Comments for reperiendi http://reperiendi.wordpress.com Figure it out Fri, 25 Jul 2008 00:30:56 +0000 http://wordpress.org/?v=MU Comment on Combinators as addresses by reperiendi http://reperiendi.wordpress.com/2008/01/30/combinators-as-addresses/#comment-103 reperiendi Mon, 04 Feb 2008 19:32:30 +0000 http://reperiendi.wordpress.com/?p=166#comment-103 Another thing to notice is that S and K are linear up to their last argument; S doubles it last input, while K deletes it. (((S I) I) x) = (x x) ((K I) x) = I Another thing to notice is that S and K are linear up to their last argument; S doubles it last input, while K deletes it.

(((S I) I) x) = (x x)
((K I) x) = I

]]> Comment on Combinators as addresses by reperiendi http://reperiendi.wordpress.com/2008/01/30/combinators-as-addresses/#comment-102 reperiendi Mon, 04 Feb 2008 05:14:53 +0000 http://reperiendi.wordpress.com/?p=166#comment-102 OK, Huet's zipper is exactly Joyal's species (invented in 1981), what Baez & Dolan translate as "structure types." (See week202 of This Week's Finds or the Fall '03 QG notes here: http://math.ucr.edu/home/baez/qg-fall2003/ ) The relation you noticed with B and C is real. In Haskell, you can have parameterized types, called "type constructors," rather like functions whose inputs are types instead of values. The "context" type constructor is just type-lifted linear logic. OK, Huet’s zipper is exactly Joyal’s species (invented in 1981), what Baez & Dolan translate as “structure types.” (See week202 of This Week’s Finds or the Fall ‘03 QG notes here: http://math.ucr.edu/home/baez/qg-fall2003/ )

The relation you noticed with B and C is real. In Haskell, you can have parameterized types, called “type constructors,” rather like functions whose inputs are types instead of values. The “context” type constructor is just type-lifted linear logic.

]]> Comment on Combinators as addresses by reperiendi http://reperiendi.wordpress.com/2008/01/30/combinators-as-addresses/#comment-101 reperiendi Sat, 02 Feb 2008 01:17:28 +0000 http://reperiendi.wordpress.com/?p=166#comment-101 OK, that's a good idea--I'll have a look. I've read your post about infinitesimal types; have you seen Joyal's species (aka "structure types")? OK, that’s a good idea–I’ll have a look.

I’ve read your post about infinitesimal types; have you seen Joyal’s species (aka “structure types”)?

]]> Comment on Combinators as addresses by sigfpe http://reperiendi.wordpress.com/2008/01/30/combinators-as-addresses/#comment-100 sigfpe Fri, 01 Feb 2008 23:11:25 +0000 http://reperiendi.wordpress.com/?p=166#comment-100 You should compare this with <a href="http://www.haskell.org/haskellwiki/Zipper" rel="nofollow">Huet's zipper</a> and Conor McBride's notion of <a href="http://citeseer.ist.psu.edu/600571.html" rel="nofollow">differentiating types</a>. Given a tree, a zipper for the tree is a type that corresponds to a tree along with the address of a slot in the tree from which an element has been excised. McBride generalised this to any (regular) type, not just trees. The cool thing is that the type of a structure along with the address of an excised element is given by a type of derivative. You should compare this with Huet’s zipper and Conor McBride’s notion of differentiating types.

Given a tree, a zipper for the tree is a type that corresponds to a tree along with the address of a slot in the tree from which an element has been excised. McBride generalised this to any (regular) type, not just trees. The cool thing is that the type of a structure along with the address of an excised element is given by a type of derivative.

]]> Comment on Yoneda embedding as contrapositive and call-cc as double negation by reperiendi http://reperiendi.wordpress.com/2008/01/26/yoneda-embedding-as-contrapositive-and-call-cc-as-double-negation/#comment-99 reperiendi Thu, 31 Jan 2008 15:55:40 +0000 http://reperiendi.wordpress.com/?p=165#comment-99 Good catch, thanks! Fixed. Good catch, thanks! Fixed.

]]> Comment on Yoneda embedding as contrapositive and call-cc as double negation by haroldtherebel http://reperiendi.wordpress.com/2008/01/26/yoneda-embedding-as-contrapositive-and-call-cc-as-double-negation/#comment-98 haroldtherebel Thu, 31 Jan 2008 06:35:46 +0000 http://reperiendi.wordpress.com/?p=165#comment-98 I believe you have a typo on the third line. While "F -> T" is certainly true, it would make more sense to mention that "F -> F" is true. I believe you have a typo on the third line. While “F -> T” is certainly true, it would make more sense to mention that “F -> F” is true.

]]> Comment on Continuation passing as a reflection by reperiendi http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-97 reperiendi Thu, 31 Jan 2008 01:24:19 +0000 http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-97 Note how application is dual to composition. In fact, if we write (xy) for "apply x to y", then the typical notation "f(x,y)" is ((fx)y) and "y(f(x))" is (y(fx)), exactly the reverse with no modifications. How does this duality appear in string diagrams? Is there a well-known transformation like this in Feynman diagrams? Note how application is dual to composition. In fact, if we write (xy) for “apply x to y”, then the typical notation “f(x,y)” is ((fx)y) and “y(f(x))” is (y(fx)), exactly the reverse with no modifications.

How does this duality appear in string diagrams? Is there a well-known transformation like this in Feynman diagrams?

]]> Comment on Continuation passing as a reflection by reperiendi http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-96 reperiendi Thu, 31 Jan 2008 01:17:00 +0000 http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-96 This article got reposted on the <a href="http://golem.ph.utexas.edu/category/2008/01/the_yoneda_embedding_as_a_refl.html" rel="nofollow">n-Category Cafe</a> This article got reposted on the n-Category Cafe

]]> Comment on The continuation passing transform and the Yoneda embedding by Yoneda embedding as contrapositive and call-cc as double negation « reperiendi http://reperiendi.wordpress.com/2007/12/19/the-continuation-passing-transform-and-the-yoneda-embedding/#comment-95 Yoneda embedding as contrapositive and call-cc as double negation « reperiendi Sat, 26 Jan 2008 21:46:53 +0000 http://reperiendi.wordpress.com/2007/12/19/the-continuation-passing-transform-and-the-yoneda-embedding/#comment-95 [...] This embedding is better known among computer scientists as the continuation passing style transformation. [...] [...] This embedding is better known among computer scientists as the continuation passing style transformation. [...]

]]> Comment on Our Lady of the Scarab by coleopterra http://reperiendi.wordpress.com/2005/02/14/our-lady-of-the-scarab/#comment-94 coleopterra Thu, 24 Jan 2008 13:50:19 +0000 http://reperiendi.wordpress.com/2005/02/14/our-lady-of-the-scarab/#comment-94 Coleop-Terra.com Coleop-Terra.com

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