Hilbert: A Latex-like math-oriented programming language

The integral example already given is one. One must wonder what is going on "under the hood" to give such a result. My hypothesis is that Riemann sums are what's going on, and that the integral uses 0 as a sample point. An interesting point is that this is one of the unit tests. https://github.com/gogotanaka/Hilbert/blob/master/test/inter...

Another is the example of lim[x->0] 1/x => oo. This is not true; the limit does not exist. If one said lim[x->0+] => oo there would be a better case. Also a unit test. https://github.com/gogotanaka/Hilbert/blob/master/test/inter...

(1 2 3; 4 5 6) * (1 2 3) => (14 32) is not how matrix multiplication is normally done. ( (1 2 3) would need to be (1; 2; 3).)

All in all, the grammar seems to be quite irregular; it seems to be the result of a sequence of wanting to solve one very particular kind of problem (take a limit, differentiate a function, take a sum) and cludging it into the parser.

https://github.com/gogotanaka/Hilbert/blob/master/lib/hilber... has seven exclamation marks in a row. That's amusing... I don't know anything about Ruby, but I feel that it must be a joke.

    S(log(x)dx)[0..1]
    => - oo

Looking through the README, the first thing that made me balk was the fact that the limit of `1/x` as `x->0` is not infinity. The limit doesn't exist! However:

* The limit as x goes to zero from the right of `1/x` is infinity, and

* The limit as x goes to zero from the left of `1/x` is negative infinity.

So, to quickly determine whether or not this was just a documentation issue, I installed Hilbert ([and eventually succeeded](https://github.com/gogotanaka/Hilbert/pull/68 )) and tried to discover the syntax for one-sided limits:

``` Enjoy! -> lim[x->0+] 1/x

Enjoy! -> ```

Hmmm...no output. Okay. Does any output work?

``` Enjoy! -> 3+2

5

Enjoy! -> ```

Okay, good, we at least have that much... Hmmm...

``` Enjoy! -> lim[x->0^+] 1/x

Enjoy! -> ```

Nope, that's not it, either. Poking at the source code, [it doesn't seem as though one-sided limits are implemented](https://github.com/gogotanaka/Hilbert/blob/1750822d0577e69ab... ).

Well, okay, how about a simpler limit?

``` Enjoy! -> lim[x->0] x+2

Enjoy! -> ```

Uhhh...okay, how about some differentiation?

``` Enjoy! -> d/dx(cos(x))

I'm so sorry, something wrong. Please feel free to report this.

Enjoy! -> ```

This error message is of no use, and I have no idea what's going on, but this language appears to be broken.

>> Fortress is being designed from the outset to have multiple syntactic stylesheets. Source code can be rendered as ASCII text, in Unicode, or as a prettied image. This would allow for support of mathematical symbols and other symbols in the rendered output for easier reading.

[1] http://en.wikipedia.org/wiki/Fortress_%28programming_languag...