尋找一套在Prolog中是否具有附加的mod K

Question

我是Prolog的初學者，我想我可以嘗試編寫一個簡單的測試來檢查一組整數mod K（L）是否是一個組。我開始試圖找出所述集合是否可加，即。如果L的每兩個元素之和也是L.

的元件I寫道：

group(A,K):-member(B,A),member(C,A),As is B+C, Bs is mod(As,K), member(Bs,A). 

我然後用這個嘗試了：

trace. group([0,1,2],3). 

這自然產生所有可能的總和，並且正確地回答所有這些答案都是正確的。

但所有這些情況後，最後打印如下：

1 1 Redo: group([0,1,2],3) ? 
    6 2 Redo: member(1,[0,1,2]) ? 
    6 2 Fail: member(1,[0,1,2]) ? 
    1 1 Fail: group([0,1,2],3) ? 
    no 

爲什麼程序會檢查這個最後的情況下，對我來說，似乎荒謬？

最後一種情況在此之前是：

1 1 Redo: group([0,1,2],3) ? 
    6 2 Redo: member(0,[0,1,2]) ? 
    6 2 Fail: member(0,[0,1,2]) ? 
    3 2 Redo: member(1,[0,1,2]) ? 
    3 2 Exit: member(2,[0,1,2]) ? 
    4 2 Call: _158 is 2+2 ? 
    4 2 Exit: 4 is 2+2 ? 
    5 2 Call: _186 is 4 mod 3 ? 
    5 2 Exit: 1 is 4 mod 3 ? 
    6 2 Call: member(1,[0,1,2]) ? 
    6 2 Exit: member(1,[0,1,2]) ? 
    1 1 Exit: group([0,1,2],3) ? 

    true 

它做什麼它應該。

Answer 1

使用示蹤劑達到這樣的目的不是很有幫助。它向你展示了許多無關緊要的細節。相反，要集中精力解決問題。專注於有意義的名字。對於該組，您使用A，對於元素使用B和C。這可以改善！

您目前的測試是什麼這樣的：

存在着一組其總和模K是在同一組的兩個元素。

要測試的是什麼：

對於所有的X，Y在S：（（X + Y）MOD K）S中

操作本身可以寫成：Z is (X+Y) mod K

示蹤劑如何向你解釋？

 
group(S, K) :- 
    \+ (
     member(X,S), member(Y,S), Z is (X+Y) mod K, 
     \+ member(Z,S) 
    ). 

?- group([0,1,2],3). 
true. 

?- group([0,2],3). 
false. 

Answer 2

我覺得示蹤劑向你展示了追蹤器跟隨的所有不同分支。爲此，它似乎否定了它嘗試過的最後一個分支的成功聲明之一，所以這次它將採用不同的解決方案。

看看整個執行過程中，你肯定會看到失敗的謂詞是真的，如第二次評估中的Fail: (7) lists:member(0, [0, 1, 2])。

[trace] ?- group([0, 1, 2], 3). 
    Call: (6) group([0, 1, 2], 3) ? creep 
    Call: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
    Call: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 0+0 ? creep 
^ Exit: (7) 0 is 0+0 ? creep 
^ Call: (7) _G724 is 0 mod 3 ? creep 
^ Exit: (7) 0 is 0 mod 3 ? creep 
    Call: (7) lists:member(0, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(0, [0, 1, 2]) ? creep 
    Fail: (7) lists:member(0, [0, 1, 2]) ? creep 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 0+1 ? creep 
^ Exit: (7) 1 is 0+1 ? creep 
^ Call: (7) _G724 is 1 mod 3 ? creep 
^ Exit: (7) 1 is 1 mod 3 ? creep 
    Call: (7) lists:member(1, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(1, [0, 1, 2]) ? creep 
    Fail: (7) lists:member(1, [0, 1, 2]) ? creep 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 0+2 ? creep 
^ Exit: (7) 2 is 0+2 ? creep 
^ Call: (7) _G724 is 2 mod 3 ? creep 
^ Exit: (7) 2 is 2 mod 3 ? creep 
    Call: (7) lists:member(2, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
    Call: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 1+0 ? creep 
^ Exit: (7) 1 is 1+0 ? creep 
^ Call: (7) _G724 is 1 mod 3 ? creep 
^ Exit: (7) 1 is 1 mod 3 ? creep 
    Call: (7) lists:member(1, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(1, [0, 1, 2]) ? creep 
    Fail: (7) lists:member(1, [0, 1, 2]) ? creep 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 1+1 ? creep 
^ Exit: (7) 2 is 1+1 ? creep 
^ Call: (7) _G724 is 2 mod 3 ? creep 
^ Exit: (7) 2 is 2 mod 3 ? creep 
    Call: (7) lists:member(2, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 1+2 ? creep 
^ Exit: (7) 3 is 1+2 ? creep 
^ Call: (7) _G724 is 3 mod 3 ? creep 
^ Exit: (7) 0 is 3 mod 3 ? creep 
    Call: (7) lists:member(0, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(0, [0, 1, 2]) ? creep 
    Fail: (7) lists:member(0, [0, 1, 2]) ? creep 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
    Call: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 2+0 ? creep 
^ Exit: (7) 2 is 2+0 ? creep 
^ Call: (7) _G724 is 2 mod 3 ? creep 
^ Exit: (7) 2 is 2 mod 3 ? creep 
    Call: (7) lists:member(2, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 2+1 ? creep 
^ Exit: (7) 3 is 2+1 ? creep 
^ Call: (7) _G724 is 3 mod 3 ? creep 
^ Exit: (7) 0 is 3 mod 3 ? creep 
    Call: (7) lists:member(0, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(0, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(0, [0, 1, 2]) ? creep 
    Fail: (7) lists:member(0, [0, 1, 2]) ? creep 
    Redo: (7) lists:member(_G718, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(2, [0, 1, 2]) ? creep 
^ Call: (7) _G721 is 2+2 ? creep 
^ Exit: (7) 4 is 2+2 ? creep 
^ Call: (7) _G724 is 4 mod 3 ? creep 
^ Exit: (7) 1 is 4 mod 3 ? creep 
    Call: (7) lists:member(1, [0, 1, 2]) ? creep 
    Exit: (7) lists:member(1, [0, 1, 2]) ? creep 
    Exit: (6) group([0, 1, 2], 3) ? creep 
true ; 
    Redo: (7) lists:member(1, [0, 1, 2]) ? creep 
    Fail: (7) lists:member(1, [0, 1, 2]) ? creep 
    Fail: (6) group([0, 1, 2], 3) ? creep 
false.