BackMath: a compile time symbolic math lib.

[Robert Fraser]

BCS wrote:
> I have written a library that allows for all of the following as native 
> syntax:
> 
> A + B - D = C;
> A - B - D = C;
> A - D - B = C;
> (B - A) - D = C;
> A - D - B - D = C;
> A - B - (D + D) = C;
> C = A + B - D;
> C = B * A;
> C = B * A + B * D;
> A / B  + D / B = C;
> 
> In all of these cases the assignment is to B.
> 
> The library is works by using term re-writing to reverse evaluate the 
> expression. The fun part is that the term re-writing is done with the 
> type system and template expressions. This results in there being little 
> inherent runtime cost.
> I hope to expand it to work with as wide a variety of equation forma as 
> I can. I wold love to be able to get it to even solve system of 
> equations like
> 
> a*B + c*D = e;
> f*B + g*D = h;
> 
> where B and D are both unknown.
> 
> Now, full disclosure:
> -it's incomplete, there a lots of cases it won't handle (but I plan on 
> improving that)
> -it is not thread safe, this is because the templates need alias to 
> variables to work correctly and the only variables that can be aliased 
> are globals.*, #
> -It's unproven, I can formally prove all the "single sided" rules, but 
> haven't figured out how to prove the "double sided" rules, yet like the 
> last 2 examples, %
> -No, I didn't bang out 400 lines of static if's, the "business logic" is 
> generated using a lisp program that is harder to read than what it 
> produces ^
> 
> Now for the challenge. Is anyone willing to try and generate a C++ 
> equivalent? I think it would be really cool to have a side by side 
> comparison of the two libs. I think the difference in readability say a 
> lot.
> 
> hosted at:
>   http://www.dsource.org/projects/scrapple/browser/trunk/backmath
> 
> * Walter can we please get this fixed??
> # I have a way in mind to fix this but it won't look near as good.
> % I'm using ACL2 to do the proofs. 
> http://www.cs.utexas.edu/users/moore/acl2/
> ^ I'll clean it up and post it as well soon. (finals week is coming soon 
> so don't hold your breath or anything)
> 
> 

Where was this lib when I was doing Algebra I in middle school :-)?

Very cool stuff; I'm always amazed at what D can do with 
metaprogramming. FWIW, I think local variables can be template alias 
parameters, I'm using just that fact to get the names of the functions a 
particular template is instantiated in. I'm not sure if this is what you 
meant, though.