bobytableaus.hs

{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE PolyKinds #-}

class Semiring a where
  zero  :: a
  one   :: a
  plus  :: a -> a -> a
  times :: a -> a -> a

class SemiringForall (f :: k -> *) where
  zeroForall  :: f a
  oneForall   :: f a
  plusForall  :: f a -> f a -> f a
  timesForall :: f a -> f a -> f a

class Semiring1 (f :: * -> *) where
  liftZero  :: a -> f a
  liftOne   :: a -> f a
  liftPlus  :: (a -> a -> a) -> f a -> f a -> f a
  liftTimes :: (a -> a -> a) -> f a -> f a -> f a

zero1, one1 :: (Semiring1 f, Semiring a) => f a
zero1 = liftZero zero
one1  = liftOne  one

plus1, times1 :: (Semiring1 f, Semiring a) => f a -> f a -> f a
plus1  = liftPlus plus
times1 = liftTimes times