'that has' or 'that is' yet to be built?

Solution 1:

The difference is one of the perception in time and also immediate relevance to the reader. Use of the auxiliary verb 'have' indicates a time relationship relative to the present, implying that this could happen in the relatively near future. This is called use of aspect in grammar. It could also be understood to indicate greater relevance to the reader. In the alternative you provide, using 'be' in the 'is' form, the sense is less immediate and carries less impact for the reader. It is not clear when this might be built in the future. It is also less immediately relevant to the reader's world. So the first version 'has yet to be built' has more impact on the reader. The 'is yet to be built' does not carry the same weight. Both are grammatically correct.

Solution 2:

I’m not a grammarian, so I expect to be shot down on this, but in theory it seems to me that you are correct. Reducing the sentence to its elements (as I did at school hundreds of years ago), the structure would seem to be:

Noun—Verb—Complement

…so if “the Ferrari” were the noun and “to be built” (no ‘yet’, yet) were the complement, then the only verb tense possible of the two is:

The Ferrari — is — to be built (in Turin, next year etc.)

Clearly, “has” will not work†.

What about “yet”? It seems to me that this has the force of a temporal qualifier, replacing “next year” by something indefinite.

The Google ngram for “is yet to be” v. “has yet to be” shows that “is” was the only form between 1800 and 1820, after which “has” appeared. The latter became equally prevalent by 1870, and started to overtake “is” in about 1940, and is now twice as popular.

I can see no grammatical justification for “has”, but imagine it has some psychological resonance, although I am not convinced by the assertions in the answer from @Matthew_Martin. I would regard them both as having the same temporal force: I personally prefer “is” as more literary and traditional.

Grammatical or not, that is the English language. Both are in current use and have been used for very many years by reputable authors, so both are ‘right’.

P.S.

I notice that Ferrari has ‘corrected’ the sentence:

And the Italian means something different, but also uses “is”. My translation:

“The best Ferrari ever built is the next one.”

(And apparently they are built in Maranello, not Turin.)

† Grammatical footnote

But this may be nonsense and the construction may be a passive infinitive. However, in this case it would still normally be is rather than has.