Comments on: Learning Number Theory and Haskell: The Division Algorithm http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/ software, programming languages, and other ideas Sat, 02 Jan 2010 04:04:11 +0000 http://wordpress.com/ hourly 1 By: Eelis http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/#comment-4 Eelis Sun, 03 Jun 2007 00:04:47 +0000 http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/#comment-4 I find the "there is no (okay, only a little) competition between testing and proof" sentiment rather unfounded. While it may apply when one's program and proof are completely separate as they are in your case with the non-Haskell proof in the book separate from your Haskell program, it simply does not apply when the two are unified in a system such as Coq ( http://coq.inria.fr/ ) which lets you write functional programs along with formal machine-checked proofs of properties of those programs. For this reason, systems such as Coq are far more suitable for building what you called "a software library that, in a sense, embodies the theory of a mathematical field" in your previous post, as they raise the status of programs from that of mere implementations that try to capture some property, to that of proper mathematical objects (defined on top of rigid logical foundations) that can be formally proven to possess the desired property. I encourage you to browse the Coq standard library; you may just find that it's the kind of thing you were looking for :). I find the “there is no (okay, only a little) competition between testing and proof” sentiment rather unfounded. While it may apply when one’s program and proof are completely separate as they are in your case with the non-Haskell proof in the book separate from your Haskell program, it simply does not apply when the two are unified in a system such as Coq ( http://coq.inria.fr/ ) which lets you write functional programs along with formal machine-checked proofs of properties of those programs.

For this reason, systems such as Coq are far more suitable for building what you called “a software library that, in a sense, embodies the theory of a mathematical field” in your previous post, as they raise the status of programs from that of mere implementations that try to capture some property, to that of proper mathematical objects (defined on top of rigid logical foundations) that can be formally proven to possess the desired property. I encourage you to browse the Coq standard library; you may just find that it’s the kind of thing you were looking for :).

]]> By: Top Posts « WordPress.com http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/#comment-3 Top Posts « WordPress.com Sun, 03 Jun 2007 00:02:37 +0000 http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/#comment-3 [...] Learning Number Theory and Haskell: The Division Algorithm This series of blog posts is a chronicle of my working my way through Gareth and Mary Jones’ Elementary Number […] [...] [...] Learning Number Theory and Haskell: The Division Algorithm This series of blog posts is a chronicle of my working my way through Gareth and Mary Jones’ Elementary Number […] [...]

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