Comments on: Replication schemes http://martijn.van.steenbergen.nl/journal/2011/01/16/replication-schemes/ Just another WordPress site Mon, 13 May 2013 18:02:27 +0000 hourly 1 http://wordpress.org/?v=3.4.1 By: Martijn http://martijn.van.steenbergen.nl/journal/2011/01/16/replication-schemes/#comment-360 Martijn Mon, 23 May 2011 11:35:13 +0000 http://martijn.van.steenbergen.nl/journal/?p=522#comment-360 Thank you Twan, that does seem to work. :-) Thank you Twan, that does seem to work. :-)

]]> By: Martijn http://martijn.van.steenbergen.nl/journal/2011/01/16/replication-schemes/#comment-359 Martijn Mon, 23 May 2011 11:34:55 +0000 http://martijn.van.steenbergen.nl/journal/?p=522#comment-359 Thanks, Dean! Fixed it. Thanks, Dean! Fixed it.

]]> By: Dean Herington http://martijn.van.steenbergen.nl/journal/2011/01/16/replication-schemes/#comment-358 Dean Herington Wed, 02 Feb 2011 19:13:18 +0000 http://martijn.van.steenbergen.nl/journal/?p=522#comment-358 The following, from your blog entry: > sizes (between 7 9 . three) [9,12,15] didn't seem right. Sure enough, with your package: > sizes (between 7 9 Control.Category.. three) [21,24,27] The following, from your blog entry:

> sizes (between 7 9 . three)
[9,12,15]

didn’t seem right. Sure enough, with your package:

> sizes (between 7 9 Control.Category.. three)
[21,24,27]

]]> By: Twan van Laarhoven http://martijn.van.steenbergen.nl/journal/2011/01/16/replication-schemes/#comment-357 Twan van Laarhoven Sun, 16 Jan 2011 23:02:22 +0000 http://martijn.van.steenbergen.nl/journal/?p=522#comment-357 It seems that `sizes (exactly n)` already needs time quadratic in n. I think this is caused by the call to fmap, there will be n calls to fmap, each of which runs over the entire list of n things. Other things exhibit even worse scaling, such as `sizes (some . some)` It might be better to do fmap lazily somehow, for example by storing in `Cons` a function that will be applied to the final result. Something like data Replicate a b = Nil | forall c. Cons (c -> b) (Maybe c) (Replicate a (a -> c)) I have not yet tried whether this will work. Also note that a value of type `Replicate a b` is equivalent to a subset of the naturals, plus for each element of this set a function of that many as to b. Your type already tries to capture this, but maybe the function and the subset could be stored separately? It seems that `sizes (exactly n)` already needs time quadratic in n. I think this is caused by the call to fmap, there will be n calls to fmap, each of which runs over the entire list of n things. Other things exhibit even worse scaling, such as `sizes (some . some)`

It might be better to do fmap lazily somehow, for example by storing in `Cons` a function that will be applied to the final result. Something like

data Replicate a b = Nil | forall c. Cons (c -> b) (Maybe c) (Replicate a (a -> c))

I have not yet tried whether this will work.

Also note that a value of type `Replicate a b` is equivalent to a subset of the naturals, plus for each element of this set a function of that many as to b. Your type already tries to capture this, but maybe the function and the subset could be stored separately?

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