The types of VP and NP might appear unintuitive because of the question as to the meaning of a noun phrase that is not simply a term.
The meaning of verb phrases VP can be expressed with that term, for example stating that a particular x satisfies sleeps(x)
This compositionality makes it possible to assign meanings reliably to arbitrarily complex sentence structures, with auxiliary clauses and many other complications.
In David Foster Wallace's novel Infinite Jest, the protagonist Hal Incandenza has written an essay entitled Montague Grammar and the Semantics of Physical Modality.
Montague grammar is also referenced explicitly and implicitly several times throughout the book.