diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,12 @@
+0.7: [2024-05-21]
+-----------------
+* Add `Data.Semiring.Directed` for the semiring of directed sets.
+* Add `Data.Ring.Ordered` to represent ordered rings (as well as a simpler
+  finitary case) and provide `signum` and `abs` via type class.
+* Modify code and CI to support GHC 8.0 and later only.
+* Support newer versions of dependencies
+* Move Generics-derived tuple instances from Data.Semiring.Generic to manually-written Data.Semiring
+
 0.6: [2021-01-07]
 -----------------
 * Remove hashable flag (only necessary was unordered-containers flag)
diff --git a/Data/Ring/Ordered.hs b/Data/Ring/Ordered.hs
new file mode 100644
--- /dev/null
+++ b/Data/Ring/Ordered.hs
@@ -0,0 +1,223 @@
+{-# LANGUAGE DeriveDataTypeable         #-}
+{-# LANGUAGE DeriveGeneric              #-}
+{-# LANGUAGE FlexibleContexts           #-}
+{-# LANGUAGE FlexibleInstances          #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE StandaloneDeriving         #-}
+{-# LANGUAGE Trustworthy                #-}
+
+-- |
+-- Module: Data.Ring.Ordered
+-- Copyright: (C) 2021 Koz Ross
+-- License: BSD3 
+-- Maintainer: Koz Ross <koz.ross@retro-freedom.nz>
+-- Stability: stable
+-- Portability: GHC only
+--
+-- An \'ordered ring\' is a ring with a total order.
+--
+-- = Mathematical pedantry note
+--
+-- Many (if not most) of the instances of the 'OrderedRing' type class are not
+-- truly ordered rings in the mathematical sense, as the
+-- [axioms](https://en.wikipedia.org/wiki/Ordered_ring) imply that the
+-- underlying set is either a singleton or infinite. Thus, the [additional
+-- properties](https://en.wikipedia.org/wiki/Ordered_ring#Basic_properties) of
+-- ordered rings do not, in general, hold. 
+--
+-- We indicate those instances that /are/ \'truly\' or \'mathematically\'
+-- ordered rings in their documentation.
+module Data.Ring.Ordered 
+  (
+    -- * Helper types
+    Modular(..),
+    -- * Ordered ring type class
+    OrderedRing(..),
+  ) where
+
+import Control.Applicative (Const (Const))
+import Data.Data (Data)
+import Data.Fixed (HasResolution, Fixed)
+import Data.Functor.Identity (Identity (Identity))
+import Data.Int (Int8, Int16, Int32, Int64)
+import Data.Monoid (Dual (Dual))
+import Data.Ord (Down (Down))
+import Data.Ratio (Ratio)
+import Data.Semiring (Ring, Semiring(zero))
+import Data.Word (Word8, Word16, Word32, Word64)
+import GHC.Generics (Generic)
+import Prelude hiding (signum, abs, negate, (-))
+import qualified Prelude as Num
+import Data.Typeable (Typeable)
+
+-- | A wrapper to indicate the type is being treated as a [modular arithmetic
+-- system](https://en.wikipedia.org/wiki/Modular_arithmetic) whose modulus is
+-- the type's cardinality.
+--
+-- While we cannot guarantee that infinite types won't be wrapped by this, we
+-- only provide instances of the relevant type classes for those types we are
+-- certain are finite.
+--
+-- @since 0.7
+newtype Modular a = Modular { getModular :: a }
+  deriving
+    ( Bounded -- ^ @since 0.7
+    , Eq -- ^ @since 0.7
+    , Ord -- ^ @since 0.7
+    , Show -- ^ @since 0.7
+    , Read -- ^ @since 0.7
+    , Generic -- ^ @since 0.7
+    , Data -- ^ @since 0.7
+    , Typeable -- ^ @since 0.7
+    )
+
+-- @since 0.7
+deriving instance Semiring (Modular Word8)
+
+-- @since 0.7
+deriving instance Semiring (Modular Word16)
+
+-- @since 0.7
+deriving instance Semiring (Modular Word32)
+
+-- @since 0.7
+deriving instance Semiring (Modular Word64)
+
+-- @since 0.7
+deriving instance Semiring (Modular Word)
+
+-- @since 0.7
+deriving instance Ring (Modular Word8)
+
+-- @since 0.7
+deriving instance Ring (Modular Word16)
+
+-- @since 0.7
+deriving instance Ring (Modular Word32)
+
+-- @since 0.7
+deriving instance Ring (Modular Word64)
+
+-- @since 0.7
+deriving instance Ring (Modular Word)
+
+-- | The class of rings which also have a total order.
+--
+-- Instance should satisfy the following laws:
+--
+-- * @'abs' 'zero' = 'zero'@
+-- * @'abs' x = 'abs' ('negate' x)@
+-- * @x 'Data.Semiring.-' 'abs' x = 'zero'@
+-- * @'signum' 'zero' = 'zero'@
+-- * If @x '>' 'zero'@, then @'signum' x = 'one'@
+-- * If @x '<' 'zero'@, then @'signum' x = 'negate' 'one'@
+--
+-- @since 0.7
+class (Ring a, Ord a) => OrderedRing a where
+  -- | Compute the absolute value.
+  abs :: a -> a
+  -- | Determine the \'sign\' of a value.
+  signum :: a -> a
+
+-- | This instance is a \'true\' or \'mathematical\' ordered ring, as it is a
+-- singleton. We assume that '()' has a zero signum.
+--
+-- @since 0.7
+instance OrderedRing () where
+  abs = const ()
+  signum = const zero
+
+-- | Where @a@ is a \'true\' or \'mathematical\' ordered ring, so is this.
+--
+-- @since 0.7
+instance (OrderedRing a) => OrderedRing (Dual a) where
+  abs (Dual x) = Dual . abs $ x
+  signum (Dual x) = Dual . signum $ x
+
+-- | Where @a@ is a \'true\' or \'mathematical\' ordered ring, so is this.
+--
+-- @since 0.7
+instance (OrderedRing a) => OrderedRing (Const a b) where
+  abs (Const x) = Const . abs $ x
+  signum (Const x) = Const . signum $ x
+
+-- | Where @a ~ 'Integer'@, this instance is a \'true\' or \'mathematical\'
+-- ordered ring, as the resulting type is infinite.
+--
+-- @since 0.7
+instance (Integral a) => OrderedRing (Ratio a) where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | Where @a@ is a \'true\' or \'mathematical\' ordered ring, so is this.
+--
+-- @since 0.7
+deriving instance (OrderedRing a) => OrderedRing (Down a)
+
+-- | Where @a@ is a \'true\' or \'mathematical\' ordered ring, so is this.
+--
+-- @since 0.7
+deriving instance (OrderedRing a) => OrderedRing (Identity a)
+
+-- | @since 0.7
+instance (HasResolution a) => OrderedRing (Fixed a) where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | @since 0.7
+instance OrderedRing Int8 where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | @since 0.7
+instance OrderedRing Int16 where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | @since 0.7
+instance OrderedRing Int32 where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | @since 0.7
+instance OrderedRing Int64 where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | @since 0.7
+instance OrderedRing Int where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | This instance is a \'true\' or \'mathematical\' ordered ring, as 'Integer'
+-- is an infinite type.
+--
+-- @since 0.7
+instance OrderedRing Integer where
+  abs = Num.abs
+  signum = Num.signum
+
+-- | @since 0.7
+instance OrderedRing (Modular Word8) where
+  abs x = x
+  signum (Modular x) = Modular . Num.signum $ x
+
+-- | @since 0.7
+instance OrderedRing (Modular Word16) where
+  abs x = x
+  signum (Modular x) = Modular . Num.signum $ x
+
+-- | @since 0.7
+instance OrderedRing (Modular Word32) where
+  abs x = x
+  signum (Modular x) = Modular . Num.signum $ x
+
+-- | @since 0.7
+instance OrderedRing (Modular Word64) where
+  abs x = x
+  signum (Modular x) = Modular . Num.signum $ x
+
+-- | @since 0.7
+instance OrderedRing (Modular Word) where
+  abs x = x
+  signum (Modular x) = Modular . Num.signum $ x
diff --git a/Data/Semiring.hs b/Data/Semiring.hs
--- a/Data/Semiring.hs
+++ b/Data/Semiring.hs
@@ -57,7 +57,7 @@
   ) where
 
 import           Control.Applicative (Applicative(..), Const(..), liftA2)
-import           Data.Bits (Bits)
+import           Data.Bits (Bits (xor))
 import           Data.Bool (Bool(..), (||), (&&), otherwise)
 import           Data.Coerce (Coercible, coerce)
 import           Data.Complex (Complex(..))
@@ -87,12 +87,10 @@
 import           Data.Monoid (Ap(..))
 #endif
 #if defined(VERSION_containers)
-#if MIN_VERSION_base(4,7,0)
 import           Data.IntMap (IntMap)
 import qualified Data.IntMap as IntMap
 import           Data.IntSet (IntSet)
 import qualified Data.IntSet as IntSet
-#endif
 import           Data.Map (Map)
 import qualified Data.Map as Map
 #endif
@@ -101,7 +99,7 @@
 import           Data.Ord (Down(..))
 import           Data.Proxy (Proxy(..))
 import           Data.Ratio (Ratio, Rational, (%))
-import           Data.Semigroup.Compat (Semigroup(..))
+import           Data.Semigroup (Semigroup ((<>), stimes))
 #if defined(VERSION_containers)
 import           Data.Set (Set)
 import qualified Data.Set as Set
@@ -129,25 +127,55 @@
 import qualified GHC.Real as Real
 import           GHC.Show (Show)
 import           Numeric.Natural (Natural)
-import           Prelude (Integer)
+import           Prelude (Integer, Ordering(..), compare, even, quot)
 
 #if !MIN_VERSION_base(4,12,0)
 import           Language.Haskell.TH.Syntax (Q, Dec, Type)
 import qualified Prelude as P
 #endif
 
-#ifdef mingw32_HOST_OS
-#define HOST_OS_WINDOWS 1
-#else
-#define HOST_OS_WINDOWS 0
+#include "HsBaseConfig.h"
+import           System.Posix.Types (
+#ifdef HTYPE_CC_T
+                 CCc(..),
 #endif
-
-#if !HOST_OS_WINDOWS
-import           System.Posix.Types
-  (CCc, CDev, CGid, CIno, CMode, CNlink,
-   COff, CPid, CRLim, CSpeed, CSsize,
-   CTcflag, CUid, Fd)
+#ifdef HTYPE_DEV_T
+                 CDev(..),
 #endif
+#ifdef HTYPE_GID_T
+                 CGid(..),
+#endif
+#ifdef HTYPE_INO_T
+                 CIno(..),
+#endif
+#ifdef HTYPE_MODE_T
+                 CMode(..),
+#endif
+#ifdef HTYPE_NLINK_T
+                 CNlink(..),
+#endif
+#ifdef HTYPE_OFF_T
+                 COff(..),
+#endif
+#ifdef HTYPE_PID_T
+                 CPid(..),
+#endif
+#ifdef HTYPE_RLIM_T
+                 CRLim(..),
+#endif
+#ifdef HTYPE_SPEED_T
+                 CSpeed(..),
+#endif
+#ifdef HTYPE_SSIZE_T
+                 CSsize(..),
+#endif
+#ifdef HTYPE_TCFLAG_T
+                 CTcflag(..),
+#endif
+#ifdef HTYPE_UID_T
+                 CUid(..),
+#endif
+                 Fd(..))
 
 infixl 7 *, `times`
 infixl 6 +, `plus`, -, `minus`
@@ -337,6 +365,20 @@
 instance Semiring a => Semigroup (Mul a) where
   Mul a <> Mul b = Mul (a * b)
   {-# INLINE (<>) #-}
+  stimes n x0 = case compare n 0 of
+    LT -> error "stimes: negative multiplier"
+    EQ -> mempty
+    GT -> f x0 n
+      where
+        f x y
+          | even y = f (x `mappend` x) (y `quot` 2)
+          | y == 1 = x
+          | otherwise = g (x `mappend` x) (y `quot` 2) x
+        g x y z
+          | even y = g (x `mappend` x) (y `quot` 2) z
+          | y == 1 = x `mappend` z
+          | otherwise = g (x `mappend` x) (y `quot` 2) (x `mappend` z)
+  {-# INLINE stimes #-}
 
 instance Semiring a => Monoid (Mul a) where
   mempty = Mul one
@@ -392,10 +434,7 @@
     )
 
 instance Semiring Mod2 where
-  -- we inline the definition of 'xor'
-  -- on Bools, since the instance did not exist until
-  -- base-4.7.0.
-  plus (Mod2 x) (Mod2 y) = Mod2 (x /= y)
+  plus (Mod2 x) (Mod2 y) = Mod2 (x `xor` y)
   times (Mod2 x) (Mod2 y) = Mod2 (x && y)
   zero = Mod2 False
   one = Mod2 True
@@ -449,9 +488,7 @@
 --     @'zero' '*' x = x '*' 'zero' = 'zero'@
 
 class Semiring a where
-#if __GLASGOW_HASKELL__ >= 708
   {-# MINIMAL plus, times, (zero, one | fromNatural) #-}
-#endif
   plus  :: a -> a -> a -- ^ Commutative Operation
   zero  :: a           -- ^ Commutative Unit
   zero = fromNatural 0
@@ -467,9 +504,7 @@
 --     @'negate' a '+' a = 'zero'@
 
 class Semiring a => Ring a where
-#if __GLASGOW_HASKELL__ >= 708
   {-# MINIMAL negate #-}
-#endif
   negate :: a -> a
 
 -- | Subtract two 'Ring' values. For any type @R@ with
@@ -504,6 +539,72 @@
   Instances (base)
 --------------------------------------------------------------------}
 
+instance (Semiring a, Semiring b) => Semiring (a,b) where
+  zero = (zero, zero)
+  one = (one, one)
+  plus (x1, x2) (y1, y2) =
+    (x1 `plus` y1, x2 `plus` y2)
+  times (x1, x2) (y1, y2) =
+    (x1 `times` y1, x2 `times` y2)
+
+instance (Semiring a, Semiring b, Semiring c) => Semiring (a,b,c) where
+  zero = (zero, zero, zero)
+  one = (one, one, one)
+  plus (x1, x2, x3) (y1, y2, y3) =
+    (x1 `plus` y1, x2 `plus` y2, x3 `plus` y3)
+  times (x1, x2, x3) (y1, y2, y3) =
+    (x1 `times` y1, x2 `times` y2, x3 `times` y3)
+
+instance (Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a,b,c,d) where
+  zero = (zero, zero, zero, zero)
+  one = (one, one, one, one)
+  plus (x1, x2, x3, x4) (y1, y2, y3, y4) =
+    (x1 `plus` y1, x2 `plus` y2, x3 `plus` y3, x4 `plus` y4)
+  times (x1, x2, x3, x4) (y1, y2, y3, y4) =
+    (x1 `times` y1, x2 `times` y2, x3 `times` y3, x4 `times` y4)
+
+instance (Semiring a, Semiring b, Semiring c, Semiring d, Semiring e) => Semiring (a,b,c,d,e) where
+  zero = (zero, zero, zero, zero, zero)
+  one = (one, one, one, one, one)
+  plus (x1, x2, x3, x4, x5) (y1, y2, y3, y4, y5) =
+    (x1 `plus` y1, x2 `plus` y2, x3 `plus` y3, x4 `plus` y4, x5 `plus` y5)
+  times (x1, x2, x3, x4, x5) (y1, y2, y3, y4, y5) =
+    (x1 `times` y1, x2 `times` y2, x3 `times` y3, x4 `times` y4, x5 `times` y5)
+
+instance (Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f) => Semiring (a,b,c,d,e,f) where
+  zero = (zero, zero, zero, zero, zero, zero)
+  one = (one, one, one, one, one, one)
+  plus (x1, x2, x3, x4, x5, x6) (y1, y2, y3, y4, y5, y6) =
+    (x1 `plus` y1, x2 `plus` y2, x3 `plus` y3, x4 `plus` y4, x5 `plus` y5, x6 `plus` y6)
+  times (x1, x2, x3, x4, x5, x6) (y1, y2, y3, y4, y5, y6) =
+    (x1 `times` y1, x2 `times` y2, x3 `times` y3, x4 `times` y4, x5 `times` y5, x6 `times` y6)
+
+instance (Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g) => Semiring (a,b,c,d,e,f,g) where
+  zero = (zero, zero, zero, zero, zero, zero, zero)
+  one = (one, one, one, one, one, one, one)
+  plus (x1, x2, x3, x4, x5, x6, x7) (y1, y2, y3, y4, y5, y6, y7) =
+    (x1 `plus` y1, x2 `plus` y2, x3 `plus` y3, x4 `plus` y4, x5 `plus` y5, x6 `plus` y6, x7 `plus` y7)
+  times (x1, x2, x3, x4, x5, x6, x7) (y1, y2, y3, y4, y5, y6, y7) =
+    (x1 `times` y1, x2 `times` y2, x3 `times` y3, x4 `times` y4, x5 `times` y5, x6 `times` y6, x7 `times` y7)
+
+instance (Ring a, Ring b) => Ring (a,b) where
+  negate (x1, x2) = (negate x1, negate x2)
+
+instance (Ring a, Ring b, Ring c) => Ring (a,b,c) where
+  negate (x1, x2, x3) = (negate x1, negate x2, negate x3)
+
+instance (Ring a, Ring b, Ring c, Ring d) => Ring (a,b,c,d) where
+  negate (x1, x2, x3, x4) = (negate x1, negate x2, negate x3, negate x4)
+
+instance (Ring a, Ring b, Ring c, Ring d, Ring e) => Ring (a,b,c,d,e) where
+  negate (x1, x2, x3, x4, x5) = (negate x1, negate x2, negate x3, negate x4, negate x5)
+
+instance (Ring a, Ring b, Ring c, Ring d, Ring e, Ring f) => Ring (a,b,c,d,e,f) where
+  negate (x1, x2, x3, x4, x5, x6) = (negate x1, negate x2, negate x3, negate x4, negate x5, negate x6)
+
+instance (Ring a, Ring b, Ring c, Ring d, Ring e, Ring f, Ring g) => Ring (a,b,c,d,e,f,g) where
+  negate (x1, x2, x3, x4, x5, x6, x7) = (negate x1, negate x2, negate x3, negate x4, negate x5, negate x6, negate x7)
+
 instance Semiring b => Semiring (a -> b) where
   plus f g    = \x -> f x `plus` g x
   zero        = const zero
@@ -926,22 +1027,48 @@
 deriving via (WrappedNum CChar) instance Semiring CChar
 deriving via (WrappedNum IntPtr) instance Semiring IntPtr
 deriving via (WrappedNum WordPtr) instance Semiring WordPtr
-#if !HOST_OS_WINDOWS
+
+#ifdef HTYPE_CC_T
 deriving via (WrappedNum CCc) instance Semiring CCc
+#endif
+#ifdef HTYPE_DEV_T
 deriving via (WrappedNum CDev) instance Semiring CDev
+#endif
+#ifdef HTYPE_GID_T
 deriving via (WrappedNum CGid) instance Semiring CGid
+#endif
+#ifdef HTYPE_INO_T
 deriving via (WrappedNum CIno) instance Semiring CIno
+#endif
+#ifdef HTYPE_MODE_T
 deriving via (WrappedNum CMode) instance Semiring CMode
+#endif
+#ifdef HTYPE_NLINK_T
 deriving via (WrappedNum CNlink) instance Semiring CNlink
+#endif
+#ifdef HTYPE_OFF_T
 deriving via (WrappedNum COff) instance Semiring COff
+#endif
+#ifdef HTYPE_PID_T
 deriving via (WrappedNum CPid) instance Semiring CPid
+#endif
+#ifdef HTYPE_RLIM_T
 deriving via (WrappedNum CRLim) instance Semiring CRLim
+#endif
+#ifdef HTYPE_SPEED_T
 deriving via (WrappedNum CSpeed) instance Semiring CSpeed
+#endif
+#ifdef HTYPE_SSIZE_T
 deriving via (WrappedNum CSsize) instance Semiring CSsize
+#endif
+#ifdef HTYPE_TCFLAG_T
 deriving via (WrappedNum CTcflag) instance Semiring CTcflag
+#endif
+#ifdef HTYPE_UID_T
 deriving via (WrappedNum CUid) instance Semiring CUid
-deriving via (WrappedNum Fd) instance Semiring Fd
 #endif
+deriving via (WrappedNum Fd) instance Semiring Fd
+
 deriving via (WrappedNum Natural) instance Semiring Natural
 #else
 -- Integral and fieldlike instances
@@ -1002,22 +1129,48 @@
    ,[t|CChar|]
    ,[t|IntPtr|]
    ,[t|WordPtr|]
-#if !HOST_OS_WINDOWS
+
+#ifdef HTYPE_CC_T
    ,[t|CCc|]
+#endif
+#ifdef HTYPE_DEV_T
    ,[t|CDev|]
+#endif
+#ifdef HTYPE_GID_T
    ,[t|CGid|]
+#endif
+#ifdef HTYPE_INO_T
    ,[t|CIno|]
+#endif
+#ifdef HTYPE_MODE_T
    ,[t|CMode|]
+#endif
+#ifdef HTYPE_NLINK_T
    ,[t|CNlink|]
+#endif
+#ifdef HTYPE_OFF_T
    ,[t|COff|]
+#endif
+#ifdef HTYPE_PID_T
    ,[t|CPid|]
+#endif
+#ifdef HTYPE_RLIM_T
    ,[t|CRLim|]
+#endif
+#ifdef HTYPE_SPEED_T
    ,[t|CSpeed|]
+#endif
+#ifdef HTYPE_SSIZE_T
    ,[t|CSsize|]
+#endif
+#ifdef HTYPE_TCFLAG_T
    ,[t|CTcflag|]
+#endif
+#ifdef HTYPE_UID_T
    ,[t|CUid|]
-   ,[t|Fd|]
 #endif
+   ,[t|Fd|]
+
    ,[t|Natural|]
    ])
 #endif
@@ -1064,22 +1217,46 @@
 deriving via (WrappedNum IntPtr) instance Ring IntPtr
 deriving via (WrappedNum WordPtr) instance Ring WordPtr
 
-#if !HOST_OS_WINDOWS
+#ifdef HTYPE_CC_T
 deriving via (WrappedNum CCc) instance Ring CCc
+#endif
+#ifdef HTYPE_DEV_T
 deriving via (WrappedNum CDev) instance Ring CDev
+#endif
+#ifdef HTYPE_GID_T
 deriving via (WrappedNum CGid) instance Ring CGid
+#endif
+#ifdef HTYPE_INO_T
 deriving via (WrappedNum CIno) instance Ring CIno
+#endif
+#ifdef HTYPE_MODE_T
 deriving via (WrappedNum CMode) instance Ring CMode
+#endif
+#ifdef HTYPE_NLINK_T
 deriving via (WrappedNum CNlink) instance Ring CNlink
+#endif
+#ifdef HTYPE_OFF_T
 deriving via (WrappedNum COff) instance Ring COff
+#endif
+#ifdef HTYPE_PID_T
 deriving via (WrappedNum CPid) instance Ring CPid
+#endif
+#ifdef HTYPE_RLIM_T
 deriving via (WrappedNum CRLim) instance Ring CRLim
+#endif
+#ifdef HTYPE_SPEED_T
 deriving via (WrappedNum CSpeed) instance Ring CSpeed
+#endif
+#ifdef HTYPE_SSIZE_T
 deriving via (WrappedNum CSsize) instance Ring CSsize
+#endif
+#ifdef HTYPE_TCFLAG_T
 deriving via (WrappedNum CTcflag) instance Ring CTcflag
+#endif
+#ifdef HTYPE_UID_T
 deriving via (WrappedNum CUid) instance Ring CUid
-deriving via (WrappedNum Fd) instance Ring Fd
 #endif
+deriving via (WrappedNum Fd) instance Ring Fd
 #else
 $(let
   deriveRing :: Q Type -> Q [Dec]
@@ -1131,21 +1308,45 @@
     ,[t|IntPtr|]
     ,[t|WordPtr|]
 
-#if !HOST_OS_WINDOWS
+#ifdef HTYPE_CC_T
     ,[t|CCc|]
+#endif
+#ifdef HTYPE_DEV_T
     ,[t|CDev|]
+#endif
+#ifdef HTYPE_GID_T
     ,[t|CGid|]
+#endif
+#ifdef HTYPE_INO_T
     ,[t|CIno|]
+#endif
+#ifdef HTYPE_MODE_T
     ,[t|CMode|]
+#endif
+#ifdef HTYPE_NLINK_T
     ,[t|CNlink|]
+#endif
+#ifdef HTYPE_OFF_T
     ,[t|COff|]
+#endif
+#ifdef HTYPE_PID_T
     ,[t|CPid|]
+#endif
+#ifdef HTYPE_RLIM_T
     ,[t|CRLim|]
+#endif
+#ifdef HTYPE_SPEED_T
     ,[t|CSpeed|]
+#endif
+#ifdef HTYPE_SSIZE_T
     ,[t|CSsize|]
+#endif
+#ifdef HTYPE_TCFLAG_T
     ,[t|CTcflag|]
+#endif
+#ifdef HTYPE_UID_T
     ,[t|CUid|]
-    ,[t|Fd|]
 #endif
+    ,[t|Fd|]
     ])
 #endif
diff --git a/Data/Semiring/Directed.hs b/Data/Semiring/Directed.hs
new file mode 100644
--- /dev/null
+++ b/Data/Semiring/Directed.hs
@@ -0,0 +1,60 @@
+{-# LANGUAGE CPP                        #-}
+{-# LANGUAGE DataKinds                  #-}
+{-# LANGUAGE DeriveDataTypeable         #-}
+{-# LANGUAGE DeriveGeneric              #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE KindSignatures             #-}
+{-# LANGUAGE ScopedTypeVariables        #-}
+{-# LANGUAGE Trustworthy                #-}
+
+-----------------------------------------------------------------------------
+-- |
+--   A "directed semiring" refers to the semiring composed of the union of upwards
+--   directed sets as multiplication, and intersection of downwards directed sets
+--   as addition.
+-----------------------------------------------------------------------------
+module Data.Semiring.Directed
+  ( -- * Directed semirings
+    Directed(..)
+  ) where
+
+import Data.Data (Data)
+import Data.Coerce (coerce)
+import Data.Semiring (Semiring(..))
+import Data.Semigroup (Min(Min), Max(Max), (<>))
+import Data.Typeable (Typeable)
+import GHC.Generics (Generic)
+
+-- | Wrapper for the semiring of upwards and downwards directed sets.
+--
+-- For the individual join/meet monoids associated with either
+-- algebra, see @'Max' 'Ordering', and @'Min' 'Ordering'@.
+newtype Directed = Directed { 
+  -- | @since 0.7
+  getDirected :: Ordering 
+  }
+  deriving ( 
+    -- | @since 0.7
+    Bounded, 
+    -- | @since 0.7
+    Enum,
+    -- | @since 0.7
+    Eq,
+    -- | @since 0.7
+    Generic,
+    -- | @since 0.7
+    Show,
+    -- | @since 0.7
+    Read,
+    -- | @since 0.7
+    Data,
+    -- | @since 0.7
+    Typeable 
+    )
+
+-- | @since 0.7
+instance Semiring Directed where
+  plus = coerce ((<>) :: Max Ordering -> Max Ordering -> Max Ordering)
+  zero = coerce (mempty :: Max Ordering)
+  times = coerce ((<>) :: Min Ordering -> Min Ordering -> Min Ordering)
+  one = coerce (mempty :: Min Ordering)
diff --git a/Data/Semiring/Generic.hs b/Data/Semiring/Generic.hs
--- a/Data/Semiring/Generic.hs
+++ b/Data/Semiring/Generic.hs
@@ -1,15 +1,8 @@
-{-# LANGUAGE CPP                  #-}
-#if MIN_VERSION_base(4,6,0)
 {-# LANGUAGE DeriveGeneric        #-}
 {-# LANGUAGE FlexibleContexts     #-}
 {-# LANGUAGE TypeOperators        #-}
 {-# LANGUAGE UndecidableInstances #-}
-#endif
 
--- below are safe orphan instances
-{-# OPTIONS_GHC -fno-warn-orphans #-}
-
-
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.Semiring.Generic
@@ -27,7 +20,6 @@
 
 module Data.Semiring.Generic
   (
-#if MIN_VERSION_base(4,6,0)
     GSemiring(..)
   , gzero
   , gone
@@ -37,10 +29,8 @@
   , GRing(..)
   , gnegate
   , GenericSemiring(..)
-#endif
   ) where
 
-#if MIN_VERSION_base(4,6,0)
 import           Data.Semiring
 import           GHC.Generics
 import           Numeric.Natural (Natural)
@@ -58,42 +48,6 @@
   times (GenericSemiring x) (GenericSemiring y) = GenericSemiring (gtimes x y)
   fromNatural x = GenericSemiring (gfromNatural x)
 
-instance (Semiring a, Semiring b) => Semiring (a,b) where
-  zero = gzero; one = gone; plus = gplus; times = gtimes; fromNatural = gfromNatural;
-
-instance (Semiring a, Semiring b, Semiring c) => Semiring (a,b,c) where
-  zero = gzero; one = gone; plus = gplus; times = gtimes; fromNatural = gfromNatural;
-
-instance (Semiring a, Semiring b, Semiring c, Semiring d) => Semiring (a,b,c,d) where
-  zero = gzero; one = gone; plus = gplus; times = gtimes; fromNatural = gfromNatural;
-
-instance (Semiring a, Semiring b, Semiring c, Semiring d, Semiring e) => Semiring (a,b,c,d,e) where
-  zero = gzero; one = gone; plus = gplus; times = gtimes; fromNatural = gfromNatural;
-
-instance (Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f) => Semiring (a,b,c,d,e,f) where
-  zero = gzero; one = gone; plus = gplus; times = gtimes; fromNatural = gfromNatural;
-
-instance (Semiring a, Semiring b, Semiring c, Semiring d, Semiring e, Semiring f, Semiring g) => Semiring (a,b,c,d,e,f,g) where
-  zero = gzero; one = gone; plus = gplus; times = gtimes; fromNatural = gfromNatural;
-
-instance (Ring a, Ring b) => Ring (a,b) where
-  negate = gnegate
-
-instance (Ring a, Ring b, Ring c) => Ring (a,b,c) where
-  negate = gnegate
-
-instance (Ring a, Ring b, Ring c, Ring d) => Ring (a,b,c,d) where
-  negate = gnegate
-
-instance (Ring a, Ring b, Ring c, Ring d, Ring e) => Ring (a,b,c,d,e) where
-  negate = gnegate
-
-instance (Ring a, Ring b, Ring c, Ring d, Ring e, Ring f) => Ring (a,b,c,d,e,f) where
-  negate = gnegate
-
-instance (Ring a, Ring b, Ring c, Ring d, Ring e, Ring f, Ring g) => Ring (a,b,c,d,e,f,g) where
-  negate = gnegate
-
 {--------------------------------------------------------------------
   Generics
 --------------------------------------------------------------------}
@@ -101,9 +55,7 @@
 -- | Generic 'Semiring' class, used to implement 'plus', 'times', 'zero',
 --   and 'one' for product-like types implementing 'Generic'.
 class GSemiring f where
-#if __GLASGOW_HASKELL__ >= 708
   {-# MINIMAL gplus', gzero', gtimes', gone', gfromNatural' #-}
-#endif
   gzero'  :: f a
   gone'   :: f a
   gplus'  :: f a -> f a -> f a
@@ -113,9 +65,7 @@
 -- | Generic 'Ring' class, used to implement 'negate' for product-like
 --   types implementing 'Generic'.
 class GRing f where
-#if __GLASGOW_HASKELL__ >= 708
   {-# MINIMAL gnegate' #-}
-#endif
   gnegate' :: f a -> f a
 
 -- | Generically generate a 'Semiring' 'zero' for any product-like type
@@ -214,4 +164,3 @@
 
 instance (Ring a) => GRing (K1 i a) where
   gnegate' (K1 x) = K1 $ negate x
-#endif
diff --git a/Data/Semiring/Tropical.hs b/Data/Semiring/Tropical.hs
--- a/Data/Semiring/Tropical.hs
+++ b/Data/Semiring/Tropical.hs
@@ -1,4 +1,3 @@
-{-# LANGUAGE CPP                 #-}
 {-# LANGUAGE DataKinds           #-}
 {-# LANGUAGE DeriveDataTypeable  #-}
 {-# LANGUAGE KindSignatures      #-}
@@ -31,14 +30,10 @@
   , EProxy(EProxy)
   ) where
 
-#if MIN_VERSION_base(4,7,0)
 import Data.Data (Data)
-#endif
 import Data.Semiring (Semiring(..))
 import Data.Star (Star(..))
-#if MIN_VERSION_base(4,7,0)
 import Data.Typeable (Typeable)
-#endif
 
 -- done for haddocks, to make sure -Wall works
 import qualified Data.Monoid as Monoid
@@ -94,10 +89,8 @@
     ( Eq
     , Show
     , Read
-#if MIN_VERSION_base(4,7,0)
     , Typeable
     , Data
-#endif
     )
 
 instance forall e a. (Ord a, Extremum e) => Ord (Tropical e a) where
diff --git a/Data/Star.hs b/Data/Star.hs
--- a/Data/Star.hs
+++ b/Data/Star.hs
@@ -1,4 +1,3 @@
-{-# LANGUAGE CPP               #-}
 {-# LANGUAGE NoImplicitPrelude #-}
 
 -----------------------------------------------------------------------------
@@ -25,9 +24,7 @@
 --
 -- @'aplus' x = x '*' 'star' x@
 class (Semiring a) => Star a where
-#if __GLASGOW_HASKELL__ >= 708
   {-# MINIMAL star | aplus #-}
-#endif
   star :: a -> a
   star a = one `plus` aplus a
 
diff --git a/semirings.cabal b/semirings.cabal
--- a/semirings.cabal
+++ b/semirings.cabal
@@ -1,6 +1,6 @@
 name:          semirings
 category:      Algebra, Data, Data Structures, Math, Maths, Mathematics
-version:       0.6
+version:       0.7
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
@@ -29,13 +29,17 @@
 
 build-type:    Simple
 extra-source-files: README.md CHANGELOG.md
-tested-with:   GHC == 7.10.3
-             , GHC == 8.0.2
-             , GHC == 8.2.2
-             , GHC == 8.4.4
-             , GHC == 8.6.5
-             , GHC == 8.8.4
-             , GHC == 8.10.2
+tested-with:
+  GHC == 8.0
+  GHC == 8.2
+  GHC == 8.4
+  GHC == 8.6
+  GHC == 8.8
+  GHC == 8.10
+  GHC == 9.0
+  GHC == 9.2
+  GHC == 9.4
+  GHC == 9.6
 
 source-repository head
   type: git
@@ -63,12 +67,13 @@
 
   build-depends:
       base >= 4.8 && < 5
-    , base-compat-batteries
   exposed-modules:
     Data.Euclidean
     Data.Field
+    Data.Ring.Ordered
     Data.Semiring
     Data.Star
+    Data.Semiring.Directed
     Data.Semiring.Tropical
     Data.Semiring.Generic
 
@@ -76,9 +81,9 @@
     build-depends: template-haskell >= 2.4.0.0
 
   if flag(containers)
-    build-depends: containers >= 0.5.4 && < 0.7
+    build-depends: containers >= 0.5.4
 
   if flag(unordered-containers)
     build-depends:
-        hashable >= 1.1  && < 1.4
-      , unordered-containers >= 0.2  && < 0.3
+        hashable >= 1.1
+      , unordered-containers >= 0.2