/* File: dfa2.pl     System: SWI-Prolog  5.2.8
   Author: MM
   Date: 10/02/2003
   Title: Explore if the DFA defined is well defined.
   
   DFA accepts words that start with a.
   Alphabet={a,b}, States={0,1,2}   Favorable={1} start is state 0.
   Transition function is:
                delta(0,a)=1    delta(0,b)=2
                delta(1,a)=1    delta(1,b)=1
                delta(2,a)=2    delta(2,b)=2
   
   Load your file:
   ?- ['C://swimm/dfa2.pl'].
    Yes
   
   See if for state 0 there are exactly two arrows. 
   That is delta(0,a) and delta(0,b) are defined.
   
   ?- check_state(0). 
    Yes   

    ?- check_dfa.
    0good
    1good
    2bad
*************************************************/
/* This is the definition of your DFA in Prolog.
*/
    delta(0,a,1).
    delta(0,b,2).
    delta(1,a,1).
    delta(1,b,1).
    delta(2,a,2).
    delta(2,b,2).  % tale this out in order to check also a "bad" situation
    
    start(0).
    
    favorable(1).
     
/*   A state appears in the delta function as argument 1 or 3.
*/   
    state(I):- delta(I,_,_) ; delta(_,_,I).
    
/*   Make the list of the states
*/   
    list_states(Res):- findall(X,state(X),L),sort(L,Res).

/*   Check if a state is correct from the DFA point of view
*/   
    check_state(S):- findall(X,delta(S,a,X),L1),length(L1,1),
                     findall(X,delta(S,b,X),L2),length(L2,1).
                     
/*   Check if all states are correct from the DFA point of view
*/                  
    check_dfa:- forall((list_states(L),member(X,L)),
                      (nl,write(X),check_state(X) -> write('good') ; write('bad'))
                      ).