Comments on: Continuation passing as a reflection http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/ Mike Stay Sun, 11 Oct 2009 21:37:26 +0000 http://wordpress.com/ hourly 1 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?

]]> 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

]]> By: reperiendi http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-70 reperiendi Thu, 27 Dec 2007 21:47:42 +0000 http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-70 Just recording this for my own information: Boudol's <a href="http://www-sop.inria.fr/meije/personnel/Gerard.Boudol/blue.html" rel="nofollow">blue calculus</a> paper describes how to transform from the standard call-by-value lambda calculus to the call-by-name calculus, and then how to encode the result in the pi calculus. Here's the homomorphism between the call-by-name transformation (CBN) and the continuation passing transformation (CPT): `cf ⇒ :k `uf `u`gf ⇒ ` `cf `ug `uv ⇒ v (v is a variable) where ` is <a href="http://www.madore.org/~david/programs/unlambda/#fun__app" rel="nofollow">Unlambda</a>'s prefix application operator, c is whatever transformation we're talking about, and u is a helper transformation. In CBN, :kx translates to "q ↦ def k = x in `qk," where q is a new variable. In CPT, :kx is the term "k ↦ `kx." In both cases, :kx is the continuization of x. Just recording this for my own information:

Boudol’s blue calculus paper describes how to transform from the standard call-by-value lambda calculus to the call-by-name calculus, and then how to encode the result in the pi calculus.

Here’s the homomorphism between the call-by-name transformation (CBN) and the continuation passing transformation (CPT):

`cf ⇒ :k `uf
`u`gf ⇒ ` `cf `ug
`uv ⇒ v (v is a variable)

where ` is Unlambda’s prefix application operator, c is whatever transformation we’re talking about, and u is a helper transformation. In CBN, :kx translates to “q ↦ def k = x in `qk,” where q is a new variable. In CPT, :kx is the term “k ↦ `kx.”

In both cases, :kx is the continuization of x.

]]> By: reperiendi http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-68 reperiendi Tue, 25 Dec 2007 20:28:46 +0000 http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-68 ccshan: I've read Wadler's paper, though I haven't digested all of its implications yet. I'd like to understand how sending on a channel in the pi calculus is relalted to the call-by-name lambda calculus. There's a paper on the "blue calculus" that combines the two. I'll have a look at your thesis to see if that clarifies anything for me. ccshan: I’ve read Wadler’s paper, though I haven’t digested all of its implications yet. I’d like to understand how sending on a channel in the pi calculus is relalted to the call-by-name lambda calculus. There’s a paper on the “blue calculus” that combines the two.

I’ll have a look at your thesis to see if that clarifies anything for me.

]]> By: ccshan http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-65 ccshan Tue, 25 Dec 2007 14:55:32 +0000 http://reperiendi.wordpress.com/2007/12/21/continuation-passing-as-a-reflection/#comment-65 The reflection you discovered is Filinski's duality between call-by-value and call-by-name. A nice presentation (by far not the first one) is Wadler's "Call-by-Value is Dual to Call-by-Name" (http://homepages.inf.ed.ac.uk/wadler/topics/call-by-need.html). I also discuss and present this duality (with delimited continuations) in my dissertation (http://www.cs.rutgers.edu/~ccshan/dissertation/book.pdf). The reflection you discovered is Filinski’s duality between call-by-value and call-by-name. A nice presentation (by far not the first one) is Wadler’s “Call-by-Value is Dual to Call-by-Name” (http://homepages.inf.ed.ac.uk/wadler/topics/call-by-need.html). I also discuss and present this duality (with delimited continuations) in my dissertation (http://www.cs.rutgers.edu/~ccshan/dissertation/book.pdf).

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