some fixed point of its argument function if it halts.)
On the other hand the article also makes statements like
: In the classical untyped lambda calculus, every function has a fixed point
which seems to me to be true in the ___domain interpretation but not in the partial function interpretation. (Although I could be wrong about that.) It also makes statements like
: Every expression has one value. This is true in general mathematics and it must be true in lambda calculus.
Which seems like it's trying to justify the ___domain semantics as the only true semantics of the lambda calculus. But really it's just a false statement, since there's nothing to stop you defining a system where an expression might have many or no values, and the partial function semantics is such a system (I think).
So it seems to me that the article has sort of mixed up two different views about the semantics of the lambda calculus and also tried to present one of them as the only semantics, without flagging up that this is a choice. I would try to fix this myself but I don't feel I have the expertise to be sure I'm getting it right - I'm just mentioning this because I think it needs attention from someone who knows what they're doing.
[[User:Nathanielvirgo|Nathaniel Virgo]] ([[User talk:Nathanielvirgo|talk]]) 04:28, 17 October 2023 (UTC)
== Article is unintelligible ==
The article, as currently written, is unintelligible to anybody who isn't already an expert in the field.
The article needs to be rewritten from the beginning, in such a way as to answer the question "What is a fixed-point combinator?" '''in terms that can be understood by somebody who does not already know the answer.'''
[[User:Geoffrey.landis|Geoffrey.landis]] ([[User talk:Geoffrey.landis|talk]]) 20:05, 21 May 2025 (UTC)
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