absolute clauses - Is 'The customer having left, ...' a dangling participle?

I found the following sentence in one of our questions: Use of "having" in English,

The customer having left, the criminal takes out a pin from his purse and scrapes off hardened glue from the edges of the keys.

It gave me a grammar warning immediately. After thinking about it for a while, I concluded two points:

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  The phrase The customer having left looks odd as a participle phrase. It should be just Having left. But then again, if the part The customer were removed, we would have gotten another kind of error, and the meaning would have been changed.

  
  


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  It seem like The customer having left is a dangling participle phrase. The phrase itself and the main clause don't seem to cohere well enough. Some conjunction such as after should have been added, or the sentence should have been revised.

  
  

So I would like to ask: Is the phrase 'the customer having left' above good English?

_{NOTE: I personally don't think it is, otherwise I could write something funny such as this:}

John walking into the woods, I followed him, we walking together for two hours, John walked, I walked, John having fallen down, I picked him up, we continuing walking, I like the woods, the woods smelling nice, John saying something, I didn't hear him, we continuing walking, John keeping walking, this was so much fun.

Answer

It is not a dangling participle per se, but rather an example of an absolute (which I was taught to call nominative absolute).

A so-called "dangling participle" is a participial phrase which is ambiguous as to what it modifies, e.g.

Watching the sunset, the beach went silent.

In the above case, the sentence reads as if the beach were watching, rather than the people.

In the construction you have cited, there is no ambiguity as to who is leaving; it is clearly the customer. The construction serves to provide contextual information, essentially modifying the entire sentence or clause. It does not modify any individual word in a sentence, and can be removed without changing the meaning, hence the term absolute (borrowed from Latin grammar and its ablative absolutes).

I would not say absolutes are especially common, but they are a familiar feature:

Economically speaking, Turkey has performed well.

The committee having completed its business, the meeting was adjourned at 12:00 noon.

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.