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 )