Henning Thielemann wrote:
On Fri, 18 Nov 2005, Paul Hudak wrote:
For example:
fe1,fe2 :: Fix Expr
fe1 e = Add (Const 1) (Const 1) -- non-recursive
fe2 e = Add (Const 1) e -- recursive
Do you mean
fe1 _ = Add (Const 1) Loop
?
No, I really meant it as written. I included this example just to point
out that an expression didn't have to be infinite to represent it as the
fixpoint of a function. Note that the least fixpoint of fe1 is "Add
(Const 1) (Const 1)".
Loop shouldn't ever be used by the user -- that's why I added the
comment that it was "not exported". It's just there to "open" the
function for inspection. In this sense, the trick is analogous to the
use of higher-order abstract syntax -- i.e. using the meta-language
(Haskell) to represent functions in the object language (expressions).
-Paul
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