Can’t and Couldn’t
As cannot and could not may be used with pronouns of the first, second, or third person, in either number, and with nouns in both numbers, no error is likely to follow the use of their contracted forms.
Why cannot is properly written as one word, and could not requires two, is not founded upon any principle of philosophy. The concurrent sanction of all classes in all parts of the English-speaking world establishes it as law.
Observe that the a in the verb can’t is broader in sound than the short a in the noun cant.
Don’t and Didn’t
Don’t is a contraction of do not. It is in very general use and in good repute. It may be employed wherever the expanded expression do not could be applied, and only there.
“One swallow don’t make a spring” is equivalent to saying, “One swallow do not make a spring.” We may say “I don’t,” “You don’t,” “We don’t,” “They don’t,” “The men (or birds, or trees) don’t,” but we must use doesn’t with he, or she, or it, or the man, the grove, the cloud, etc.
Unlike the verb do, its past tense form did undergoes no change in conjugation, hence the contraction didn’t is also uniform.
Haven’t, Hasn’t, and Hadn’t
The verb have, like the verb do, has a distinct form for the third person singular. The same change affects the contraction. I haven’t, you haven’t, he hasn’t. The construction hadn’t undergoes no change.