http://conal.net/blog/posts/beautiful-differentiation/ Inspirations & experiments, mainly about denotational programming in Haskell Tue, 09 Mar 2010 23:08:02 +0000 http://wordpress.org/?v=2.9.1 hourly 1 http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-36447 Aleksandar Bakic Thu, 21 Jan 2010 14:38:59 +0000 http://conal.net/blog/?p=43#comment-36447 <p>I believe <a href="ftp://ftp.kestrel.edu/pub/papers/pavlovic/lapl-LICS98.pdf" rel="nofollow">Calculus in Coinductive Form</a> is relevant.</p> I believe Calculus in Coinductive Form is relevant.

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-35182 Conal Elliott » Blog Archive » Garbage collecting the semantics of FRP Mon, 04 Jan 2010 21:56:34 +0000 http://conal.net/blog/?p=43#comment-35182 <p>[...] interactive behaviors are some sort of function with all of its derivatives. See Beautiful differentiation for an specification and derived implementation of numeric operations, and more generally of [...]</p> [...] interactive behaviors are some sort of function with all of its derivatives. See Beautiful differentiation for an specification and derived implementation of numeric operations, and more generally of [...]

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-34989 Conal Elliott » Blog Archive » Is program proving viable and useful? Sun, 03 Jan 2010 03:21:52 +0000 http://conal.net/blog/?p=43#comment-34989 <p>[...] For more examples of formally simple specifications, see the papers Denotational design with type class morphisms and Beautiful differentiation. [...]</p> [...] For more examples of formally simple specifications, see the papers Denotational design with type class morphisms and Beautiful differentiation. [...]

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-34986 Conal Elliott » Blog Archive » Why program with continuous time? Sun, 03 Jan 2010 02:39:53 +0000 http://conal.net/blog/?p=43#comment-34986 <p>[...] has been integral to FRP since the first incarnation as ActiveVRML. I’ve written several things recently about denotational [...]</p> [...] has been integral to FRP since the first incarnation as ActiveVRML. I’ve written several things recently about denotational [...]

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-14794 Conal Elliott » Blog Archive » What is automatic differentiation, and why does it work? Wed, 28 Jan 2009 20:09:49 +0000 http://conal.net/blog/?p=43#comment-14794 <p>[...] can also be made prettier, as in Beautiful differentiation. Add an operator that captures the chain rule, which is behind the differentiation laws listed [...]</p> [...] can also be made prettier, as in Beautiful differentiation. Add an operator that captures the chain rule, which is behind the differentiation laws listed [...]

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-6827 Samuel Bronson Sat, 28 Jun 2008 04:34:21 +0000 http://conal.net/blog/?p=43#comment-6827 <p>What's with the funky <code>"’"</code> characters??? Why not normal <code>"'"</code>?</p> What’s with the funky "’" characters??? Why not normal "'"?

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-5788 Conal Elliott » Blog Archive » Higher-dimensional, higher-order derivatives, functionally Wed, 21 May 2008 05:29:36 +0000 http://conal.net/blog/?p=43#comment-5788 <p>[...] post Beautiful differentiation showed some lovely code that makes it easy to compute not just the values of user-written [...]</p> [...] post Beautiful differentiation showed some lovely code that makes it easy to compute not just the values of user-written [...]

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-5617 Nikolay Thu, 08 May 2008 21:55:32 +0000 http://conal.net/blog/?p=43#comment-5617 <p>multiplication may pull x' and y' while result is just requested for (D (x*y) _ _), I think</p> multiplication may pull x’ and y’ while result is just requested for (D (x*y) _ _), I think

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-5607 conal Thu, 08 May 2008 14:57:00 +0000 http://conal.net/blog/?p=43#comment-5607 <p>Jaak & Perehene: I've added source files: <a href='http://conal.net/blog/wp-content/uploads/2008/05/NumInstances.hs' rel="nofollow">NumInstances.hs</a> and <a href='http://conal.net/blog/wp-content/uploads/2008/05/Dif.hs' rel="nofollow">Dif.hs</a>. Enjoy!</p> Jaak & Perehene: I’ve added source files: NumInstances.hs and Dif.hs. Enjoy!

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-5606 Perehene Thu, 08 May 2008 14:02:13 +0000 http://conal.net/blog/?p=43#comment-5606 <p>Very interesting post. I am a newbie in haskell and I wanted to give it a try, but I get a bunch of errors in ghci. Could you put the source code and the required options to use it in ghc? Thanks a lot!</p> Very interesting post. I am a newbie in haskell and I wanted to give it a try, but I get a bunch of errors in ghci. Could you put the source code and the required options to use it in ghc? Thanks a lot!

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-5599 Jaak Thu, 08 May 2008 10:38:16 +0000 http://conal.net/blog/?p=43#comment-5599 <p>It's pretty and all, but either you have something missing or something wrong. Because the code doesn't simply work (lots of complaints along the lines of "Could not deduce..." and "Couldn't match expected type..."), something funky seems to be going on with dlift. I'd appreciate full working code.</p> <ul> <li>Jaak</li> </ul> It’s pretty and all, but either you have something missing or something wrong. Because the code doesn’t simply work (lots of complaints along the lines of “Could not deduce…” and “Couldn’t match expected type…”), something funky seems to be going on with dlift. I’d appreciate full working code.

• Jaak

]]> http://conal.net/blog/posts/beautiful-differentiation/comment-page-1/#comment-5591 Punya Thu, 08 May 2008 06:21:57 +0000 http://conal.net/blog/?p=43#comment-5591 <p>Abelson and Sussman's <a href="http://mitpress.mit.edu/SICM/" rel="nofollow"><em>Structure and Interpretation of Classical Mechanics</em></a> has a Scheme implementation of this idea, which they use to implement an environment for symbolically <em>and</em> numerically manipulating physical systems.</p> Abelson and Sussman’s Structure and Interpretation of Classical Mechanics has a Scheme implementation of this idea, which they use to implement an environment for symbolically and numerically manipulating physical systems.

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