[Haskell-cafe] Re: The Worker/Wrapper Transformation
Achim Schneider wrote: ...is a paper about automatic specialisation of functions by unboxing arguments, one could say. I'm only on page 6, but already survived the first formalisms, which is bound to mean that the rest of the paper is likewise accessible, as hinted on at ltu. http://www.cs.nott.ac.uk/~gmh/wrapper.pdf The transformation itself is mindbogglingly easy, which makes this a good start: You only have to understand the formalisms, not so much what the formalisms are representing. To quote spj: It usually turns out to be more interesting and challenging than it seemed at first. I'm tempted to write that this is a paper for everyone trying to figure out what the heck Jonathan is talking about. Hey Achim many thanks for bringing this wonderful paper to my attention. Dijkstra's soul breethes out of every equation... Cheers Ben ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: The Worker/Wrapper Transformation
Isaac Dupree wrote: Achim Schneider wrote: http://www.cs.nott.ac.uk/~gmh/wrapper.pdf on page 6, stronger vs weaker seemed backwards to me... isn't (wrap ◦ unwrap = idA) a stronger condition than (wrap ◦ unwrap ◦ body = body), because it tells you more, and is true in fewer cases? (which is also why you want to assume (wrap ◦ unwrap = idA) when you can, because it's the most useful one for subsequent program transformation) Ah, thanks you say that, I have been asking myself if that was just me, having things backward. In my book, stronger = weaker, too. Cheers Ben ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: The Worker/Wrapper Transformation
Achim Schneider [EMAIL PROTECTED] wrote: [...] I'm trying to grok that [] = id ++ = . in the context of Hughes lists. I guess it would stop to slip away if I knew what : corresponds to. -- (c) this sig last receiving data processing entity. Inspect headers for past copyright information. All rights reserved. Unauthorised copying, hiring, renting, public performance and/or broadcasting of this signature prohibited. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: The Worker/Wrapper Transformation
On Jan 3, 2008 6:08 AM, Achim Schneider [EMAIL PROTECTED] wrote: Achim Schneider [EMAIL PROTECTED] wrote: [...] I'm trying to grok that [] = id ++ = . in the context of Hughes lists. I guess it would stop to slip away if I knew what : corresponds to. Well, (:) has type a - [a] - [a], so a function corresponding to (:) for Hughes lists should have type foo :: a - H a - H a that is, foo :: a - ([a] - [a]) - [a] - [a] so it can be written foo x h = (x:) . h which lambdabot informs me can also be written as (.) . (:). But in the end I'm not sure how helpful that is for understanding Hughes lists! I think the key sentence from the paper is this: by representing a list xs as the function (xs ++) that appends this list to another list that has still to be supplied. If you understand that sentence, then you can understand why [] is id and (++) is (.). -Brent ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: The Worker/Wrapper Transformation
Brent Yorgey [EMAIL PROTECTED] wrote: Well, (:) has type a - [a] - [a], so a function corresponding to (:) for Hughes lists should have type foo :: a - H a - H a [...] I think the key sentence from the paper is this: by representing a list xs as the function (xs ++) that appends this list to another list that has still to be supplied. If you understand that sentence, then you can understand why [] is id and (++) is (.). Yes, I did. They key was not thinking that : has type (:) :: a - a - [a] , or, put differently, beat the lisp out of me, thanks. The problem is merely that Haskell and lisp are too similar in a much too different way. -- (c) this sig last receiving data processing entity. Inspect headers for past copyright information. All rights reserved. Unauthorised copying, hiring, renting, public performance and/or broadcasting of this signature prohibited. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: The Worker/Wrapper Transformation
Achim Schneider [EMAIL PROTECTED] wrote: Brent Yorgey [EMAIL PROTECTED] wrote: Well, (:) has type a - [a] - [a], so a function corresponding to (:) for Hughes lists should have type foo :: a - H a - H a [...] I think the key sentence from the paper is this: by representing a list xs as the function (xs ++) that appends this list to another list that has still to be supplied. If you understand that sentence, then you can understand why [] is id and (++) is (.). Yes, I did. They key was not thinking that : has type (:) :: a - a - [a] , or, put differently, beat the lisp out of me, thanks. What the hell am I talking about? (define (cons x y) (lambda (m) (m x y))) (define (car z) (z (lambda (p q) p))) (define (cdr z) (z (lambda (p q) q))) : is, in a sense, \. -- (c) this sig last receiving data processing entity. Inspect headers for past copyright information. All rights reserved. Unauthorised copying, hiring, renting, public performance and/or broadcasting of this signature prohibited. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: The Worker/Wrapper Transformation
Achim Schneider wrote: Achim Schneider [EMAIL PROTECTED] wrote: [...] I'm trying to grok that [] = id ++ = . in the context of Hughes lists. they are also known as difference lists, and also used at type String in the Prelude as ShowS, to help avoid quadratic behavior when making complicated Strings. the [a]-[a] is not an ordinary function -- it's expected not to examine its argument, just to use it exactly once (is there a formal way to say that?) ~Isaac ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: The Worker/Wrapper Transformation
Achim Schneider [EMAIL PROTECTED] wrote: (define (cons x y) (lambda (m) (m x y))) (define (car z) (z (lambda (p q) p))) (define (cdr z) (z (lambda (p q) q))) , which, just for completeness, can be of course also be done in Haskell: cons :: a - b - (a - b - c) - c cons x y m = m x y car :: ((a - b - a) - c) - c car z = z $ \p q - p cdr :: ((a - b - b) - c) - c cdr z = z $ \p q - q Prelude car $ cdr $ cdr $ cons 1 $ cons 2 $ cons 3 () 3 -- (c) this sig last receiving data processing entity. Inspect headers for past copyright information. All rights reserved. Unauthorised copying, hiring, renting, public performance and/or broadcasting of this signature prohibited. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: The Worker/Wrapper Transformation
On 3 Jan 2008, at 4:49 AM, Isaac Dupree wrote: Achim Schneider wrote: Achim Schneider [EMAIL PROTECTED] wrote: [...] I'm trying to grok that [] = id ++ = . in the context of Hughes lists. they are also known as difference lists, and also used at type String in the Prelude as ShowS, to help avoid quadratic behavior when making complicated Strings. the [a]-[a] is not an ordinary function -- it's expected not to examine its argument, just to use it exactly once (is there a formal way to say that?) f xn = f [] ++ xn is the first thing off the top of my head. OTOH, examining your argument (while, strictly speaking unsafe) is pretty darn cool: f [] = foo f (c:s) | isAlphaNum c = foo ++c:s | otherwise= foo++c:s Token prepend. jcc ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
