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Jonathan Fischoff

29 Dec 2009 29 Dec '09

3:32 a.m.

Hi, I would to create a list of tuples (or something similar) of invertible functions [((a -> b), (b -> a)), ((b -> c), (c -> b)), .... Such that I could call forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas? -Jonathan

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Dan Weston

29 Dec 29 Dec

3:41 a.m.

This might be pertinent: Alimarine et al, "There and Back Again: Arrows for Invertible Programming" http://www.cs.ru.nl/A.vanWeelden/bi-arrows/ Jonathan Fischoff wrote:

Hi,

I would to create a list of tuples (or something similar) of invertible functions

[((a -> b), (b -> a)), ((b -> c), (c -> b)), ....

Such that I could call

forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

-Jonathan

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Jonathan Fischoff

3:40 p.m.

This seems like exactly what I want, but there are two problems: I can't access the paper and it requires Generic Haskell. I'm just too much of newb to jump into generic Haskell :). On Mon, Dec 28, 2009 at 7:41 PM, Dan Weston wrote:

This might be pertinent:

Alimarine et al, "There and Back Again: Arrows for Invertible Programming" http://www.cs.ru.nl/A.vanWeelden/bi-arrows/

Jonathan Fischoff wrote:

...
Hi, I would to create a list of tuples (or something similar) of invertible functions

[((a -> b), (b -> a)), ((b -> c), (c -> b)), ....

Such that I could call

forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

-Jonathan

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Eugene Kirpichov

3:43 p.m.

data IList a b where Id :: IList a a ICons :: (a -> b) -> (b -> a) -> IList b c -> IList a c 2009/12/29 Jonathan Fischoff :

This seems like exactly what I want, but there are two problems: I can't access the paper and it requires Generic Haskell. I'm just too much of newb to jump into generic Haskell :).

On Mon, Dec 28, 2009 at 7:41 PM, Dan Weston wrote:

...
This might be pertinent:

Alimarine et al, "There and Back Again: Arrows for Invertible Programming" http://www.cs.ru.nl/A.vanWeelden/bi-arrows/

Jonathan Fischoff wrote:

...
Hi, I would to create a list of tuples (or something similar) of invertible functions

[((a -> b), (b -> a)), ((b -> c), (c -> b)), ....

Such that I could call

forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

-Jonathan

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

-- Eugene Kirpichov Web IR developer, market.yandex.ru

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Eugene Kirpichov

3:45 p.m.

forward Id a = a forward (ICons f _ r) a = forward r (f a) backward Id a = a backward (ICons _ f r) a = f (backward r a) 2009/12/29 Eugene Kirpichov :

data IList a b where Id :: IList a a ICons :: (a -> b) -> (b -> a) -> IList b c -> IList a c

2009/12/29 Jonathan Fischoff :

...
This seems like exactly what I want, but there are two problems: I can't access the paper and it requires Generic Haskell. I'm just too much of newb to jump into generic Haskell :).

On Mon, Dec 28, 2009 at 7:41 PM, Dan Weston wrote:

...
This might be pertinent:

Alimarine et al, "There and Back Again: Arrows for Invertible Programming" http://www.cs.ru.nl/A.vanWeelden/bi-arrows/

Jonathan Fischoff wrote:

...
Hi, I would to create a list of tuples (or something similar) of invertible functions

[((a -> b), (b -> a)), ((b -> c), (c -> b)), ....

Such that I could call

forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

-Jonathan

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

-- Eugene Kirpichov Web IR developer, market.yandex.ru

-- Eugene Kirpichov Web IR developer, market.yandex.ru

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Ryan Ingram

3:41 a.m.

Do you need to be able to extract the intermediate types? If not, then the only observable value for your function list is the composition (forward/backward), and you can easily represent it like this: data Inv a b = Inv { forward :: (a -> b), backward :: (b -> a) } nil :: Inv a a nll = Inv id id cat :: Inv a b -> Inv b c -> Inv a c cat ab bc = Inv (forward bc . forward ab) (backward ab . backward bc) reverse :: Inv a b -> Inv b a reverse ab = Inv (backward ab) (forward ab) -- ryan On Mon, Dec 28, 2009 at 8:32 PM, Jonathan Fischoff wrote:

Hi, I would to create a list of tuples (or something similar) of invertible functions [((a -> b), (b -> a)), ((b -> c), (c -> b)), .... Such that I could call forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas? -Jonathan _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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Antoine Latter

3:43 a.m.

On Mon, Dec 28, 2009 at 10:32 PM, Jonathan Fischoff wrote:

Hi, I would to create a list of tuples (or something similar) of invertible functions [((a -> b), (b -> a)), ((b -> c), (c -> b)), .... Such that I could call forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

It looks like the thrist package should help you out: http://hackage.haskell.org/cgi-bin/hackage-scripts/package/thrist You could define some sort of type Iso: data Iso a b = Iso (a -> b) (b -> a) And then build a Thrist and fold over it, the functions forward and backwards can both be implemented with right-folds.

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Jonathan Fischoff

3:45 p.m.

Thirst will work I think. I tested a demo and the only problem I can see is the unwieldiness of the syntax, i.e testThirst = f `Cons` (g `Cons` (h `Cons` Nil)) Maybe there is a way to sugar up the syntax to get rid of the parentheses? On Mon, Dec 28, 2009 at 7:43 PM, Antoine Latter wrote:

On Mon, Dec 28, 2009 at 10:32 PM, Jonathan Fischoff wrote:

...
Hi, I would to create a list of tuples (or something similar) of invertible functions [((a -> b), (b -> a)), ((b -> c), (c -> b)), .... Such that I could call forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

It looks like the thrist package should help you out:

http://hackage.haskell.org/cgi-bin/hackage-scripts/package/thrist

You could define some sort of type Iso:

data Iso a b = Iso (a -> b) (b -> a)

And then build a Thrist and fold over it, the functions forward and backwards can both be implemented with right-folds.

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Eugene Kirpichov

4:07 p.m.

Use operator precedence: infixr . I don't remember exactly how it is used, but it should do the trick and let you get rid of the parentheses. 2009/12/29 Jonathan Fischoff :

Thirst will work I think. I tested a demo and the only problem I can see is the unwieldiness of the syntax, i.e testThirst = f `Cons` (g `Cons` (h `Cons` Nil)) Maybe there is a way to sugar up the syntax to get rid of the parentheses? On Mon, Dec 28, 2009 at 7:43 PM, Antoine Latter wrote:

...
On Mon, Dec 28, 2009 at 10:32 PM, Jonathan Fischoff wrote:

...
Hi, I would to create a list of tuples (or something similar) of invertible functions [((a -> b), (b -> a)), ((b -> c), (c -> b)), .... Such that I could call forward invertibleFuctionList domainValue = ? -- composite all the functions backward invertibleFuctionList rangeValue = forward (reverse invertibleFuctionList) rangeValue -- or something similar

I would also like to concat them. This sounds like a job for GADT that someone might have already tackled. Any ideas?

It looks like the thrist package should help you out:

http://hackage.haskell.org/cgi-bin/hackage-scripts/package/thrist

You could define some sort of type Iso:

data Iso a b = Iso (a -> b) (b -> a)

And then build a Thrist and fold over it, the functions forward and backwards can both be implemented with right-folds.

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

-- Eugene Kirpichov Web IR developer, market.yandex.ru

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participants (5)

Antoine Latter
Dan Weston
Eugene Kirpichov
Jonathan Fischoff
Ryan Ingram