It so happens that you can make a set data type that is a Monad, but it's not exactly the best possible sets.<div><br></div><div><div>module SetMonad where</div><div><br></div><div>newtype Set a = Set { unSet :: [a] }</div>
<div><br></div><div>singleton :: a -> Set a</div><div>singleton x = Set [x]</div><div><br></div><div>unions :: [Set a] -> Set a</div><div>unions ss = Set $ concatMap unSet ss</div><div><br></div><div>member :: (Eq a) => a -> Set a -> Bool</div>
<div>member x s = x `elem` unSet s</div><div><br></div><div>instance Monad Set where</div><div> return = singleton</div><div> x >>= f = unions (map f (unSet x))</div><div><br></div><br><div class="gmail_quote">
On Sat, Jan 8, 2011 at 9:28 PM, Peter Padawitz <span dir="ltr"><<a href="mailto:peter.padawitz@udo.edu">peter.padawitz@udo.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Hi,<br>
<br>
is there any way to instantiate m in Monad m with a set datatype in order to implement the usual powerset monad?<br>
<br>
My straightforward attempt failed because the bind operator of this instance requires the Eq constraint on the argument types of m.<br>
<br>
Peter<br>
<br>
<br>
<br>
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</blockquote></div><br></div>