[Haskell-cafe] Re: Heterogeneous Data Structures - Nested Pairs and functional references

[Alexander Solla]

>
> sry for being a bit thick, but how would this code be used?
>
> I'm unable to figure out the application yet. Could you give some  
> examples how you use it?
>
>
> Günther

So, the type (View view) -- ignoring class instances -- is basically  
isomorphic to this (slightly simpler) type:

data View = EmptyView | TextView String | ConcatView View View |  
NestViews View View View | ...
instance Monoid View where ...

Now, consider the problem of "generic programming" on the simpler  
type:   you quantify over the data constructors "generically", and in  
doing so you gain "traversals" for the type.[1]  You gain the same  
things by turning View into (View view) --  a functor, a foldable  
functor, and so on.  When it comes time to "render" a format for a  
View (for example, a bit of Html from Text.XHtml.Strict), I use some  
higher order functions I'm already familiar with.  Something like

renderXHtml :: (View view) -> Html
renderXHtml (ConcatViews l r) = fold $ renderXHtml (ConcatViews l r)
renderXHtml (NestViews l m r) = fold $ renderXHtml (NestViews l m r)
renderXHtml (TextView string) = stringToHtml string
renderXHtml (PageView v_title, v_heading, v_header, v_footer,  
v_contents) =
	(the_title << (renderXHtml v_title)) +++         -- (We assume  
v_title is a TextView String)
         (body << ( renderXHtml v_header )  +++
		 (render_page_contents v_contents v_heading) +++
		 (renderXHtml v_footer) )
		 where render_page_contents contents heading = undefined -- takes a  
View and uses the page's heading View
									 -- so I guess we assume v_heading is a function
						                         -- into a TextView

...

You could potentially use (>>=) for this, directly.

And if you were using the simpler type, you could do the same thing  
with Uniplate, for example.  It's going to construct an automorphism  
for you.

[1]  Actually, it's "the other way around".  But the container/ 
contained adjunction makes them equivalent.
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