Let's have some fun with 'No smoking'. One common way we come across this phrase is as a sign in public places. If we apply what DfE 'grammar' has to say about the phrase, as I have put it on the page here, we get this:
'smoking' is a present participle. Because it has the word 'no' in front of it, we can deduce that it is being used here as a noun. The word for this is a 'gerund'.
The word 'no' here is being used as some kind of 'determiner' along the lines of words like 'some', 'any', 'both', 'all' or 'my' or 'your' and so on.
Put this together and we have a phrase that describes a situation: a state of being in which there is not any smoking. That's to say, 'there is no smoking in this place'.
But this is absurd. We all know that the phrase in the context of public signs means, 'Don't smoke'. How do we know this? From experience and context. We hold that bit of knowledge and grammar in our heads every time we see the sign. But DfE 'grammar' doesn't tell us this.
DfE 'grammar' does have words about 'commands' though. These are apparently restricted to the kinds of sentences where verbs are used in the 'imperative' as with 'Go out', or 'Do this'.
This is nonsense too. We 'command' in lots of different ways in English, each one dependent on who's speaking/writing, who is the intended audience, what is the theme, what is the genre. So in some contexts we might say, 'You mustn't do that!' Historically, in the Bible it says, 'Thou shalt not...' And here with 'No smoking' is another way we have developed to issue commands on notices in public places: 'No ball games' and the like.
So what can DfE 'grammar' make of this? One way is to park it. There's a trick that grammarians play where whenever they meet a phrase or sentence that doesn't fit their schemas add systems. They say that the grammar of the phrase is particular to itself. Some proverbs pose them problems like this: 'More haste, less speed'. They sometimes describe these things as 'contracted' or with words that are 'understood'. Or that they are part of 'block language'. This is a nonsense: these phrases are what they are. If the people using them understand them, they are doing the job we designed them to do. It's just a fudge to park them in these 'exception' categories. They are part of how we are creative and inventive in making language and making meaning.
Clearly then, 'No smoking' has got its grammar. If it didn't, it would be meaningless. Its grammar is not to be found in 'grammar' though! Its true grammar is to be found in descriptions of its contexts which tell us that it is a form of command or order or direction and that this 'construction': 'no'+ a noun or gerund - will do the job. However, we can only determine this 'grammar' from the context. The context isn't separate from the grammar. It's part of the grammar, mixed in with it, as inseparable from it as flour is from egg in a baked cake!
