The initial version which the OP posted doesn't have a terminal value.
The point is that it doesn't need a terminal value. Infinite lists like
oddsFrom3 and (repeat "foo") and (let xs = 1 : xs) are all perfectly valid
Haskell values.
On Mon, Aug 17, 2015 at 6:17 AM Doug McIlroy
oddsFrom3 :: [Integer] oddsFrom3 = 3 : map (+2) oddsFrom3
Thanks for your help.
Try to expand a few steps of the recursion by hand e.g.:
3 : (map (+2) (3 : map (+2) (3 : map (+2) ...)))
As you can see, the deeper you go more 'map (+2)' are applied to '3'.
Some more ways to describe the program, which may be useful:
As with any recursive function, assume you know the whole series and then confirm that by verifying the inductive step. In this case oddsFrom3 = [3,5,7,9,11,...] map (+2) oddsFrom3 = [5,7,9,11,13,...] voila oddsFrom3 = 3 : map (+2) oddsFrom3
Assuming we have the whole series, we see its tail is computed from the whole by adding 2 to each element. Notice that we don't actually have to know the values in the tail in order to write the formula for the tail.
Yet another way to describe the program: the "output" is taken as "input". This works because the first element of the output, namely 3, is provided in advance. Each output element can then be computed before it is needed as input.
In an imperative language this would be done so: integer oddsFrom3[0:HUGE] oddsFrom3[0] := 3 for i:=1 to HUGE do oddsFrom3[i] = oddsFrom3[i-1] + 2 _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners