/************************************************
 File: gen0.pl
 Author: Mihaela Malita
 Title: Generate words over an alphabet [a,b]
  Example.
    Generate all words of length 3.
        ?- gen(3,[a,b],L).
        L = [a, a, a] ;  % type ; for more solutions
        L = [a, a, b] ;
        L = [a, b, a] ;
        L = [a, b, b] ;
        L = [b, a, a] ;
        L = [b, a, b] ;
        L = [b, b, a] ;
        L = [b, b, b] ;
        No % means there are no more solutions
    Generate all words of length from 1 to 3
       ?- generate(3,[a,b],L),write(L),nl,fail. % provoke backtracking with fail
        [a]
        [b]
        [a, a]
        [a, b]
        [b, a]
        [b, b]
        [a, a, a]
        [a, a, b]
        [a, b, a]
        [a, b, b]
        [b, a, a]
        [b, a, b]
        [b, b, a]
        [b, b, b]
         No
***************************************************/ 
/* mem(L1,L2). Force all elements from L1 to be members of L2.
    ?- mem([X,Y],[a,b,c]).
    X = Y = a ;
    X = a ,Y = b ;
    X = a ,Y = c ;
    X = b ,Y = a ;  
    X = Y = b ;
    X = b ,Y = c ;
    X = c ,Y = a ;
    X = c ,Y = b ;
    X = Y = c ;
*/
    mem([],L2).
    mem([H|T],L2):-member(H,L2),mem(T,L2). 

%  Make a list with variables of length N and fill it with elements from L
    gen(N,L,R):-length(R,N),mem(R,L).

% Generate all words with length 1 to N
    generate(N,L,R):- between(1,N,K),gen(K,[a,b],R).