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<http://infothread.org/Maths/Mathematical%20Relationships.jpg>
As a complement, here you have an illustration of the relations between
some algebraic structures.

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<div dir=3D"ltr"><p style=3D"text-align: center; clear: both;" class=3D"sep=
arator"><a style=3D"margin-left: 1em; margin-right: 1em;" href=3D"http://in=
fothread.org/Maths/Mathematical%20Relationships.jpg" imageanchor=3D"1"><img=
 src=3D"http://infothread.org/Maths/Mathematical%20Relationships.jpg" style=
=3D"" border=3D"0" height=3D"320" width=3D"302"></a></p>As a complement, he=
re you have an illustration of the relations between some algebraic structu=
res.<br><br></div>

<p></p>

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Concepts is a compile time type restriction; it seems like most of the chec=
ks there only make sense at run time, where inputs are known.

Sent from a touchscreen. Please excuse the brevity and tpyos.

----- Reply message -----
From: "Vincent Reverdy" <vince.rev@gmail.com>
To: <std-proposals@isocpp.org>
Subject: [std-proposals] Theoretical computer science and conceptification =
of category theory?
Date: Fri, Dec 27, 2013 4:19 PM

Hello all.

Since we expect (or at least I expect) to have concepts for C++17, I wonder=
 whether there is a project to provide concepts related to category theory =
(wikipedia link to category theory: notice the first section title "an abst=
raction of other mathematical concepts"). I am not a theoretical computer s=
cientist and neither a mathematician, but from an external point of view, I=
 think it would be relevant to design a set of concepts corresponding to th=
e most used algebraic structures (wikipedia link to algebraic structure)  i=
n order to have an extremely rigorous and well-defined tools to constrain t=
emplates related to mathematical function, classes or algorithms. Do you kn=
ow if there is any plan to do that? Do you think that it could be relevant?

Thank you and happy end of the year,

Vincent R.




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<div style=3D"font-size: 12pt; font-family: Calibri,sans-serif;"><div>Conce=
pts is a compile time type restriction; it seems like most of the checks th=
ere only make sense at run time, where inputs are known.</div><div><br></di=
v><div>Sent from a touchscreen. Please excuse the brevity and tpyos.</div><=
br><div id=3D"htc_header">----- Reply message -----<br>From: &quot;Vincent =
Reverdy&quot; &lt;vince.rev@gmail.com&gt;<br>To: &lt;std-proposals@isocpp.o=
rg&gt;<br>Subject: [std-proposals] Theoretical computer science and concept=
ification of category theory?<br>Date: Fri, Dec 27, 2013 4:19 PM</div></div=
><br><div dir=3D"ltr">Hello all.<br><br>Since we expect (or at least I expe=
ct) to have concepts for C++17, I wonder whether there is a project to prov=
ide concepts related to category theory (<a href=3D"http://en.wikipedia.org=
/wiki/Category_theory">wikipedia link to category theory</a>: notice the fi=
rst section title "an abstraction of other mathematical <b>concepts</b>"). =
I am not a theoretical computer scientist and neither a mathematician, but =
from an external point of view, I think it would be relevant to design a se=
t of concepts corresponding to the most used algebraic structures (<a href=
=3D"http://en.wikipedia.org/wiki/Algebraic_structure">wikipedia link to alg=
ebraic structure</a>)&nbsp; in order to have an extremely rigorous and well=
-defined tools to constrain templates related to mathematical function, cla=
sses or algorithms. Do you know if there is any plan to do that? Do you thi=
nk that it could be relevant?<br><br>Thank you and happy end of the year,<b=
r><br>Vincent R.<br></div>

<p></p>

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<p></p>

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Of course, the term concept is very generic, but it reminds me some remarks
of Bjarne/Andrew during this talk
<http://channel9.msdn.com/Events/GoingNative/GoingNative-2012/A-Concept-Design-for-C->(I
think they mentioned the "monoids" as examples at some point during the
talk). If you look to Boost.Geometry they seem to use a concept named "ring<http://www.boost.org/doc/libs/1_55_0/libs/geometry/doc/html/geometry/reference/concepts/concept_ring.html>".
Additionnaly, I think that at some point the standard library would need a
concept of vector space particularly in a context of 2D or 3D graphics. I
originally asked this question because, if we expect to need some of these
algebraic structures as concepts for the standard library, it may be wise
to design their relations as a whole, instead of separate things when we
will have a specific need. But I do not have a sufficient knowledge of
category theory to say whether it is possible and relevant to design
something both simple and useful and to avoid an heavy machinery.

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<div dir=3D"ltr">Of course, the term concept is very generic, but it remind=
s me some remarks of Bjarne/Andrew during this <a href=3D"http://channel9.m=
sdn.com/Events/GoingNative/GoingNative-2012/A-Concept-Design-for-C-">talk <=
/a>(I think they mentioned the "monoids" as examples at some point during t=
he talk). If you look to Boost.Geometry they seem to use a concept named "<=
a href=3D"http://www.boost.org/doc/libs/1_55_0/libs/geometry/doc/html/geome=
try/reference/concepts/concept_ring.html">ring</a>". Additionnaly, I think =
that at some point the standard library would need a concept of vector spac=
e particularly in a context of 2D or 3D graphics. I originally asked this q=
uestion because, if we expect to need some of these algebraic structures as=
 concepts for the standard library, it may be wise to design their relation=
s as a whole, instead of separate things when we will have a specific need.=
 But I do not have a sufficient knowledge of category theory to say whether=
 it is possible and relevant to design something both simple and useful and=
 to avoid an heavy machinery.<br></div>

<p></p>

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.