I would like to have a good conceptual understanding of the semantics of programming languages: operational-, denotational-, axiomatic-, categorical-.
Is there a good (standard?) textbook for this?
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There are many depending on where you want to start and what exactly you want.
Usually textbook start with giving semantics to the
IMP language and then give references to semantics of lambda calculus (typed untyped) unless you are reading Gunter. I am listing down a few below that I have referenced a number of times:
Operational Denotational and Axiomatic:
Denotational semantics: Denotational Semantics by Stoy
Mostly operational semantics (may be with types involved):