Message 内部的逻辑

问题描述

我想弄清楚Message行为的逻辑.

I am trying to figure out the logic of Message behavior.

考虑评估以下内容:

On[]
Sin[1,1]

评估上述内容后，您将获得大约 830 (!) 个 Messages(在 Mathematica 7 中).

After evaluating the above you will get about 830 (!) Messages (in Mathematica 7).

所有这些Messages都是在制作过程中出现的:

All these Messages have arisen during producing the one:

Sin::argx: Sin called with 2 arguments; 1 argument is expected. >>

(这是最后一个Message).

最后一个Message

Message::trace: Message[Sin::argx,Sin,2] --> Null. >>

对应于完成Mathematica内部的Message函数的工作.大多数其他 Messages 来自对 $NewMessage 和 $MessagePrePrint 的评估.

corresponds to finishing of the work of internal Mathematica's Message function. Most of the other Messages go from evaluation of $NewMessage and $MessagePrePrint.

我的问题是:

1) 为什么没有Message生成的无限循环?如果调用 Message[Sin::argx,Sin,2] 会产生超过 830 条其他 Messages 为什么它们每个不会产生相似数量的 Messages>?如何模拟这种行为(通过编写 Message 的模拟)?

1) Why there are no infinite loop of Message generation? If calling Message[Sin::argx,Sin,2] produces more than 830 other Messages why each of them does not produce similar number of Messages? How such behavior can be simulated (by writing an analog of Message)?

2) 是否可以强制 Message 在跟踪模式下调用时不产生任何额外的 Messages(我的意思是评估 On 后的模式)[])?

2) Is it possible to force Message do not produce any additional Messages when it is called in the tracing mode (I mean the mode after evaluating On[])?

推荐答案

我似乎找到了一种用内置函数 Message 实现我想要的方法:

It seems that I have found one way to achieve with built-in function Message what I want:

Unprotect[Message];
Message[_, HoldForm[Block[List[$MyMagicalTag$, ___], _]], _] := Null;
Message[args___] /; 
   Block[{$MyMagicalTag$, Message}, Not@TrueQ[inMsg]] := 
  Block[{$MyMagicalTag$, inMsg = True, lastargs = HoldComplete[args]},
    Message[args]];
Message[args___] /; 
   Block[{$MyMagicalTag$, 
     Message}, (inMsg && (HoldComplete[args] =!= lastargs))] := Null;
Protect[Message];

现在一切按预期进行:

In[6]:= On[]
In[7]:= Sin[1,1]//AbsoluteTiming
During evaluation of In[7]:= Message::trace: Message[Sin::argx,Sin,2] --> Block[{$MyMagicalTag$,inMsg=True,lastargs=HoldComplete[Sin::argx,Sin,2]},Message[Sin::argx,Sin,2]]. >>
During evaluation of In[7]:= Sin::argx: Sin called with 2 arguments; 1 argument is expected. >>
During evaluation of In[7]:= AbsoluteTiming::trace: AbsoluteTiming[Sin[1,1]] --> {0.1502160,Sin[1,1]}. >>
Out[7]= {0.1502160,Sin[1,1]}

上述唯一的问题是 CPU 负载仍然很高，正如您从时序中看到的那样.

The only problem with the above is that CPU load is still high as you can see from the timings.

其他经过测试的案例也能正常工作:

Other tested cases also work correctly:

In[8]:= 1+1//AbsoluteTiming
During evaluation of In[8]:= Plus::trace: 1+1 --> 2. >>
During evaluation of In[8]:= AbsoluteTiming::trace: AbsoluteTiming[1+1] --> {0.0400576,2}. >>
Out[8]= {0.0400576,2}

感谢 Mr.Wizard 的 帮助.

Thanks to Mr.Wizard for his help.

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