prolog - 在 CLPQ/R (Prolog) 中解决一个简单的几何难题

Question

考虑以下正方形:

You are given three constraints:

1. All rectangles (A, B, C, D and E) have the same area;
2. Their geometric layout constitutes a square; and
3. The height of A is 2.

现在，我知道手动解决这个问题非常简单，但我认为这将是一个很好的例子来展示 CLP(Q/R) 与 Prolog 的功能:

剧透警报:如果您想先自己解决难题，请不要继续阅读本文，因为存在一些限制条件会泄露解决方案。

无论如何，这是我尝试用 CLP(Q/R) 定义(我认为包括冗余约束)这个难题:

:- use_module(library(clpr)).

solve(Eh) :-
  A = B, B = C, C = D, D = E,

  { A  >= 1, B  >= 1, C  >= 1, D  >= 1, E  >= 1,
    Aw >= 1, Bw >= 1, Cw >= 1, Dw >= 1, Ew >= 1 },
  
  { Ah = 2 },
  
  { A = Ah * Aw,
    B = Bh * Bw,
    C = Ch * Cw,
    D = Dh * Dw,
    E = Eh * Ew },

  { (Bw + Cw) = Aw,
     Dw = Cw,
    (Ah + Bh) = Eh,
    (Ch + Dh) = Bh,
    (Aw + Ew) = Eh },

  minimize(Eh).

查询时:

?- solve(Eh).
false.

...让我伤心。这样一个约束求解器的美丽例子......有人愿意消除我的悲伤吗？

附录:我使用了 Mathematica 和 FindMinimum函数来检查我的约束。它似乎有效:

domain = a >= 1 && b >= 1 && c >= 1 && d >= 1 && e >= 1 && ah == 2.0 && a == b == c == d == e && aw >= 1 && bw >= 1 && cw >= 1 && dw >= 1 && ew >= 1
rectangles = (a == ah*aw && b == bh*bw && c == ch*cw && d == dh*dw && e == eh*ew)

FindMinimum[{eh, 
  domain && rectangles &&
  ((bw + cw ) == aw && dw == cw && (ah + bh) == eh && (ch + dh) == bh && (aw + ew) == eh)}, 
  {a, b, c, d, e, ah, aw, bh, bw, ch, cw, dh, dw, eh, ew}]

答案:

{8., {a -> 12.8, b -> 12.8, c -> 12.8, d -> 12.8, e -> 12.8, 
      ah -> 2., aw -> 6.4, bh -> 6., bw -> 2.13333, ch -> 3., 
      cw -> 4.26667, dh -> 3., dw -> 4.26667, 
      eh -> 8., ew -> 1.6}}

Answer 1

CLP 中有一个旧/新条目，clpBNR .您可以将其安装在最新版本的 SWI-Prolog 中。
我认为需要将方程组合成一个 {}。

?- pack_install(clpBNR).

:- use_module(library(clpBNR)).

solve_(Eh) :-
  Vs = [A,B,C,D,E, Aw,Bw,Cw,Dw,Ew, Ah,Bh,Ch,Dh,Eh],
  Vs::real(1,100),

  { Ah == 2,

    A is Ah * Aw,
    B is Bh * Bw,
    C is Ch * Cw,
    D is Dh * Dw,
    E is Eh * Ew,

    A == B,
    B == C,
    C == D,
    D == E,

    (Bw + Cw) == Aw,
     Dw == Cw,
    (Ah + Bh) == Eh,
    (Ch + Dh) == Bh,
    (Aw + Ew) == Eh
  },

  solve(Vs).

?- solve_(Eh).
::(Eh, ...( 8.000000)) .