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I'm messing around with a polarized sequent calculus thing and wanted to index (co)terms by polarity… just one bit of information! just the one! and I crashed headlong into a wall.
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My advice is to never, ever use multiple environments. Instead use a single environment where each member has additional info (is this a positive/negative variable? a value/continuation?).
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I mean, agreed, but the problem moves around, e.g. the variable is negative but the value at that index is positive. Resolvable, but still, ew. (Counter to what I just said, I pretty strongly prefer leaving Γ and Δ separate. Would love to know more about why you'd combine them!)
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This is also the direction the Graded Types folks have gone in. I find it makes everything simpler - metatheory, implementation, datatypes. I would be interested to see an example where a unified context *isn't* simpler to deal with.
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