I'm a Japanese, learning English in Japan.

When you use "had to", can a "but" follow it?
For example, can you say
"I had to do my homework but I didn't."

In a Japanese grammar book,
It says "had to" is used only when you
"did" the thing you "had to" such as,
"I had to work last night, so I didn't watch the program."

Is it true?

I understand you can say,
"I should have worked last night, but I watched the program."
But I also have a feeling that
"I had to do my homework but I didn't."
Is also correct...

Congratulations on your efforts. Learning English is not easy as you will hear many variations in the same language. To answer your question... Yes, contemporary English usage does allow you to say, "I had to do my homework, but I didn't." When I was growiing up the rules of grammar and syntax and order were much stricter than they are now. I even doubt that diagraming sentecnes is taught anymore.
Best of luck to you in your learning!

Hi shyg,
I understand your question show your keen interest in finer aspects of the subject. Yes, you are correct. Should have... is surely a better alternative. Using had to is not advisible to use in the given context.
If you are above intermediate level student of english, I very strongly advise you to go through a book. ' a guide to english patters and strucutre' by hornby. Though the total book may not be useful to you, the last chapter gives you a very authentic info about the concepts. If you want a similar book, you can go to you can go through 'communicative grammar of english' by svartik and leech.
The all -time fav of eng grammar book is of course... practical english grammar by thomson and martinet.
I am suggesting these books as I find you fit enough to go through any one of them.
With best compliments,
ramanamlv