I propose to add to Data.Bool: -- | Boolean implication. implies :: Bool -> Bool -> Bool implies True x = x implies False _ = True infix 4 `implies` -- same as (==) The request for this is quite old (see e.g. http://neilmitchell.blogspot.de/2007/02/logical-implication-in-haskell.html). I believe that by not trying to use an operator for it, and keeping it in Data.Bool, we can avoid doing anything wrong. A quick superficial search on Stackage Hoogle suggests that adding this function should create no breakage (4 packages define their own function called `implies`, none of them import Data.Bool). `infix` instead of `infixl` or `infixr` to force you to bracket it; for the same reason it has the same precedence as `==`.