[Haskell-beginners] Program reliability and multiple data constructors; polymorphism

[umptious]

One of the programming exercises I keep evolving as I learn Haskell is a
toy 2D shape editor with four primitives:

data Shape =   Circle   {origin::Pt2, radius::Float}
                       | Square   {origin::Pt2, side  ::Float}
                       | Rect     {origin::Pt2, other ::Pt2}
                       | Composite {shapes::[Shape]}
                         deriving (Show, Read)

The intent  is Composites can contain Shapes of any kind, including other
Composites so that you can apply transformations to a Composite and these
will be applied to the contained Shapes recursively. So an arm might
contain a hand which constains a dozen or so Rects. Transform the arm and
the hand and rects should transform; transform the hand and its rects
should transform but the not arm. Big deal.

And the above makes that really easy when you know you're talking to a
Composite. But now I've hit an intellectual stumbling point and the books
and source I have don't seem to address it:  I can apply the destructuring
command "shapes" defined in the cstr "Composite" to ANY Shape. And if I do
that to say a circle, BLAM! Or if I apply "radius" to Rect, BLAM! At
runtime. No type checking support (because yes, they're the same type.)

To me this seems alarming. It means that I can't reason about the safety of
my program based on type checking as I'd like. And none of the answers I
can think seem at all elegant:

- I could use exception handling, but that means carefully checking which
data declarations are potential bombs and using exceptions only when they
are involved - hideously error prone - or using exceptions everywhere.
Which is just hideous.

- I could hack run time type checking using the ctsr info in "show". But
again I'd have to know when to use it or use it everywhere. And it seems
like a ridiculous kludge to bring to a language that has been designed for
elegance.

..So what is the Haskell idiom for dealing with this??? In fact I suppose
I'm asking two questions:

1. How do I re-design this program so it is safe (use class and instance
maybe, abandoning use of a single data type? but I then have to have
separate Lists for each type, even if they derived from a common class?)

2. How can one use compile time checking or (less good) coding practices to
eliminate the possibilty of such runtime exceptions?

And come to think of it

3. is there a Haskell book which addresses design and structural problems
like this one - which I would have thought was both obvious and fundamental
- because of the books I've looked at so far seem to do a tolerable job.
The best of them present an adequate "on rails" tour, but none of them seem
to give you the tools to address issues like this one. Whereas with C++and
Stroustrupp, Common Lisp and Graham, the Smalltalk book, and I Erlang and
Armstrong I'd know exactly what to do. Admittedly the C++ solutions
wouldn't be pretty, but anything the compiled would be safe to run (unless
I went to great efforts otherwise..)
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