Re: Curry-on to infinity

From: Michael Hanus <mh_at_informatik.uni-kiel.de>
Date: Mon, 07 Dec 2015 16:48:12 +0100

Hi,

just a short comment. I think the reason why your example works
is not due to the features of Curry but due to the unintended use
of some features. The non-strict unification operator (=:<=)
is intended to implement functional patterns, i.e., a rule like

   last (_++[x]) = x

is transformed into

   last xs | _++[x] =:<= xs =x where x free

in order to implement the intended semantics of functional patterns.
As an invariant, the second argument is always a variable denoting
some actual argument. Without this invariant, as in your fib example,
I don't see some declarative meaning of this operator (at least,
it has not be explored).

Best regards,

Michael

On 12/04/2015 09:04 AM, Sebastian Hanowski wrote:
>
> Hi all,
>
>
> Haskell sometimes get's critisized for collapsing the notion of finite
> and infinite data because the latter should be opaque like functions
> or that it requires you to mention lazy evaluation when explaining
> non-terminating recursive definitions.
>
> Applying the same critique to Curry seems somehow unfair since it
> already contains a remedy!
>
> Instead of writing for example the fibonaci sequence in terms of
> constructors and self reference
>
> -- fib = 1 : 1 : zipWith (+) fib (tail fib)
>
> Curry alternativly let's you define it this way
>
> fib | head x =:<= 1
> & head (tail x) =:<= 1
> & tail (tail x) =:<= zipWith (+) x (tail x) = x where x free
>
> Since we know now that it's possible to define the program without
> having to mention constructors, the next step would be to completely
> hide the concrete representation in a module with only the selection
> functions being exported.
>
> module Stream(Stream,sHead,sTail) where ...
>
> However since the fibonacci sequence is my running example please allow=

> that we assume this as already working, induct on this and proceed
> directly to the next next step by combining both previous results ;)
>
> If we seal a definition of an infinite data structure in a module
> aliasing it's constructor with a defined function e. g. by saving the
> following to a file
>
> module Stream(Stream,(>:)) where
>
> data Stream a = SCons a (Stream a)
>
> infix r 5
> (>:) :: a -> Stream a -> Stream a
> a >: as = SCons a as
>
> we not only do justice to progamming by just specifying an abstract
> implementation
>
> import Stream
>
> fib :: Stream a
> fib | sHead x =:<= 1
> & sHead (sTail x) =:<= 1
> & sTail (sTail x) =:<= sZipWith (+) x (sTail x) = x where x f=
ree
>
> but also do we get back our familiar mode of programming with pattern
> matching and constructor calls.
>
> sHead :: Stream a -> a
> sHead (a>:_) = a
>
> sTail :: Stream a -> Stream a
> sTail (_>:as) = as
>
> sZipWith :: (a -> b -> c) -> Stream a -> Stream b -> Stream c
> sZipWith f (a>:as) (b>:bs) = f a b >: sZipWith f as bs
>
> -- just a utility for use on the console
> sTake :: Int -> Stream a -> [a]
> sTake n (a>:as) | n == 0 = [] | otherwise = a : sTake (n-1) as
>
> Have your choice!
> Please note that the latter also is still independent of the concrete
> implementation of Stream.
> You could silently switch the imported module back to say
>
> type Stream a = [a]
> (>:) = (:)
>
> and my program wouldn't (have to) recognise it.
>
> If you find this as interesting as I do, can you write other sequences =
in
> either way? Primes? Hamming numbers?
>
> Your PAKCS source code distribution contains a file examples/inflists.c=
urry if
> you want to cut short on the maths part of that tasks. (As I did).
>
> So my point is just that free variables seem to be a nice tool for hand=
ling
> abstract data (what infinite data should be, as some argue) and that fu=
nction
> calls on the left can be used to restore a convenient interface to it.
> They can be used to visualize data our program never gets to see.
>
>
> Have a nice weekend
>
> Sebastian
> _______________________________________________
> curry mailing list
> curry_at_lists.RWTH-Aachen.DE
> http://MailMan.RWTH-Aachen.DE/mailman/listinfo/curry
>






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Received on Mon Dec 07 2015 - 16:49:41 CET

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