# Generates an infinite list of strings, following this
# sequence:
# 
#   ["a", "b" ..."z", 
#    "aa", "ab" ... "az",
#    "ba", "bb" ... "bz",
#    ...
#    "za", "zb" ... "zz",
#    "aaa", "aab" ... "aaz",
#    "aba", "abb" ... "abz",
#    ...
#    "zza", "zzb" ... "zzz",
#    ...
#
# In Haskell you would define it this way:
#
#   ns = [x ++ [y] | x <- []:ns, y <- ['a'..'z']]
#
# Author: Bernie Pope
# Date:   10 October 2004

forallWorker 
   = !f -> !list1 -> !list2 -> !list3 -> 
        ite (null list1) 
            (ite (null list3) 
                 [] 
                (forallWorker f list2 list2 (tail list3)))
            (ite (null list3) 
                 [] 
                 (Cons (f (head list1) (head list3)) 
                       (forallWorker f (tail list1) list2 list3)));

forall 
   = !f -> !list1 -> !list2 -> 
        forallWorker f list1 list1 list2;

ns 
   = forall (\x -> \y -> append y (single x)) 
            aToZ 
            (Cons [] ns);

single = \x -> Cons x [];

aToZ 
   = ['a','b','c','d','e','f','g','h','i','j','k','l','m',
      'n','o','p','q','r','s','t','u','v','w','x','y','z'];