For a recent research project, I had to write a function that generates all the strings of a given alphabet. It was (as always) very easy to figure it out in Python, only 5 minutes; below is the code (with modifications, I've polished the idea a bit):
def allstrings(alphabet, length):
"""Find the list of all strings of 'alphabet' of length 'length'"""
if length == 0: return []
c = [[a] for a in alphabet[:]]
if length == 1: return c
c = [[x,y] for x in alphabet for y in alphabet]
if length == 2: return c
for l in range(2, length):
c = [[x]+y for x in alphabet for y in c]
return c
Then, suppose you want the possible strings of length 4 of alphabet {1,2,3}; then just write:
allstrings([1,2,3], 4)
And here is the Haskell version:
allstrings alphabet n
| n == 0 = []
| n == 1 = [alphabet]
| n == 2 = [[a,b] | a<-alphabet, b<-alphabet]
| otherwise =
[[a] ++ b | a<-alphabet, b<-(allstrings alphabet (n - 1))]