4 ms·

That's a sort of function, yes, but it's numerical analysis. In a Lisp you can pass in the equivalent of "4x^3 + (x^2)/2 -5X + 6" and get back "12x^2 + x - 5" -

That's a sort of function, yes, but it's numerical analysis. In a Lisp you can pass in the equivalent of "4x^3 + (x^2)/2 -5X + 6" and get back "12x^2 + x - 5" - a function that is the derivative of the function you put in, rather than a function that approximates the value of the derivative at a value. You'd be manipulating the function rather than its return value.

QuadrupleA 8y ago
Lisp is definitely not doing symbolic algebra and finding a pure analytical answer like that under the hood - symbolic math, differentiation rules etc. are a whole other beast (see SymPy for example). Maybe that's the misunderstanding in the original article that made it seem so mindblowing? Evaluating (f(5.0001) - f(5.0)) / 0.0001 just gives an approximation of the derivative at a certain point in the function (aka the "finite difference method").
- taeric 8y ago
  Symbolic derivatives are one of the very next sections in the famous lisp lectures that this was watching.
  - QuadrupleA 8y ago
    Interesting - for symbolic differentiation I imagine it's about code-manipulation rules for e.g. calculus' product rule, chain rule etc.?
    - taeric 8y ago
      Essentially, yes. And if you want it to be pretty, it gets complicated quickly. https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-16.html#%_sec_2.3.2 https://mitpress.mit.edu/sites/default/files/sicp/full-text/... is the chapter. Turns out it wasn't the "very next" one. But it is in my head.
- yen223 8y ago
  Here's symbolic differentiation done in ~20 lines of Haskell: https://www.quora.com/What-are-20-lines-of-code-that-capture-the-essence-of-Haskell-Try-to-follow-standard-Haskell-style-Comments-and-spaces-between-code-do-not-count-as-lines-They-can-also-consist-of-individual-snippets-of-code-but-have-to-add-up-to-20-lines https://www.quora.com/What-are-20-lines-of-code-that-capture...

QuadrupleA 8y ago

Lisp is definitely not doing symbolic algebra and finding a pure analytical answer like that under the hood - symbolic math, differentiation rules etc. are a whole other beast (see SymPy for example). Maybe that's the misunderstanding in the original article that made it seem so mindblowing? Evaluating (f(5.0001) - f(5.0)) / 0.0001 just gives an approximation of the derivative at a certain point in the function (aka the "finite difference method").

taeric 8y ago
Symbolic derivatives are one of the very next sections in the famous lisp lectures that this was watching.
- QuadrupleA 8y ago
  Interesting - for symbolic differentiation I imagine it's about code-manipulation rules for e.g. calculus' product rule, chain rule etc.?
  - taeric 8y ago
    Essentially, yes. And if you want it to be pretty, it gets complicated quickly. https://mitpress.mit.edu/sites/default/files/sicp/full-text/book/book-Z-H-16.html#%_sec_2.3.2 https://mitpress.mit.edu/sites/default/files/sicp/full-text/... is the chapter. Turns out it wasn't the "very next" one. But it is in my head.
yen223 8y ago
Here's symbolic differentiation done in ~20 lines of Haskell: https://www.quora.com/What-are-20-lines-of-code-that-capture-the-essence-of-Haskell-Try-to-follow-standard-Haskell-style-Comments-and-spaces-between-code-do-not-count-as-lines-They-can-also-consist-of-individual-snippets-of-code-but-have-to-add-up-to-20-lines https://www.quora.com/What-are-20-lines-of-code-that-capture...