I wrote:
...the main monad at work here is the Exit monad.
Ross Paterson wrote:
...if we define
exitMaybe :: Exit e () -> Maybe e
exitMaybe (Continue _) = Nothing
exitMaybe (Exit e) = Just e
then we have
runExit m = fromJust (exitMaybe m)
exitMaybe (x >> y) = exitMaybe x `mplus` exitMaybe y
exitMaybe (maybeExit m) = m
so we can replace the Exit monad with Maybe.
Maybe monads quit on failure and
continue on success. We want the opposite
semantics for guards, pattern matching, and
the like. The Exit monad is the dual of the
Maybe monad in this sense.
In particular, your identity
exitMaybe (x >> y) = exitMaybe x `mplus` exitMaybe y
is not true. If we let x = Continue () and y = Exit z, then
exitMaybe (x >> y) = Just z
but
exitMaybe x `mplus` exitMaybe y = Nothing
-Yitz
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