Where did the name <*> first begin to appear in literature or code, and did it come with any explanation for the choice of symbol?
What is the etymology of <*> from Applicative in Haskell?
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The original idioms paper already uses ⊛ for application; <*> was picked as an ASCII-art approximation of that, since (*) isn't available (it is the syntax of the prefix form of the infix operator *).
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It's an ASCIIification of the notation used in the original idioms paper: "Idioms: applicative programming with effects". That notation, was in turn, inspired by an already ASCIIified version from Sweirstra's and Duponcheel's paper on error-correcting parser combinators: "Deterministic, Error-Correcting Combinator Parsers". That came from "Functional Parsers" by Jeroen Fokker. This paper does not indicate where it came from which may mean it originated it. I would not be surprised if it was used for parsing before then.