错误：我的 Prolog 代码中超出本地堆栈

我无法弄清楚为什么给定 Prolog 代码的以下查询会生成错误Out of local stack.

序言代码：

likes(g,c).
likes(c,a).
likes(c,b).
likes(b,a).
likes(b,d).

likes(X,Z) :- likes(X,Y), likes(Y,Z).

查询

?- likes(g,X).

结果是

X = c ;
X = a ;
X = b ;
ERROR: Out of local stack

Edit 1这就是我认为 Prolog 应该处理这个查询的方式，

likes(g,c) is a fact, so X={c}
likes(g,b) <= likes(g,c) and likes(c,b), so X={c,b}
likes(g,a) <= likes(g,b) and likes(b,a), so X={c,b,a}
likes(g,d) <= likes(g,b) and likes(b,d), so X={c,b,a,d}
              likes(g,a) and false, so nothing to add to X
              likes(g,d) and false, so nothing to add to X 
end of backtracking search.

Edit 2我设法通过对代码进行以下修改来获得我正在寻找的内容：

likes(g,c).
likes(c,a).
likes(c,b).
likes(b,a).
likes(b,d).

indirect_likes(A,B):- likes(A,B).
indirect_likes(A,C):- likes(B,C), indirect_likes(A,B).

查询

？- 间接喜欢（g，哪个）。

结果是

Which = c ;
Which = a ;
Which = b ;
Which = a ;
Which = d ;
false.

然而，我仍然无法弄清楚背后的原理。如果我将最后一条规则更改为

indirect_likes(A,C):- indirect_likes(A,B), likes(B,C).

然后我得到ERROR: Out of local stack！据我所知，逻辑合取是可交换的。

为了得到传递闭包 /questions/tagged/transitive-closure二元关系的R_2, use 元谓词 /questions/tagged/meta-predicate closure/3 https://stackoverflow.com/questions/26946133/definition-of-reflexive-transitive-closure像这样：

?- closure(R_2,From,To).
  

让我们运行一个示例查询closure/3和...一起likes/2!

?- closure(likes,X,Y).
  X = g, Y = c
; X = g, Y = a
; X = g, Y = b
; X = g, Y = a                    % redundant
; X = g, Y = d
; X = c, Y = a
; X = c, Y = b
; X = c, Y = a                    % redundant
; X = c, Y = d
; X = b, Y = a
; X = b, Y = d
; false.                          % query terminates universally
  

当我们使用时我们得到相同的答案indirect_likes/2，但顺序不同：

?- indirect_likes(X,Y).
  X = g, Y = c
; X = c, Y = a
; X = c, Y = b
; X = b, Y = a
; X = b, Y = d
; X = g, Y = a
; X = g, Y = b
; X = c, Y = a                    % redundant
; X = g, Y = a                    % redundant
; X = c, Y = d
; X = g, Y = d
; false.                          % query terminates universally
  

正如您在对 @C.B. 的回答的评论中所述，二元关系不一定是自反的和/或对称的。根据你给出的定义，likes/2 is neither:

?- likes(X,X).
false.                            % not reflexive (not even close)

?- likes(X,Y), likes(Y,X).
false.                            % not symmetric (not even close)

到目前为止，一切都很好！

Let's 姑且将以下附加事实添加到您的数据库中：

likes(b,b).

有了这个扩展的定义，indirect_likes/2行为异常：

?- indirect_likes(b,b).
  true
; true
; true
...                               % does not terminate universally

?- indirect_likes(X,Y), false.    % do we get finite failure?
...                               % no! query does not terminate universally
  

我们可以做什么？让我们使用元谓词 /questions/tagged/meta-predicate closure/3与扩展版本likes/2!

?- closure(likes,b,b).
  true                            % succeeds non-deterministically
; false.                          % query terminates universally

?- closure(likes,X,Y), false.     % do we get finite failure?
false.                            % yes! query terminates universally
  

底线是什么？

在纯粹的 Prolog 中，就逻辑意义而言，合取是可交换的。

由于 Prolog 的SLD分辨率 https://en.wikipedia.org/wiki/SLD_resolution， 目标false,repeat有限地失败，但是repeat,false才不是。 程序员需要处理终止，但通常这对于 Prolog 提供的原始性能和控制来说只是一个很小的代价。

在这个答案中，我将“终止担忧”传递给了实施者元谓词 /questions/tagged/meta-predicate closure/3 https://stackoverflow.com/questions/26946133/definition-of-reflexive-transitive-closure :)