You only have a Num constraint when type checking that code:

(+) :: Num a => a -> a -> a

For better or worse, you don't get strictness in the type signatures in Haskell. 

We do not separate codata from data here.

Without knowing about the particular instance of Num and even the direction of recursion on (+) there is no information for such a strictness analyzer to work with.

many :: Alternative m => m a -> m [a]
many p = ps where
  ps = (:) <$> p <*> ps 
   <|> pure []

is another perfectly cromulent example of "value" recursion, and one that is far nearer and dearer to my heart and is similarly opaque to any such analysis.

-Edward



On Wed, Jul 24, 2013 at 4:14 AM, Andreas Abel <andreas.abel@ifi.lmu.de> wrote:
Sure.  I have not looked a concrete strictness analyses, but I expect they would treat Conat differently than Integer.  In particular,

  x   does *not* appear strictly in  S x

if S is a lazy constructor.


On 22.07.13 4:54 PM, Edward Kmett wrote:
let x = x +1

is perfectly cromulent when x is sufficiently lazy, e.g. in the one point compactification of the naturals:

data Conat = S Conat | Z

There it represents infinity with proper sharing.

-Edward

On Jul 22, 2013, at 10:24 AM, Andreas Abel <andreas.abel@ifi.lmu.de> wrote:

On 22.07.2013 10:50, MigMit wrote:

On Jul 22, 2013, at 12:27 PM, Andreas Abel <andreas.abel@ifi.lmu.de>
wrote:

On 20.07.13 9:36 PM, Evan Laforge wrote:
However, I'm also not agitating for a non-recursive let, I think
that ship has sailed.  Besides, if it were added people would
start wondering about non-recursive where, and it would introduce
an exception to haskell's pretty consistently order-independent
declaration style.

For functions, recursive-by-default let makes sense.  But for
*values*, intended recursion is rather the exception.  It is useful
for infinite lists and the like.  For values of atomic type like
Int or Bool, recursive let is a bug.

It seems hard to distinguish between them. What about values that
contain functions, like data T = T Int (Int -> Int)? What about
polymorphic values, that could be functions and could be not?

I agree.  It cannot be implemented like that.  A thing that could be implemented is that

  let x = e

is an error if x appears strictly in e.  In practice, this could catch some unintended cases of recursion like

  let x = x +1

, but not all of them.

Cheers,
Andreas

--
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Theoretical Computer Science, University of Munich
Oettingenstr. 67, D-80538 Munich, GERMANY

andreas.abel@ifi.lmu.de
http://www2.tcs.ifi.lmu.de/~abel/

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--
Andreas Abel  <><      Du bist der geliebte Mensch.

Theoretical Computer Science, University of Munich
Oettingenstr. 67, D-80538 Munich, GERMANY

andreas.abel@ifi.lmu.de
http://www2.tcs.ifi.lmu.de/~abel/