OK, so the writer monad allows you to write stuff to [usually] some kind of container, and get that container back at the end. In most implementations, the "container" can actually be any monoid.

Now, there is also a "reader" monad. This, you might think, would offer the dual operation - incrementally reading from some kind of container, one item at a time. In fact, this is not the functionality that the usual reader monad provides. (Instead, it merely offers easy access to a semi-global constant.)

To actually write a monad which is dual to the usual writer monad, we would need some kind of structure which is dual to a monoid.

  1. Does anybody have any idea what this dual structure might be?
  2. Has anybody written this monad? Is there a well-known name for it?
haskell monads
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