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How does this proof that the halting pro​blem is undecidable work?

I am essentially asking how something works; in this case "this proof that the halting problem is undecidable."

BONUS: Is the following sentence, which is how someone "corrected" me, grammatically correct?

How does this prove that the halting pro​blem is undecidable work?

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    It's essentially a "garden path" sentence. When they read it, they thought you were asking "How does this prove that the halting problem is undecidable?" Of course, they should have gotten to the last word and realized that they were wrong. – Peter Shor Dec 7 '11 at 0:54
  • @PeterShor That's what I thought. I didn't know this had a name... Thanks! – Orion Dec 7 '11 at 0:57
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Yes, your original is correct. The relative content clause in the middle may be leading to confusion. How does this proof (that the halting pro​blem is undecidable) work?

The second is also grammatical if we take work to be a noun, but it doesn't mean what you intend. In fact, I have no idea what it might mean for a problem to be undecidable work.

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5

How does this proof that the halting pro​blem is undecidable work?

is correct. Alternatively use

How does this prove that the halting pro​blem is undecidable?

It is wrong to write

How does this prove that the halting pro​blem is undecidable work?

to mean what is intended. In the examples above, proof is a noun while prove is a verb.

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  • 4
    Proof is a verb too; it is probably not the verb that should be used, but it is still a verb. – kiamlaluno Dec 7 '11 at 0:58
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    It is not ungrammatical to write "How does this prove that the halting problem is undecidable work?" because it can be based as "How does this prove that (the halting problem is (undecidable work))?". I don't know what "undecidable work" is, but the words form a valid grammatical construct. – Hellion Dec 7 '11 at 2:41
3

Your sentence is grammatically correct but stylistically hard to understand. I recommend breaking it into two sentences. For instance:

This proof shows the halting problem is undecidable. How does this proof work?

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2

Grammatically correct, but possibly misleading, as other posters have pointed out. Obfuscated code, or obfuscated language can be an entertaining pastime, but does not lead to clear communications.

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