Fragment answers may convey a complete thought, hence being complete sentences on their own. They've been analysed to involve either sluicing or the elision of a copular construction (pseudosluicing).
What did Mary eat?
Mary ate t1
it was t1
An imperative may convey a complete thought and is regarded as a complete sentence even if it is only a VP, because it actually is underlyingly a complete sentence - the subject is omitted.
Has anyone ever regarded isolated NPs like the ones below as complete sentences and extended the pseudosluice analysis to such isolated NPs?
Look! A bird.
What a pretty flower!
It does seem that pseudosluicing is involved.
it is t1
[What a pretty flower]1
it is t1
This could be supported by data from Japanese where such phrases are ended with the copula だ(da)/です(desu).
見て！ 鳥 だ. Mite! Tori da. Look! Bird COP Look! It's a bird. なんて きれい-な 花 だ! Nante kirei-na hana da! EMPH pretty flower COP What a pretty flower it is.