Modals in the first conditional

Main clause

We can use modals other than will in the main clause of a sentence in the first conditional:

If you ask George, he may/might be able to help you. (possibility)
You can/may leave the room if you've finished the test. (permission)
If he doesn't come soon, we must / will have to leave without him. (obligation)
If you ever go to Chicago, you should take a boat trip on the river. (suggestion)
If you don't watch your steps, you are going to fall over. (prediction)

If-clause

We can use be going to in the if-clause to express intention:

If you are going to speak like that, you'll have to leave.

Should in the if-clause makes the condition less likely:

If you should see Kate, say hi from me.

In the if-clause, willingness can be expressed by will and refusal by won't. In this sense will and won't are always stressed in speech and cannot be contracted with the subject in writing:

If you will take me to the airport tomorrow, I won't have to take a taxi.
If Greg won't answer the phone, I'll speak to his roommate.

We can also use will in the if-clause to express a polite request. Sometimes the main clause is omitted:

If you will wait for a moment, I'll see if Mr Hawking is available.
If you'll just fill in this form, please.