This just too cool to pass up:
~:$ cat count.hs
fix f = f (fix f) -- return fixed point
-- prepend 1 to the result of adding 1 to
each value
g f = 1 : map (+1) f
counting = fix g -- return the "list" that is fixed
~:$ hugs
__ __ __ __ ____ ___
_________________________________________
|| || || || || || ||__ Hugs 98: Based on the Haskell 98
standard
||___|| ||__|| ||__|| __|| Copyright (c) 1994-2005
||---|| ___|| World Wide Web: http://haskell.org/hugs
|| || Report bugs to: [email protected]
|| || Version: March 2005
_________________________________________
Haskell 98 mode: Restart with command line option -98 to enable
extensions
Type :? for help
Hugs.Base> :load count.hs
Main> take 5 counting
[1,2,3,4,5]
Main> take 10 counting
[1,2,3,4,5,6,7,8,9,10]
Main> [Leaving Hugs]
~:$
The three line program described above may be paraphrased as follows:
1. Define a function f and return a fixed point of (i.e. if fix f =
x, then f(x) = x).
2. Define g to the function that takes f, adds 1 to every element of
the list it returns and prepend 1 to that list
3. Call that fixed point counting
4. Now, suppose you take the "infinite" list [1, 2, 3 ...] and add 1
to each list element. The result is, of course, [2, 3, 4 ..]. If you
put a 1 in front of that list, you get [1, 2, 3 ...]
5. So, the "list" returned by taking a fixed point of g is "counting
to infinity"
Finally, I use the built-in take to display the first 5 or 10
elements of the list to demonstrate that it really does "count to
infinity".
===
Gregory Woodhouse
[EMAIL PROTECTED]
"Good acts are like good poems. One may easily get their drift, but
they are not rationally understood."
--Albert Einstein
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