The form Had (he) is a formal variation of If (he) had
Had the management acted sooner, the strike wouldn t have happened
A negative inversion is possible with the full form
Had it not been for the unusually bad weather the rescue party would have been able to save the stranded climber (Not *Hadn t*)
Other uses of if and similar conjunctions
14.19 Type 3, Variation 1: 'If + past perfect + modal
'if'-clause: past perfect tense main clause: modal [> 11.1]
Imagined condition imagined outcome
If he had known the facts he could have told us what to do
If he could have got the facts might
Another modal can replace would in Type 3 conditionals e g when we feel that the imagined consequences were less likely or when we are referring to ability [> 11.15] possibility [> 11.28] etc
Imagined condition imagined outcome
If he had been here yesterday he could have told us (ability)
If he had been here yesterday he might have told us (possibility) If he had received a present he should have thanked her (duty)
Progressive and perfect combinations with modals are possible If he had been here he could have been helping us in the shop If she had been here she could have met my sister
Other uses of 'if and similar conjunctions
14.20 Negatives with 'if...not' and 'unless'
If not and unless are sometimes interchangeable but there are occasions when it is impossible to use one in place of the other