Lab 12: Programming with cut and not

A tic-tac-toe table is encoded as a list [ [X1,Y1,Z1], [X2,Y2,Z2], [X3,Y3,Z3] ] where a variable is bound to atom x or z (zero) if the position has been played or it is uninstantiated otherwise.

1. Write the predicate diags(Tbl,R) which computes the list R of diagonals in table Tbl.

2. Write the predicate cols(Tbl,R) which computes the list of columns in table Tbl. Hint: use maplist/3.

3. Write the predicate winner(X,Tbl) which verifies if Tbl is winning for player X.

4. Write the predicate succ/2 where -? R = SomePos, succ(X,SomePos) binds variable R to all possible moves which player X can play in SomePos. Example: 

?- R = [[_,_,_],[z,_,x],[x,_,z]], succ(x,R).
R = [[x, _12646, _12652], [z, _12670, x], [x, _12694, z]] ;
R = [[_12640, x, _12652], [z, _12670, x], [x, _12694, z]] ;
R = [[_12640, _12646, x], [z, _12670, x], [x, _12694, z]] ;
R = [[_12640, _12646, _12652], [z, x, x], [x, _12694, z]] ;
R = [[_12640, _12646, _12652], [z, _12670, x], [x, x, z]] ;

5. Write a predicate csp(X,G,Dom,R) where X is an uninstantiated variable, G is a goal which contains the uninstantiated variable X, Dom is a list of possible values for X. R will be bound to the set of values for X from Dom which satisfy G.

6. Write the predicate ncsp(Vars,G,Doms,Tuples), where:

  1. Vars is a list $ X_1, X_2, \ldots, X_n$ of uninstantiated variables.
  2. G is a goal containing $ X_1, X_2, \ldots, X_n$ .
  3. Doms is a list of $ D_1, D_2, \ldots, D_n$ of domains for each variable
  4. Tuples will be bound to a list of tuples (encoded themselves as lists) $ v_1, v_2, \ldots, v_n$ such that $ v_i \in D_i$ and $ v_1, v_2, \ldots, v_n$ satisfies G.

Example: 

?- nscp([X,Y], (X+Y>4, X+Y<10), [[1,2,3,4], [2,3,8,9]], R).
R = [[1,8],[2,2],[2,3],[3,2],[3,3],[4,2],[4,3]].