[Haskell-cafe] Fwd: incorrect MonadPlus law "v >> mzero = mzero"?

Petr Pudlák petr.mvd at gmail.com
Mon Feb 3 20:21:49 UTC 2014

Since nobody replied so far, I'm also forwarding to cafe.

---------- Forwarded message ----------
From: Petr Pudlák <petr.mvd at gmail.com>
Date: 2014-01-29
Subject: incorrect MonadPlus law "v >> mzero = mzero"?
To: "libraries at haskell.org" <libraries at haskell.org>


this law apparently fails for a MonadPlus instance that has more than one
possible failure value. Consider:

   runIdentity . runErrorT $
    ((ErrorT . Identity $ Left "failure") >> mzero :: ErrorT String
Identity ())

evaluates to `Left "failure"`, which isn't equal to ErrorT's mzero `Left

This isn't just the case of ErrorT, it fails for any MonadPlus with
multiple failure values. For example

  lift (tell "foo") >> mzero :: MaybeT (Writer String) ()

is again distinct from mzero.

Actually, no monad transformer with a MonadPlus instance can satisfy the
law, because the first part in front of `>> mzero` can introduce side
effects in the underlying monad.

I'm not sure what should be the proper solution. Perhaps to change the laws

  return x >> mzero  =  mzero
  (v >> mzero) >>= f  =  (v >> mzero)`

That is, if an expression ends with `mzero`, it behaves like `mzero`.

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