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From: Sebastian Hanowski <sebastian_hanowski_at_gmx.de>

Date: Mon, 21 Dec 2015 09:15:18 +0100

On Tue, Dec 15, 2015 at 10:15:09AM -0800, h7sa_at_pdx.edu wrote:

*> Sebastian,
*

*>
*

*> This program is clever, but I like more your original one:
*

*>
*

*> fib | head x =?= 1
*

*> & head (tail x) =?= 1
*

*> & tail (tail x) =?= zipWith (+) x (tail x) = x where x free
*

*>
*

*> since it more clearly shows the conditions that you impose on the output. I
*

*> changed the syntax of the equality operator, since I think that you want some
*

*> kind of equality less strict than the standard one and different from (=:<=)
*

*> which is intended for a different use.
*

Hi Sergio

how nice. I couldn't have asked for more.

And yes, I prefer the origininal formulation too because it closely resemlbles

the traditional definition of the function N -> N computing the nth fibonacci

number.

However there's some sort of 'negative' twist in here. Which of course is no

wonder, since we are dealing with infinite objects.

I immediately came up with the first program when I was contemplating on some

work by Andreas Abel. But this topic has gained some momentum in my text

editor.

For example here's some of this weekends findings: a 'slide' variation of the

fibonacci theme featuring a 'questionable' variant of Markus Schnell's stream

transducer.

slide :: ([a] -> a) -> [a] -> [a]

slide f as | head xs =?= f as

& tail xs =?= slide f (tail as) = xs where xs free

fibstep :: [Int] -> Int

fibstep xs = head xs + head (tail xs)

fibs | head xs =?= 1

& head (tail xs) =?= 1

& tail (tail xs) =?= slide fibstep xs = xs where xs free

And here's a new way to define cycles:

Instead of writing e.g.

-- l_1_23rc = 1 : 2 : 3 : tail l_1_23rc

for [1,2,3,2,3,....]

you can also use back pointers.

l_1_23rc | head xs =?= 1

& head (tail xs) =?= 2

& head (tail (tail xs)) =?= 3

& tail (tail (tail xs)) =?= tail xs = xs where xs free

,-------\

v /

1 : 2 : 3 :

Cyclic data structures are essentially quotients. Which is another good

reason for not using constructors.

Best regards

Sebastian

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curry_at_lists.RWTH-Aachen.DE

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Received on Mon Dec 21 2015 - 17:47:17 CET

Date: Mon, 21 Dec 2015 09:15:18 +0100

On Tue, Dec 15, 2015 at 10:15:09AM -0800, h7sa_at_pdx.edu wrote:

Hi Sergio

how nice. I couldn't have asked for more.

And yes, I prefer the origininal formulation too because it closely resemlbles

the traditional definition of the function N -> N computing the nth fibonacci

number.

However there's some sort of 'negative' twist in here. Which of course is no

wonder, since we are dealing with infinite objects.

I immediately came up with the first program when I was contemplating on some

work by Andreas Abel. But this topic has gained some momentum in my text

editor.

For example here's some of this weekends findings: a 'slide' variation of the

fibonacci theme featuring a 'questionable' variant of Markus Schnell's stream

transducer.

slide :: ([a] -> a) -> [a] -> [a]

slide f as | head xs =?= f as

& tail xs =?= slide f (tail as) = xs where xs free

fibstep :: [Int] -> Int

fibstep xs = head xs + head (tail xs)

fibs | head xs =?= 1

& head (tail xs) =?= 1

& tail (tail xs) =?= slide fibstep xs = xs where xs free

And here's a new way to define cycles:

Instead of writing e.g.

-- l_1_23rc = 1 : 2 : 3 : tail l_1_23rc

for [1,2,3,2,3,....]

you can also use back pointers.

l_1_23rc | head xs =?= 1

& head (tail xs) =?= 2

& head (tail (tail xs)) =?= 3

& tail (tail (tail xs)) =?= tail xs = xs where xs free

,-------\

v /

1 : 2 : 3 :

Cyclic data structures are essentially quotients. Which is another good

reason for not using constructors.

Best regards

Sebastian

_______________________________________________

curry mailing list

curry_at_lists.RWTH-Aachen.DE

http://MailMan.RWTH-Aachen.DE/mailman/listinfo/curry

Received on Mon Dec 21 2015 - 17:47:17 CET

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