Hilbert: A Latex-like math-oriented programming language

by atmosx • 12 years ago

90 22 12 years ago

fdej• 12 years ago

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

It's not very convincing when one of your examples is mathematically wrong (the integral should be -1).

roryokane3• 12 years ago

Link to confirm that the integral should be -1: http://www.wolframalpha.com/input/?i=integral+of+%28log%28x%...

Edit: GitHub Issue filed at https://github.com/gogotanaka/Hilbert/issues/60.

perlgeek• 12 years ago

Also writing infinity as oo is questionable, IMHO. Use Inf or Infinity or ∞.

chestervonwinch• 12 years ago

I believe this notation might be borrowed from SymPy, a symbolic math lib for python --- not that this justifies it; I don't quite care for it much either.

rnhmjoj• 12 years ago

It's wrong even in the tests: https://github.com/gogotanaka/Hilbert/blob/master/test/inter...

chris_wot• 12 years ago

Ummmm... what is TURE?

roryokane3• 12 years ago

I made a pull request that fixes that typo: https://github.com/gogotanaka/Hilbert/pull/58

tpaksoy• 12 years ago

You along with 7 others it seems. They didn't even bother checking whether a PR was already filed for it.

unwind• 12 years ago

It's a first name in Sweden, which sometimes makes me smile when doing that particular typo.

Something about suddenly SCREAMING someone's name right in the middle of the code feels like a (harmless, virtual) version of Tourette's. :) Of course no disrespect meant to people who actually suffer from that.

clintonc• 12 years ago

The information on the pretty website is spare. However, there are a few issues which give me pause.

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.

gus_massa• 12 years ago

lim[x->0] 1/x => oo

This is one of the grey areas of the mathematical notation. When you are teaching this, you should confirm that the other teachers are using the same notation.

I usually use oo as "I don't care about the sign infinity", so with the notation I use this is correct. For the positive infinity I use +oo and for the negative infinity I use -oo. So

lim[x->0+] => +oo

lim[x->0-] => -oo

Nevertheless, I don't know if the difference between oo, +oo and -oo is implemented in this language.

jackmaney4• 12 years ago

Can you point to a single reference anywhere dealing with calculus on the reals that is lazy enough to use infinity as "meh, I don't care if it's positive or negative infinity"? Even one? I've never seen it, and I've taught calculus to college students for nine years.

pfortuny• 12 years ago

On the limit issue: you are assuming the x is real. In the complex domain inf has no sign and the limit is pretty correct. But yes, this depends on assumptions.

jackmaney4• 12 years ago

This is a possible loophole, yes. However, if the repo author intended to work with functions of a complex variable, then why aren't the integrals in the README contour integrals?

moomin2• 12 years ago

If you really want to program mathematics, look at Coq, Agda or Idris.

tel• 12 years ago

Well, there's a significant difference there. Hilbert seems aimed at computational mathematics more in line with Mathematica rather than the logical foundational work occurring in Coq/Agda/Idris.

moomin2• 12 years ago

It'd be nice to achieve both... you wouldn't get some of the silly errors documented elsewhere in the thread.

Admittedly, that's way more ambitious than anything anyone's actually implemented, ever...

marktangotango• 12 years ago

Fortress[1] had stylesheets that allowed rendering mathematical formula. Never gained much traction needless to say:

> 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...

jackmaney4• 12 years ago

It would appear as though the repo owner is no longer accepting new issues (the "Submit new Issue" button is greyed out). So, in lieu of submitting a new issue, here is the issue that I would have opened (in Markdown):

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

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.

fmoralesc• 12 years ago

I think you need to call `postulate zfc_analysis`. With that, I get:

    Enjoy! -> lim[x->0] 1/x
    oo
    Enjoy! -> d/dx(cos(x))
    - sin( x )
    Enjoy! -> lim[x->0] x+2
    2.0

jackmaney4• 12 years ago

W...why would that not automatically be called?

roryokane3• 12 years ago

It would appear as though the repo owner is no longer accepting new issues (the "Submit new Issue" button is greyed out).

The button on https://github.com/gogotanaka/Hilbert/issues/new is enabled for me now, and was enabled yesterday too. I think you forgot to fill in the title of the issue as well as the body – the button stays grayed out if you don’t have a title.

I posted that issue for you at https://github.com/gogotanaka/Hilbert/issues/69.

Hilbert: A Latex-like math-oriented programming language

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