module HasElem where

{-@ LIQUID "--reflection" @-}
{-@ LIQUID "--ple"        @-}
{-@ LIQUID "--no-termination" @-}

data L a = Nil | Cons a (L a)

{-@ reflect hasElem @-}
hasElem :: Eq a => a -> L a -> Bool
hasElem x Nil = False
hasElem x (Cons y ys) = x == y || hasElem x ys

{-@ prop :: {v:Bool | v} @-}
prop :: Bool
prop = hasElem 1 (Cons 1 Nil)

{-@ prop1 :: {v:Bool | not v } @-}
prop1 :: Bool
prop1 = hasElem 1 (Cons 2 Nil)

{-@ prop2 :: {v:Bool | not v } @-}
prop2 :: Bool
prop2 = hasElem 1 Nil
