====== 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:
<code>
?- 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]] ;
</code>  

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

Example:
<code prolog>
?- 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]].
</code>