[Haskell-cafe] An arrow transformer

[Roman Cheplyaka]

I wrote (and found useful) the following arrow transformer:

  data Partial ar a b
    = Partial (ErrorArrow () ar a b)
    | Total (ar a b)

  toPartial :: ArrowChoice ar => Partial ar a b -> ErrorArrow () ar a b
  toPartial (Partial f) = f
  toPartial (Total sf) = liftError sf

  instance ArrowChoice ar => Category (Partial ar) where
    id = Total id
    Total f . Total g = Total $ f . g
    f . g = Partial $ toPartial f . toPartial g

  instance ArrowChoice ar => Arrow (Partial ar) where
    arr = Total . arr
    first (Total f) = Total $ first f
    first (Partial f) = Partial $ first f

It allows to work with partial functions/arrows and at the same time
tracks which of them are actually total.

I wonder if it is already defined somewhere or is perhaps an instance of
a more general construction.

Roman
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