In a broader sense, verbs are generally of two types - Auxiliary verbs and Lexical verbs.
Auxiliary Verbs are further classified into two - Modal auxiliary verbs and Non-Modal Auxiliary Verbs.
So to know whether have to is a modal verb or not, we have to first know whether it's a lexical verb or an auxiliary verb.
LEXICAL VERB vs AUXILIARY VERBS
A good device to distinguish an auxiliary verb from other lexical verbs is NICE. It stands for (N)egation, (I)nversion, (C)ode and (E)mphasis.
- NEGATION - (Primary Verb negation)
A lexical verb takes do support for negation, generally, but an auxiliary verb doesn't.
I don't want it any more. [want - A lexical verb, needs do-support]
He is not a thief. [is - is an auxiliary verb, and so don't need any do-support]
But have to behaves little differently in case of negation. For negation, it can take do-support, or it can go without it. Both constructions are fine.
He doesn't have to be that cautious.
We have not to repeat it again.
You know, you have to not be somebody who takes all of their anger.
For inversion also, a lexical verb takes do-support, but an auxiliary verb doesn't.
Do you want another drink? [The lexical verb - want - takes do-support for inversion]
Is he a film star? [The auxiliary verb - is - doesn't take do-support for inversion]
Let's check how have to behaves during INVERSION -
Do I have to study hard?
I have to study hard -> * Have to I study hard? [INCORRECT]
I have to study hard -> * Have I to study hard? [INCORRECT]
So in this construction, have to behaves like a lexical verb.
It's like ellipsis. The Verb Phrase (VP) of a clause is reduced. And the reduced portion is recovered from the context. In the following sentences the reduced or elliptical position is denoted by a "___". An auxiliary verb can take part in such way, but a lexical verb can't.
I can drive this car, and Bill can ____ too. [The elliptical portion - drive this car - is denoted by a "___"]
This sentence is correct because the auxiliary verb - can - take part in such constructions.
I want to drive that car, and my friend wants ___ too. [INCORRECT - because lexical verb - want - can't take part in such constructions]
Now let's examine have to with such constructions -
Maybe I'll go over there if I really have to ___. [In the gap we can write go over there]
Like an auxiliary verb, have to can take part in such constructions.
The emphasis is on the auxiliary verb, when there is no auxiliary verb we need a dummy do for emphasis or stress.
I never imagined that he could pass the test, but he COULD pass the test. [STRESSED]
I never imagined that he passed the test, but he PASSED the test. [NO STRESS]
I never imagined that he passed the test, but he DID pass the test. [STRESSED]
Now let's examine how have to behave in such cases.
I have to win the race, and I DO have to win the race. [STRESSED]
The verb have to needs do support for stress. It's a property of a lexical verb.
Apart from NICE, there are other ways to determine whether a verb is an auxiliary verb or a lexical verb.
- Placement of adverbs
Negative inflection and reduced form
Frequency adverbs (like always, often etc) and modal adverbs (like possibly, certainly etc) generally precedes lexical verbs, and follows auxiliary verbs.
He is always after money. [always follows an auxiliary verb - is]
He always wants money. [always precedes a lexical verb - want]
Now check how have to takes such adverbs -
He always have to ask Charlie.
You have to always evolve.
You have always to talk.
- Negative inflection and reduced form -
Well, like auxiliary verb, have to has a reduced form - haven't to.
Some wives earn a lot of money and so their husbands haven't to work.
She said I can't tell you, I haven't to tell you!
So judging from the above, it's clear that have to has both the property of a lexical verb and the property of an auxiliary verb. So some grammarians (for example Quirk et el. in A Comprehensive Grammar of English Language) call have to a Semi-Auxiliary Verb. Some grammarians don't call it that. For them, have is the verb, and it have dual property. It can either be a lexical verb or an auxiliary verb.
So even if it's an auxiliary verb, it's not a modal verb.
[To be continued - Discussion regarding why it's not a modal verb]