Category theory has virally spread from Haskell to Scala, PureScript, and other languages because fundamentally, it's a *language of composition*. It lets us talk about the way functional programs compose from smaller pieces.
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Also, unify the notation for both implication and function as x→y for all levels of types, and use x⇒y to distinguish depth of discourse (quotation / internalization).
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I get why you would prefer x→y and I do too normally. But yˣ opens a fascinating box.
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I would go the other way: yˣ should be written x→y with a # sign stacked onto the arrow.
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