Indexed Kan Extension #7
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optimization via Cayley representation of indexed monad transformers
echatav
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Nov 18, 2025
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| newtype CodensityIx t i j m a = CodensityIx | ||
| { runCodensityIx :: forall b k. (a -> t j k m b) -> t i k m b } | ||
| deriving Functor |
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The indexed codensity monad transformer type which I found in sessiontypes by @Ferdinand-vW.
echatav
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Nov 19, 2025
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| instance IxMonadTransReader t => IxMonadTransState (CodensityIx t) where | ||
| putIx s = CodensityIx (localIx (const s) . ($ ())) | ||
| instance (s ~ t, Monad m, IxMonadTransFree freeIx) | ||
| => MonadReader s (freeIx (Ixer AskIx) s t m) where | ||
| ask = liftFreerIx AskIx | ||
| local = localIx | ||
| instance IxMonadTransFree freeIx | ||
| => IxMonadTransReader (freeIx (Ixer AskIx)) where | ||
| localIx f | ||
| = lowerCodensityIx | ||
| . (\m -> Ix.do {i <- get; putIx (f i); m}) | ||
| . liftCodensityIx |
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This is broken. putIx and localIx reference one another and cause an inf-loop
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Optimization via Cayley representation of Atkey indexed monad transformers.