If/had I needed to express a counterfactual

[Please note that this is a scheduled post, and I am taking part in the ongoing industrial action by my union, UCU.]

In a recent tweet, which I won't quote because the subject was too serious and grim for this light and fluffy discussion of linguistics, I saw the construction had/if. Like this: 

This is who I'd have spoken to had/if I needed help. 

It's like when you use and/or, to be clear that it's inclusive. If I write You'll enjoy this if you like fantasy and/or thrillers, then you'll like it if you like just one of those things or both of them. In other words, fantasy and thrillers, or fantasy, or thrillers. It just makes explicit the 'inclusive disjunction' (one or both are ok). 

But with had/if, there's no equivalent thing to make explicit. We can indeed use either of them in this sentence: This is who I'd have spoken to if I needed help and This is who I'd have spoken to had I needed help. But although had is a bit more formal, the meaning is the same, unlike with and/or. They both give a conditional interpretation. This made me wonder about the difference between them and after some struggle with finding out what the 'had' construnction was called (honestly it's hard to google linguistic things sometimes), I found Iatridou and Embick's 1994 article 'Conditional inversion'. 

It's called conditional inversion because it's used in conditionals, and the verb had is inverted with the subject: I had needed help vs Had I needed help. We use inversion a lot, including in questions (Had I needed help? Who can say.). 

So, if and inversion both indicate a conditional: 

If Sabine had eaten the calamari, she might be better by now.

Had Sabine eaten the calamari, she might be better by now. 

(Examples are all taken from Iatridou and Embick 1994, but with the name 'John' changed to 'Sabine' because John is in way too many linguistics example sentences.) 

Here's one difference between them, though. If can be used in situations where the thing might be true, and we just don't know the facts: 

If Sabine has eaten the calamari, there'll be none left for us. 

Inversion, meanwhile, can only be used in what are called counterfactuals, where we know the thing isn't the case, and you're talking about if it had been (but it isn't). In the equivalent example to the one just above, where it may or may not be true, it doesn't sound at all natural:  

*Has Sabine eaten the calamari, there'll be none left for us. 

(Remember the convention that an asterisk means that a sentence is not grammatical for speakers of the language under discussion.) 

And while if can be used with contracted negation (n't), inversion can't: 

If he hadn't seen the car coming, he would have been killed. 

*Hadn't he seen the car coming, he would have been killed.

Had he not seen the car coming, he would have been killed.

So there are some differences. But in the sentence I saw, where we began this, either would have been fine, because it was a counterfactual (she didn't need help), so inversion is ok, and if works in all conditionals so that would have been ok. So there's no reason to include both for covering more bases. It looks like one of those times when it feels like they mean something more than just using one of them, so you include both for the feeling of completeness.