module HalfSpaces.Constraint
  where
-- import           Data.Ratio                   (Rational)#
import           HalfSpaces.LinearCombination (LinearCombination, constant)

data Sense = Gt | Lt
  deriving Eq

instance Show Sense where
  show Gt = ">="
  show Lt = "<="

data Constraint = Constraint LinearCombination Sense LinearCombination
  deriving (Eq, Show)

(.>=.) :: LinearCombination -> LinearCombination -> Constraint
(.>=.) lhs rhs = Constraint lhs Gt rhs

(.<=.) :: LinearCombination -> LinearCombination -> Constraint
(.<=.) lhs rhs = Constraint lhs Lt rhs

(.>=) :: LinearCombination -> Rational -> Constraint
(.>=) lhs x = (.>=.) lhs (constant x)

(.<=) :: LinearCombination -> Rational -> Constraint
(.<=) lhs x = (.<=.) lhs (constant x)

infix 4 .<=., .>=.