Question

我在Prolog中在线找到了用于矩阵乘法的代码，有Prolog经验的人可以向我解释吗？

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Answer 1

以%开头的行是注释

大多数编程语言都有方法和功能。 Prolog的predicates成功或失败，可以将值传递给变量。

谓词由其名称和别名transpose/2表示。

大多数编程语言都使用赋值，但是Prolog使用unification。对于解决数学表达式的特殊情况，Prolog具有is/2

:- use_module(library(clpfd)).

是指令:-，它引入了一个名为clpfd的库。 clpfd通常用于约束，但在这种情况下，用于访问transpose/2谓词。

dot(V1, V2, N) :- 
    maplist(product,V1,V2,P), 
    sumlist(P,N).

dot/3是一个包含两个向量的谓词，我想在这种情况下实现为Prolog list，并将dot product绑定为N。
maplist/4将乘积/ 3谓词应用于V1和V2中的值以创建列表P。
sumlist/2将P中的值列表加起来并绑定N。

product(N1,N2,N3) :- N3 is N1*N2.

product/3是一个辅助谓词，取两个数字N1和N2并将它们相乘。

N3 is N1*N2可以被认为是N3 = (N1 * N2)

mmult(M1, M2, M3) :- 
    transpose(M2,MT), 
    maplist(mm_helper(MT), M1, M3).

transpose/2是典型的数组转置。
maplist/3使用mm_helper/3和MT来绑定M1来使用辅助谓词M3。

mm_helper(M2, I1, M3) :- 
    maplist(dot(I1), M2, M3).

maplist/3将dot/3应用于I1和M2来绑定M3。

我认为您是从RosettaCode那里获取代码的，或者它是与之交叉的。

示例运行：

?- mmult([[1,2],[3,4]],[[5,6],[7,8]],R).
R = [[19, 22], [43, 50]] ;
true.

Verification的示例。

来自评论。

I1在mm_helper谓词中代表什么？

有关详细信息，请参见下面的跟踪

mm_helper/3的签名为mm_helper(M2, I1, M3)，因此第二个参数包含I1。从跟踪中的行

Exit: (11) mm_helper([[5, 7], [6, 8]], [3, 4], [43, 50])

第二个参数是[3,4]。

Call: (10) mm_helper([[5, 7], [6, 8]], [1, 2], _3596)

第二个参数是[1,2]。

所以I2是第一个矩阵的行切片。

请小心您的要求，您可能会得到超出预期的收益？：）

完整的运行轨迹：

仅在这里是因为评论中有一个问题。

[trace]  ?- mmult([[1,2],[3,4]],[[5,6],[7,8]],R).


   Call: (8) mmult([[1, 2], [3, 4]], [[5, 6], [7, 8]], _3238)
   Unify: (8) mmult([[1, 2], [3, 4]], [[5, 6], [7, 8]], _3238)
   Call: (9) clpfd:transpose([[5, 6], [7, 8]], _3536)
   Unify: (9) clpfd:transpose([[5, 6], [7, 8]], _3536)
   Call: (10) error:must_be(list(list), [[5, 6], [7, 8]])
   Unify: (10) error:must_be(list(list), [[5, 6], [7, 8]])
   Exit: (10) error:must_be(list(list), [[5, 6], [7, 8]])
   Call: (10) clpfd:lists_transpose([[5, 6], [7, 8]], _3540)
   Unify: (10) clpfd:lists_transpose([[5, 6], [7, 8]], _3540)
   Call: (11) clpfd:'__aux_maplist/2_same_length+1'([[7, 8]], [5, 6])
   Unify: (11) clpfd:'__aux_maplist/2_same_length+1'([[7, 8]], [5, 6])
   Call: (12) lists:same_length([5, 6], [7, 8])
   Unify: (12) lists:same_length([5, 6], [7, 8])
   Exit: (12) lists:same_length([5, 6], [7, 8])
   Call: (12) clpfd:'__aux_maplist/2_same_length+1'([], [5, 6])
   Unify: (12) clpfd:'__aux_maplist/2_same_length+1'([], [5, 6])
   Exit: (12) clpfd:'__aux_maplist/2_same_length+1'([], [5, 6])
   Exit: (11) clpfd:'__aux_maplist/2_same_length+1'([[7, 8]], [5, 6])
^  Call: (11) apply:foldl(transpose_, [5, 6], _3548, [[5, 6], [7, 8]], _3552)
^  Unify: (11) apply:foldl(clpfd:transpose_, [5, 6], _3554, [[5, 6], [7, 8]], _3558)
   Call: (12) apply:foldl_([5, 6], _3552, clpfd:transpose_, [[5, 6], [7, 8]], _3558)
   Unify: (12) apply:foldl_([5, 6], [_3536|_3538], clpfd:transpose_, [[5, 6], [7, 8]], _3564)
   Call: (13) clpfd:transpose_(5, _3536, [[5, 6], [7, 8]], _3562)
   Unify: (13) clpfd:transpose_(5, _3536, [[5, 6], [7, 8]], _3562)
   Call: (14) clpfd:'__aux_maplist/4_list_first_rest+0'([[5, 6], [7, 8]], _3536, _3560)
   Unify: (14) clpfd:'__aux_maplist/4_list_first_rest+0'([[5, 6], [7, 8]], [_3542|_3544], [_3548|_3550])
   Call: (15) clpfd:list_first_rest([5, 6], _3542, _3548)
   Unify: (15) clpfd:list_first_rest([5, 6], 5, [6])
   Exit: (15) clpfd:list_first_rest([5, 6], 5, [6])
   Call: (15) clpfd:'__aux_maplist/4_list_first_rest+0'([[7, 8]], _3544, _3550)
   Unify: (15) clpfd:'__aux_maplist/4_list_first_rest+0'([[7, 8]], [_3554|_3556], [_3560|_3562])
   Call: (16) clpfd:list_first_rest([7, 8], _3554, _3560)
   Unify: (16) clpfd:list_first_rest([7, 8], 7, [8])
   Exit: (16) clpfd:list_first_rest([7, 8], 7, [8])
   Call: (16) clpfd:'__aux_maplist/4_list_first_rest+0'([], _3556, _3562)
   Unify: (16) clpfd:'__aux_maplist/4_list_first_rest+0'([], [], [])
   Exit: (16) clpfd:'__aux_maplist/4_list_first_rest+0'([], [], [])
   Exit: (15) clpfd:'__aux_maplist/4_list_first_rest+0'([[7, 8]], [7], [[8]])
   Exit: (14) clpfd:'__aux_maplist/4_list_first_rest+0'([[5, 6], [7, 8]], [5, 7], [[6], [8]])
   Exit: (13) clpfd:transpose_(5, [5, 7], [[5, 6], [7, 8]], [[6], [8]])
   Call: (13) apply:foldl_([6], _3538, clpfd:transpose_, [[6], [8]], _3588)
   Unify: (13) apply:foldl_([6], [_3566|_3568], clpfd:transpose_, [[6], [8]], _3594)
   Call: (14) clpfd:transpose_(6, _3566, [[6], [8]], _3592)
   Unify: (14) clpfd:transpose_(6, _3566, [[6], [8]], _3592)
   Call: (15) clpfd:'__aux_maplist/4_list_first_rest+0'([[6], [8]], _3566, _3590)
   Unify: (15) clpfd:'__aux_maplist/4_list_first_rest+0'([[6], [8]], [_3572|_3574], [_3578|_3580])
   Call: (16) clpfd:list_first_rest([6], _3572, _3578)
   Unify: (16) clpfd:list_first_rest([6], 6, [])
   Exit: (16) clpfd:list_first_rest([6], 6, [])
   Call: (16) clpfd:'__aux_maplist/4_list_first_rest+0'([[8]], _3574, _3580)
   Unify: (16) clpfd:'__aux_maplist/4_list_first_rest+0'([[8]], [_3584|_3586], [_3590|_3592])
   Call: (17) clpfd:list_first_rest([8], _3584, _3590)
   Unify: (17) clpfd:list_first_rest([8], 8, [])
   Exit: (17) clpfd:list_first_rest([8], 8, [])
   Call: (17) clpfd:'__aux_maplist/4_list_first_rest+0'([], _3586, _3592)
   Unify: (17) clpfd:'__aux_maplist/4_list_first_rest+0'([], [], [])
   Exit: (17) clpfd:'__aux_maplist/4_list_first_rest+0'([], [], [])
   Exit: (16) clpfd:'__aux_maplist/4_list_first_rest+0'([[8]], [8], [[]])
   Exit: (15) clpfd:'__aux_maplist/4_list_first_rest+0'([[6], [8]], [6, 8], [[], []])
   Exit: (14) clpfd:transpose_(6, [6, 8], [[6], [8]], [[], []])
   Call: (14) apply:foldl_([], _3568, clpfd:transpose_, [[], []], _3618)
   Unify: (14) apply:foldl_([], [], clpfd:transpose_, [[], []], [[], []])
   Exit: (14) apply:foldl_([], [], clpfd:transpose_, [[], []], [[], []])
   Exit: (13) apply:foldl_([6], [[6, 8]], clpfd:transpose_, [[6], [8]], [[], []])
   Exit: (12) apply:foldl_([5, 6], [[5, 7], [6, 8]], clpfd:transpose_, [[5, 6], [7, 8]], [[], []])
^  Exit: (11) apply:foldl(clpfd:transpose_, [5, 6], [[5, 7], [6, 8]], [[5, 6], [7, 8]], [[], []])
   Exit: (10) clpfd:lists_transpose([[5, 6], [7, 8]], [[5, 7], [6, 8]])
   Exit: (9) clpfd:transpose([[5, 6], [7, 8]], [[5, 7], [6, 8]])
   Call: (9) '__aux_maplist/3_mm_helper+1'([[1, 2], [3, 4]], _3238, [[5, 7], [6, 8]])
   Unify: (9) '__aux_maplist/3_mm_helper+1'([[1, 2], [3, 4]], [_3596|_3598], [[5, 7], [6, 8]])
   Call: (10) mm_helper([[5, 7], [6, 8]], [1, 2], _3596)
   Unify: (10) mm_helper([[5, 7], [6, 8]], [1, 2], _3596)
   Call: (11) '__aux_maplist/3_dot+1'([[5, 7], [6, 8]], _3596, [1, 2])
   Unify: (11) '__aux_maplist/3_dot+1'([[5, 7], [6, 8]], [_3602|_3604], [1, 2])
   Call: (12) dot([1, 2], [5, 7], _3602)
   Unify: (12) dot([1, 2], [5, 7], _3602)
   Call: (13) '__aux_maplist/4_product+0'([1, 2], [5, 7], _3626)
   Unify: (13) '__aux_maplist/4_product+0'([1, 2], [5, 7], [_3608|_3610])
   Call: (14) product(1, 5, _3608)
   Unify: (14) product(1, 5, _3608)
   Call: (15) _3608 is 1*5
   Exit: (15) 5 is 1*5
   Exit: (14) product(1, 5, 5)
   Call: (14) '__aux_maplist/4_product+0'([2], [7], _3610)
   Unify: (14) '__aux_maplist/4_product+0'([2], [7], [_3620|_3622])
   Call: (15) product(2, 7, _3620)
   Unify: (15) product(2, 7, _3620)
   Call: (16) _3620 is 2*7
   Exit: (16) 14 is 2*7
   Exit: (15) product(2, 7, 14)
   Call: (15) '__aux_maplist/4_product+0'([], [], _3622)
   Unify: (15) '__aux_maplist/4_product+0'([], [], [])
   Exit: (15) '__aux_maplist/4_product+0'([], [], [])
   Exit: (14) '__aux_maplist/4_product+0'([2], [7], [14])
   Exit: (13) '__aux_maplist/4_product+0'([1, 2], [5, 7], [5, 14])
   Call: (13) backward_compatibility:sumlist([5, 14], _3602)
   Unify: (13) backward_compatibility:sumlist([5, 14], _3602)
   Call: (14) lists:sum_list([5, 14], _3602)
   Unify: (14) lists:sum_list([5, 14], _3602)
   Exit: (14) lists:sum_list([5, 14], 19)
   Exit: (13) backward_compatibility:sumlist([5, 14], 19)
   Exit: (12) dot([1, 2], [5, 7], 19)
   Call: (12) '__aux_maplist/3_dot+1'([[6, 8]], _3604, [1, 2])
   Unify: (12) '__aux_maplist/3_dot+1'([[6, 8]], [_3644|_3646], [1, 2])
   Call: (13) dot([1, 2], [6, 8], _3644)
   Unify: (13) dot([1, 2], [6, 8], _3644)
   Call: (14) '__aux_maplist/4_product+0'([1, 2], [6, 8], _3668)
   Unify: (14) '__aux_maplist/4_product+0'([1, 2], [6, 8], [_3650|_3652])
   Call: (15) product(1, 6, _3650)
   Unify: (15) product(1, 6, _3650)
   Call: (16) _3650 is 1*6
   Exit: (16) 6 is 1*6
   Exit: (15) product(1, 6, 6)
   Call: (15) '__aux_maplist/4_product+0'([2], [8], _3652)
   Unify: (15) '__aux_maplist/4_product+0'([2], [8], [_3662|_3664])
   Call: (16) product(2, 8, _3662)
   Unify: (16) product(2, 8, _3662)
   Call: (17) _3662 is 2*8
   Exit: (17) 16 is 2*8
   Exit: (16) product(2, 8, 16)
   Call: (16) '__aux_maplist/4_product+0'([], [], _3664)
   Unify: (16) '__aux_maplist/4_product+0'([], [], [])
   Exit: (16) '__aux_maplist/4_product+0'([], [], [])
   Exit: (15) '__aux_maplist/4_product+0'([2], [8], [16])
   Exit: (14) '__aux_maplist/4_product+0'([1, 2], [6, 8], [6, 16])
   Call: (14) backward_compatibility:sumlist([6, 16], _3644)
   Unify: (14) backward_compatibility:sumlist([6, 16], _3644)
   Call: (15) lists:sum_list([6, 16], _3644)
   Unify: (15) lists:sum_list([6, 16], _3644)
   Exit: (15) lists:sum_list([6, 16], 22)
   Exit: (14) backward_compatibility:sumlist([6, 16], 22)
   Exit: (13) dot([1, 2], [6, 8], 22)
   Call: (13) '__aux_maplist/3_dot+1'([], _3646, [1, 2])
   Unify: (13) '__aux_maplist/3_dot+1'([], [], [1, 2])
   Exit: (13) '__aux_maplist/3_dot+1'([], [], [1, 2])
   Exit: (12) '__aux_maplist/3_dot+1'([[6, 8]], [22], [1, 2])
   Exit: (11) '__aux_maplist/3_dot+1'([[5, 7], [6, 8]], [19, 22], [1, 2])
   Exit: (10) mm_helper([[5, 7], [6, 8]], [1, 2], [19, 22])
   Call: (10) '__aux_maplist/3_mm_helper+1'([[3, 4]], _3598, [[5, 7], [6, 8]])
   Unify: (10) '__aux_maplist/3_mm_helper+1'([[3, 4]], [_3686|_3688], [[5, 7], [6, 8]])
   Call: (11) mm_helper([[5, 7], [6, 8]], [3, 4], _3686)
   Unify: (11) mm_helper([[5, 7], [6, 8]], [3, 4], _3686)
   Call: (12) '__aux_maplist/3_dot+1'([[5, 7], [6, 8]], _3686, [3, 4])
   Unify: (12) '__aux_maplist/3_dot+1'([[5, 7], [6, 8]], [_3692|_3694], [3, 4])
   Call: (13) dot([3, 4], [5, 7], _3692)
   Unify: (13) dot([3, 4], [5, 7], _3692)
   Call: (14) '__aux_maplist/4_product+0'([3, 4], [5, 7], _3716)
   Unify: (14) '__aux_maplist/4_product+0'([3, 4], [5, 7], [_3698|_3700])
   Call: (15) product(3, 5, _3698)
   Unify: (15) product(3, 5, _3698)
   Call: (16) _3698 is 3*5
   Exit: (16) 15 is 3*5
   Exit: (15) product(3, 5, 15)
   Call: (15) '__aux_maplist/4_product+0'([4], [7], _3700)
   Unify: (15) '__aux_maplist/4_product+0'([4], [7], [_3710|_3712])
   Call: (16) product(4, 7, _3710)
   Unify: (16) product(4, 7, _3710)
   Call: (17) _3710 is 4*7
   Exit: (17) 28 is 4*7
   Exit: (16) product(4, 7, 28)
   Call: (16) '__aux_maplist/4_product+0'([], [], _3712)
   Unify: (16) '__aux_maplist/4_product+0'([], [], [])
   Exit: (16) '__aux_maplist/4_product+0'([], [], [])
   Exit: (15) '__aux_maplist/4_product+0'([4], [7], [28])
   Exit: (14) '__aux_maplist/4_product+0'([3, 4], [5, 7], [15, 28])
   Call: (14) backward_compatibility:sumlist([15, 28], _3692)
   Unify: (14) backward_compatibility:sumlist([15, 28], _3692)
   Call: (15) lists:sum_list([15, 28], _3692)
   Unify: (15) lists:sum_list([15, 28], _3692)
   Exit: (15) lists:sum_list([15, 28], 43)
   Exit: (14) backward_compatibility:sumlist([15, 28], 43)
   Exit: (13) dot([3, 4], [5, 7], 43)
   Call: (13) '__aux_maplist/3_dot+1'([[6, 8]], _3694, [3, 4])
   Unify: (13) '__aux_maplist/3_dot+1'([[6, 8]], [_3734|_3736], [3, 4])
   Call: (14) dot([3, 4], [6, 8], _3734)
   Unify: (14) dot([3, 4], [6, 8], _3734)
   Call: (15) '__aux_maplist/4_product+0'([3, 4], [6, 8], _3758)
   Unify: (15) '__aux_maplist/4_product+0'([3, 4], [6, 8], [_3740|_3742])
   Call: (16) product(3, 6, _3740)
   Unify: (16) product(3, 6, _3740)
   Call: (17) _3740 is 3*6
   Exit: (17) 18 is 3*6
   Exit: (16) product(3, 6, 18)
   Call: (16) '__aux_maplist/4_product+0'([4], [8], _3742)
   Unify: (16) '__aux_maplist/4_product+0'([4], [8], [_3752|_3754])
   Call: (17) product(4, 8, _3752)
   Unify: (17) product(4, 8, _3752)
   Call: (18) _3752 is 4*8
   Exit: (18) 32 is 4*8
   Exit: (17) product(4, 8, 32)
   Call: (17) '__aux_maplist/4_product+0'([], [], _3754)
   Unify: (17) '__aux_maplist/4_product+0'([], [], [])
   Exit: (17) '__aux_maplist/4_product+0'([], [], [])
   Exit: (16) '__aux_maplist/4_product+0'([4], [8], [32])
   Exit: (15) '__aux_maplist/4_product+0'([3, 4], [6, 8], [18, 32])
   Call: (15) backward_compatibility:sumlist([18, 32], _3734)
   Unify: (15) backward_compatibility:sumlist([18, 32], _3734)
   Call: (16) lists:sum_list([18, 32], _3734)
   Unify: (16) lists:sum_list([18, 32], _3734)
   Exit: (16) lists:sum_list([18, 32], 50)
   Exit: (15) backward_compatibility:sumlist([18, 32], 50)
   Exit: (14) dot([3, 4], [6, 8], 50)
   Call: (14) '__aux_maplist/3_dot+1'([], _3736, [3, 4])
   Unify: (14) '__aux_maplist/3_dot+1'([], [], [3, 4])
   Exit: (14) '__aux_maplist/3_dot+1'([], [], [3, 4])
   Exit: (13) '__aux_maplist/3_dot+1'([[6, 8]], [50], [3, 4])
   Exit: (12) '__aux_maplist/3_dot+1'([[5, 7], [6, 8]], [43, 50], [3, 4])
   Exit: (11) mm_helper([[5, 7], [6, 8]], [3, 4], [43, 50])
   Call: (11) '__aux_maplist/3_mm_helper+1'([], _3688, [[5, 7], [6, 8]])
   Unify: (11) '__aux_maplist/3_mm_helper+1'([], [], [[5, 7], [6, 8]])
   Exit: (11) '__aux_maplist/3_mm_helper+1'([]

Answer 2

这看起来太可怕了！但这是有道理的。

很明显％是评论的开头（以防万一，不清楚）

：-正在定义一个函数

一个函数是一系列其他函数，用逗号分隔。

参数通过引用传递（因此没有返回值），在最后一个参数上方的代码中，每个函数的结果都存储在该参数中。我想这是序言中的某种约定，因为库函数似乎也是如此。

maplist听起来像是将一个函数应用于传递的列表中的每个元素（即列表中的map），将值存储在结果列表中（最后一个参数）。您可以用谷歌此功能进行确认。但这对于定义点积函数的方式很有用。

转置大概只是普通的矩阵转置（从库中导入-根据顶部注释）。

涵盖了我所看到的所有语法。因此最终它定义了mmult（）函数，该函数需要3个输入，M1和M2是数字（即矩阵）列表的列表，而M3是输出。

矩阵乘法序言

2 个答案: