{-@ LIQUID "--short-names" @-}

module Goo where

import Data.Set

{- the "error message" is garbled thanks to all the ill-formatted
   "Eq [Contravariant]" stuff. Can we remove it, or at least NOT show
   it when running in --short-names mode. -}

{-@ foo :: (Eq a) => x:a -> xs:[a] -> {v:Bool | v <=> (Data.Set.member x (Data.Set.elems xs))} @-}
foo          :: (Eq a) => a -> [a] -> Bool
foo x (y:ys) = x == y || elem x ys
foo _ []     = False

{-@ measure elements @-}
elements  []    = empty
elements (x:xs) = singleton x `union` elements xs

{- append :: xs:_ -> ys:_ -> {v:_ | elements v = union (elements xs) (elements ys) }@-}
append :: [a] -> [a] -> [a]
append = undefined