slide: useful function?

[Andreas Abel]

Markus.Schnell@infineon.com wrote:
> =

> I want to propose the following function slide, which is like map, but
> depends not on one value of
> a list, but on several consecutive ones.
> =

> slide :: ([a] -> b) -> [a] -> [b]
> slide f [] =3D []
> slide f xs =3D f xs : slide f (tail xs)

The function is interesting from the theoretical side since it is an inst=
ance of *redecoration*.  Written as

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

one sees a similarity with the monadic multiplication (or substitution, h=
ere for the case of lists)

>>=3D   :: [a] -> (a -> [b]) -> [b] .

Indeed, slide is the multiplication operation of lists viewed as a *comon=
ad* and hence the dual of ">>=3D".

Read more in

T Uustalu, V Vene. The dual of substitution is redecoration. In K Hammond=
, S Curtis, eds, Trends in Functional Programming 3, pp 99-110. Intellect=
,
      Bristol / Portland, OR, 2002. - .ps.gz, 46K (=A9 Intellect) =


http://www.cs.ioc.ee/~tarmo/papers/sfp01-book.ps.gz ,

if you want to be bothered with categorical nonsence ;-)

Cheers,
Andreas

-- =

Andreas Abel     --<>--    What if Jesus is right?  =


Theoretical Computer Science, University of Munich
http://www.tcs.informatik.uni-muenchen.de/~abel/