An example usage of pattern synonyms

PatternSynonymExample.hs

{-# LANGUAGE PatternSynonyms, ViewPatterns #-}

type Var = Int
type Monomial k = (k, [Var])
newtype Polynomial k = Polynomial [Monomial k]
 
pattern Var x = Polynomial [(1, [x])]

pattern Const k <- (asConst -> Just k) where
  Const 0 = Polynomial []
  Const k = Polynomial [(k, [])]

asConst :: (Eq k, Num k) => Polynomial k -> Maybe k
asConst (Polynomial []) = Just 0
asConst (Polynomial [(k,[])]) = Just k
asConst _ = Nothing