====== Minimax principle ======
{{tag>problem_solving}}
===== Description =====
A straightforward implementation of the minimax principle.

**Source**:  PROLOG programming for artificial intelligence, 3rd Edition, Harlow, 2001, ISBN 0-201-40375-7.
===== Download =====
Program source code: {{minimax_principle.pl}}
===== Listing =====
<code prolog>
% Figure 22.3  A straightforward implementation of the minimax principle.


% minimax( Pos, BestSucc, Val):
%    Pos is a position, Val is its minimax value;
%    best move from Pos leads to position BestSucc

minimax( Pos, BestSucc, Val)  :-
  moves( Pos, PosList), !,               % Legal moves in Pos produce PosList
  best( PosList, BestSucc, Val)
   ;
   staticval( Pos, Val).                 % Pos has no successors: evaluate statically 

best( [ Pos], Pos, Val)  :-
  minimax( Pos, _, Val), !.

best( [Pos1 | PosList], BestPos, BestVal)  :-
  minimax( Pos1, _, Val1),
  best( PosList, Pos2, Val2),
  betterof( Pos1, Val1, Pos2, Val2, BestPos, BestVal).

betterof( Pos0, Val0, Pos1, Val1, Pos0, Val0)  :-        % Pos0 better than Pos1
  min_to_move( Pos0),                                    % MIN to move in Pos0
  Val0 > Val1, !                                         % MAX prefers the greater value
  ;
  max_to_move( Pos0),                                    % MAX to move in Pos0
  Val0 < Val1, !.                                % MIN prefers the lesser value 

betterof( Pos0, Val0, Pos1, Val1, Pos1, Val1).           % Otherwise Pos1 better than Pos0
</code>
===== Comments =====