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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 <http://en.wikipedia.org/wiki/Category_theory>:
notice the first section title "an abstraction of other mathematical
*concepts*"). 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 set of concepts corresponding to the most used
algebraic structures (wikipedia link to algebraic structure<http://en.wikipedia.org/wiki/Algebraic_structure>)
in order to have an extremely rigorous and well-defined tools to constrain
templates related to mathematical function, classes or algorithms. Do you
know 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 dir=3D"ltr">Hello all.<br><br>Since we expect (or at least I expect) t=
o have concepts for C++17, I wonder whether there is a project to provide c=
oncepts related to category theory (<a href=3D"http://en.wikipedia.org/wiki=
/Category_theory">wikipedia link to category theory</a>: notice the first s=
ection 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 set of =
concepts corresponding to the most used algebraic structures (<a href=3D"ht=
tp://en.wikipedia.org/wiki/Algebraic_structure">wikipedia link to algebraic=
 structure</a>)&nbsp; in order to have an extremely rigorous and well-defin=
ed tools to constrain templates related to mathematical function, classes o=
r algorithms. Do you know if there is any plan to do that? Do you think tha=
t it could be relevant?<br><br>Thank you and happy end of the year,<br><br>=
Vincent R.<br></div>

<p></p>

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I think the naming congruence here is just a coincidence; the term
"concept" is very generic. C++ (non-lite) concepts are very similar to
Haskell's type classes, and Haskell does use type classes to model several
algebraic structures (functors, monads, etc.).
However, many "interesting" mathematical objects (e.g. ordered fields) are
necessarily infinite and cannot be represented using computers if you don't
want to introduce some heavy machinery. Conversely, objects in programming
(e.g. floating-point numbers) are rather boring mathematics-wise (e.g.
floating-point numbers are only magmas, and then only if FPEs are ignored).
While a formalization of some programming tasks in terms of algebraic
structures sounds interesting and could be desirable for some use cases, my
gut feeling says that its usefulness in real-world programs would be rather
limited.

On Sat Dec 28 2013 at 01:19:10, Vincent Reverdy <vince.rev@gmail.com> wrote:

> 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<http://en.wikipedia.org/wiki/Category_theory>:
> notice the first section title "an abstraction of other mathematical
> *concepts*"). 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 set of concepts corresponding to the most used
> algebraic structures (wikipedia link to algebraic structure<http://en.wikipedia.org/wiki/Algebraic_structure>)
> in order to have an extremely rigorous and well-defined tools to constrain
> templates related to mathematical function, classes or algorithms. Do you
> know 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.
>
> --
>
> ---
> You received this message because you are subscribed to the Google Groups
> "ISO C++ Standard - Future Proposals" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to std-proposals+unsubscribe@isocpp.org.
> To post to this group, send email to std-proposals@isocpp.org.
> Visit this group at
> http://groups.google.com/a/isocpp.org/group/std-proposals/.
>

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I think the naming congruence here is just a coincidence; the term &quot;co=
ncept&quot; is very generic. C++ (non-lite) concepts are very similar to Ha=
skell&#39;s type classes, and Haskell does use type classes to model severa=
l algebraic structures (functors, monads, etc.).<div>
However, many &quot;interesting&quot; mathematical objects (e.g. ordered fi=
elds) are necessarily infinite and cannot be represented using computers if=
 you don&#39;t want to introduce some heavy machinery. Conversely, objects =
in programming (e.g. floating-point numbers) are rather boring mathematics-=
wise (e.g. floating-point numbers are only magmas, and then only if FPEs ar=
e ignored).</div>
<div>While a formalization of some programming tasks in terms of algebraic =
structures sounds interesting and could be desirable for some use cases, my=
 gut feeling says that its usefulness in real-world programs would be rathe=
r limited.<br>
<br><div>On Sat Dec 28 2013 at 01:19:10, Vincent Reverdy &lt;<a href=3D"mai=
lto:vince.rev@gmail.com">vince.rev@gmail.com</a>&gt; wrote:</div><blockquot=
e class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc sol=
id;padding-left:1ex">
<div dir=3D"ltr">Hello all.<br><br>Since we expect (or at least I expect) t=
o have concepts for C++17, I wonder whether there is a project to provide c=
oncepts related to category theory (<a href=3D"http://en.wikipedia.org/wiki=
/Category_theory" target=3D"_blank">wikipedia link to category theory</a>: =
notice the first section title &quot;an abstraction of other mathematical <=
b>concepts</b>&quot;). I am not a theoretical computer scientist and neithe=
r a mathematician, but from an external point of view, I think it would be =
relevant to design a set of concepts corresponding to the most used algebra=
ic structures (<a href=3D"http://en.wikipedia.org/wiki/Algebraic_structure"=
 target=3D"_blank">wikipedia link to algebraic structure</a>)=A0 in order t=
o have an extremely rigorous and well-defined tools to constrain templates =
related to mathematical function, classes or algorithms. Do you know if the=
re is any plan to do that? Do you think that it could be relevant?<br>
<br>Thank you and happy end of the year,<br><br>Vincent R.<br></div>

<p></p>

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=A0<br>
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"_blank">std-proposals+unsubscribe@isocpp.org</a>.<br>
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..org" target=3D"_blank">std-proposals@isocpp.org</a>.<br>
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std-proposals/" target=3D"_blank">http://groups.google.com/a/isocpp.org/gro=
up/std-proposals/</a>.<br>
</blockquote></div>

<p></p>

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