Yes, so I've done something similar. It is, however, not possible to give "f x" a meaning other than simply "apply the value x to the function f". You can't have "invisible functions". As for making -> an instance, you should be able to just write: class MyC f where g :: f a b -> a -> b instance MyC (->) where g = ($) Or soemthing like that. -- Hal Daume III "Computer science is no more about computers | hdaume@isi.edu than astronomy is about telescopes." -Dijkstra | www.isi.edu/~hdaume On Tue, 29 Oct 2002, Lloyd Allison wrote:
Almost certainly this is either . easy and obvious or . unnecessary or . impossible for some a well-known reason. Which is it please? ...
I would like to have a ``class Function'' which has the operators ``$'', ``.'', etc. and *most* particularly ``'', so that one can define sub-classes of Function (e.g. functions having inverses, say) that can still be applied in the usual way, i.e. ``f x''.
Lloyd
PS. [How] can one make ``->'' an instance of some new class? -- Lloyd ALLISON, CSSE, Monash University, Victoria, Australia 3168. web: http://www.csse.monash.edu.au/~lloyd/ tel: +61 3 9905 5205 --
This catches the spirit but falls short at ``f x'' :-
module Main where -- ------------------------------------------10/2002--L.A.--CSSE--Monash--.au-- -- Would like there to be a ``class Function'' having -- an apply operator, why not ($), and perhaps others such as (.), -- with ``->'' being an instance of class Function (as it is of Show 6.1.6) -- (come to that, how do you make ``->'' an instance of anything new?), -- and would like to define new instances and subclasses of class Function -- along the lines of...
class Function fnType where -- would like Function to be in Prelude and ($) :: (fnType t u) -> t -> u -- rather use Prelude's ($) or is it "" ? apply :: (fnType t u) -> t -> u
f $ x = apply f x -- and then would like to write f x apply f x = f Main.$ x
data Arrow t u = FN (t->u) -- i.e. ``->''
instance Function Arrow where -- ? in Prelude ? apply (FN f) x = f x
class (Function fnType) => Invertible fnType where -- a subclass, i.e. inverse :: fnType t u -> fnType u t -- invertible Functions
data IArrow t u = IFN (t->u) (u->t)
instance Function IArrow where apply (IFN f i) x = f x
instance Invertible IArrow where inverse (IFN f i) = IFN i f
successor = IFN (\x -> x+1) (\x -> x-1) -- e.g. an Invertible Function
linRec p f x = -- e.g. yer typical linear recursive schema let x0 = x -- slightly contrived (OK, a toy) up x = if p x then dn x else x : (up (apply f x)) dn x = x : if x==x0 then [] else dn (apply (inverse f) x) in up x0
main = print "L.A., CSSE, Monash, 10/2002: Re a hypothetical class Function"
print( successor `apply` 6 ) -- prefer successor 6 print( successor Main.$ 6 ) -- prefer successor $ 6 print( (inverse successor) `apply` 6 ) -- prefer (inverse successor) 6 print( linRec ((<=) 4) successor 1 ) print( linRec (\_->True) successor 1 )
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