Earlier quoted context omitted.
I'm not sure who Moggi is. Category theory, the lambda calculus and the principle of compositionality were employed in linguistics since the 1930's, for instance with categorical grammar. I don't think we're talking about the same thing.
What kind of Category Theory are you talking about? [Category Theory]( https://plato.stanford.edu/entries/category-theory/ ) in the mathematical sense, and in the sense that it can be used to describe Lambda Calculi, appeared in 1945, in the field of Algebraic Topology and Homological Algebra. I'd be really surprised if it was employed in linguistics in the 1930s.
What I had in mind in particular was the application of concepts from formal language analysis to natural language processing, which wikipedia confirms started in the 1970's with the work of Richard Montague [2]. Somehow I had convinced myself this work hails from much earlier, around the time of (Chomsky's) Syntactic Structures - but that again is from the late '50s. Anyway, this kind of analysis does make use of the lambda calculus and category theory _today_ but perhaps Montague's early work didn't specifically do so.
Like I say the lambda calculus is not my specialty and I'm always a bit surprised when I realise how far back Church's original work goes. Considering how long it took for the relevant concepts to percolate down to the mainstream of programming languages, that is. That should help explain my confusion with the dates.
As a side note- a lot of what I know about semantic analysis is just "lore" - things I've picked up here and there while looking at structure, which is my main dish usually. Sometimes I struggle to point out how I know some things I'm sure I know :/
Edit: I think my reply to the original question, about why Lisp was used in computational linguistics, is mostly correct, even if I got my dates wrong: using formal logic tools in analysing meaning in natural languages was popular around the time Winograd wrote his thesis and he would have leaned heavily on it for SHRDLU. I'm not getting the dates wrong here, either- Alain Colmerauer and Definite Clause Grammar goes back to at least 1972 and he didn't just come up with the idea out of nowhere, there was a lot of activity in logics and grammars around that time.
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[1] As a for instance see the preface on this ebook (Computing Meaning) on google books: https://books.google.co.uk/books?id=nyFa5ngYThMC&redir_esc=y