From b4b12e5078a5a3120687cc97f59bc0011d8576e8 Mon Sep 17 00:00:00 2001
From: cmk <chris.mckinlay@gmail.com>
Date: Mon, 2 Dec 2019 00:20:21 -0800
Subject: [PATCH] Deconflict w/ semigroups.

---
 connections.cabal            |   5 +-
 src/Data/Connection/Float.hs |   4 +-
 src/Data/Prd.hs              | 120 +++++++++++++++++------------------
 src/Data/Prd/Lattice.hs      |  21 +++---
 test/Test/Data/Prd.hs        |   4 +-
 5 files changed, 76 insertions(+), 78 deletions(-)

diff --git a/connections.cabal b/connections.cabal
index 3421bc8..d3c63bb 100644
--- a/connections.cabal
+++ b/connections.cabal
@@ -1,5 +1,5 @@
 name:                connections
-version:             0.0.2
+version:             0.0.2.1
 synopsis:            Partial orders & Galois connections.
 description:         A library for precision rounding using Galois connections.
 homepage:            https://github.com/cmk/connections
@@ -7,7 +7,8 @@ license:             BSD3
 license-file:        LICENSE
 author:              Chris McKinlay
 maintainer:          chris.mckinlay@gmail.com
-category:            Math
+category:            Math, Numerical
+stability:           Experimental
 build-type:          Simple
 extra-source-files:  ChangeLog.md
 cabal-version:       >=1.10
diff --git a/src/Data/Connection/Float.hs b/src/Data/Connection/Float.hs
index 8e2640b..0df495f 100644
--- a/src/Data/Connection/Float.hs
+++ b/src/Data/Connection/Float.hs
@@ -31,10 +31,10 @@ instance Prd Ulp32 where
            | ulp32Nan x || ulp32Nan y = False
            | otherwise                = on (<~) unUlp32 x y
 
-instance Min Ulp32 where
+instance Minimal Ulp32 where
     minimal = Ulp32 $ -2139095041
 
-instance Max Ulp32 where
+instance Maximal Ulp32 where
     maximal = Ulp32 $ 2139095040
 
 instance Bounded Ulp32 where
diff --git a/src/Data/Prd.hs b/src/Data/Prd.hs
index 6507a6e..412a16d 100644
--- a/src/Data/Prd.hs
+++ b/src/Data/Prd.hs
@@ -281,7 +281,7 @@ pmax x y = do
     EQ -> Just y
     LT -> Just y
 
-pjoin :: Eq a => Min a => Foldable f => f a -> Maybe a
+pjoin :: Eq a => Minimal a => Foldable f => f a -> Maybe a
 pjoin = foldM pmax minimal
 
 -- | A partial version of 'Data.Ord.min'. 
@@ -296,7 +296,7 @@ pmin x y = do
     EQ -> Just x
     LT -> Just x
 
-pmeet :: Eq a => Max a => Foldable f => f a -> Maybe a
+pmeet :: Eq a => Maximal a => Foldable f => f a -> Maybe a
 pmeet = foldM pmin maximal
 
 sign :: Eq a => Num a => Prd a => a -> Maybe Ordering
@@ -416,11 +416,11 @@ instance Prd All where
 instance (Eq a, Semigroup a) => Prd (S.First a) where 
     (<~) = (==)
 
-instance Ord a => Prd (S.Max a) where 
-    pcompare (S.Max x) (S.Max y) = Just $ compare x y
+instance Ord a => Prd (S.Maximal a) where 
+    pcompare (S.Maximal x) (S.Maximal y) = Just $ compare x y
 
-instance Ord a => Prd (S.Min a) where 
-    pcompare (S.Min x) (S.Min y) = Just $ compare y x
+instance Ord a => Prd (S.Minimal a) where 
+    pcompare (S.Minimal x) (S.Minimal y) = Just $ compare y x
 
 -}
 
@@ -496,7 +496,6 @@ instance Prd a => Prd (IntMap.IntMap a) where
 instance Prd IntSet.IntSet where
     (<~) = IntSet.isSubsetOf
 
-
 -- Helper type for 'DerivingVia'
 newtype Ordered a = Ordered { getOrdered :: a }
   deriving ( Eq, Ord, Show, Data, Typeable, Generic, Generic1, Functor, Foldable, Traversable)
@@ -504,123 +503,124 @@ newtype Ordered a = Ordered { getOrdered :: a }
 instance Ord a => Prd (Ordered a) where
     (<~) = (<=)
 
-type Bound a = (Min a, Max a) 
+-------------------------------------------------------------------------------
+-- Minimal
+-------------------------------------------------------------------------------
+
+type Bound a = (Minimal a, Maximal a) 
 
--- | Min element of a partially ordered set.
+-- | Minimal element of a partially ordered set.
 -- 
 -- \( \forall x: x \ge minimal \)
 --
 -- This means that 'minimal' must be comparable to all values in /a/.
 --
-class Prd a => Min a where
+class Prd a => Minimal a where
     minimal :: a
 
-instance Min () where minimal = ()
+instance Minimal () where minimal = ()
 
-instance Min Natural where minimal = 0
+instance Minimal Natural where minimal = 0
 
-instance Min Bool where minimal = minBound
+instance Minimal Bool where minimal = minBound
 
-instance Min Ordering where minimal = minBound
+instance Minimal Ordering where minimal = minBound
 
-instance Min Int where minimal = minBound
+instance Minimal Int where minimal = minBound
 
-instance Min Int8 where minimal = minBound
+instance Minimal Int8 where minimal = minBound
 
-instance Min Int16 where minimal = minBound
+instance Minimal Int16 where minimal = minBound
 
-instance Min Int32 where minimal = minBound
+instance Minimal Int32 where minimal = minBound
 
-instance Min Int64 where minimal = minBound
+instance Minimal Int64 where minimal = minBound
 
-instance Min Word where minimal = minBound
+instance Minimal Word where minimal = minBound
 
-instance Min Word8 where minimal = minBound
+instance Minimal Word8 where minimal = minBound
 
-instance Min Word16 where minimal = minBound
+instance Minimal Word16 where minimal = minBound
 
-instance Min Word32 where minimal = minBound
+instance Minimal Word32 where minimal = minBound
 
-instance Min Word64 where minimal = minBound 
+instance Minimal Word64 where minimal = minBound 
 
-instance Prd a => Min (IntMap.IntMap a) where
+instance Prd a => Minimal (IntMap.IntMap a) where
     minimal = IntMap.empty
 
-instance Ord a => Min (Set.Set a) where
+instance Ord a => Minimal (Set.Set a) where
     minimal = Set.empty
 
-instance (Ord k, Prd a) => Min (Map.Map k a) where
+instance (Ord k, Prd a) => Minimal (Map.Map k a) where
     minimal = Map.empty
 
-instance (Min a, Min b) => Min (a, b) where
+instance (Minimal a, Minimal b) => Minimal (a, b) where
     minimal = (minimal, minimal)
 
-instance (Min a, Prd b) => Min (Either a b) where
+instance (Minimal a, Prd b) => Minimal (Either a b) where
     minimal = Left minimal
 
-instance Prd a => Min (Maybe a) where
+instance Prd a => Minimal (Maybe a) where
     minimal = Nothing 
 
-instance Max a => Min (Down a) where
+instance Maximal a => Minimal (Down a) where
     minimal = Down maximal
 
--- | Max element of a partially ordered set.
+-------------------------------------------------------------------------------
+-- Maximal
+-------------------------------------------------------------------------------
+
+-- | Maximal element of a partially ordered set.
 --
 -- \( \forall x: x \le maximal \)
 --
 -- This means that 'maximal' must be comparable to all values in /a/.
 --
-class Prd a => Max a where
+class Prd a => Maximal a where
     maximal :: a
 
-instance Max () where maximal = ()
+instance Maximal () where maximal = ()
 
-instance Max Bool where maximal = maxBound
+instance Maximal Bool where maximal = maxBound
 
-instance Max Ordering where maximal = maxBound
+instance Maximal Ordering where maximal = maxBound
 
-instance Max Int where maximal = maxBound
+instance Maximal Int where maximal = maxBound
 
-instance Max Int8 where maximal = maxBound
+instance Maximal Int8 where maximal = maxBound
 
-instance Max Int16 where maximal = maxBound
+instance Maximal Int16 where maximal = maxBound
 
-instance Max Int32 where maximal = maxBound
+instance Maximal Int32 where maximal = maxBound
 
-instance Max Int64 where maximal = maxBound
+instance Maximal Int64 where maximal = maxBound
 
-instance Max Word where maximal = maxBound
+instance Maximal Word where maximal = maxBound
 
-instance Max Word8 where maximal = maxBound
+instance Maximal Word8 where maximal = maxBound
 
-instance Max Word16 where maximal = maxBound
+instance Maximal Word16 where maximal = maxBound
 
-instance Max Word32 where maximal = maxBound
+instance Maximal Word32 where maximal = maxBound
 
-instance Max Word64 where maximal = maxBound
+instance Maximal Word64 where maximal = maxBound
 
-instance (Max a, Max b) => Max (a, b) where
+instance (Maximal a, Maximal b) => Maximal (a, b) where
     maximal = (maximal, maximal)
 
-instance (Prd a, Max b) => Max (Either a b) where
+instance (Prd a, Maximal b) => Maximal (Either a b) where
     maximal = Right maximal
 
-instance Max a => Max (Maybe a) where
+instance Maximal a => Maximal (Maybe a) where
     maximal = Just maximal
 
-instance Min a => Max (Down a) where
+instance Minimal a => Maximal (Down a) where
     maximal = Down minimal
 
-{-
-instance (Universe a, Prd a) => Prd (k -> a) where
-
-instance Min a => Min (k -> a) where
-    minimal = const minimal
-
-instance Max a => Max (k -> a) where
-    maximal = const maximal
--}
- 
+-------------------------------------------------------------------------------
+-- Iterators
+-------------------------------------------------------------------------------
 
 {-# INLINE until #-}
 until :: (a -> Bool) -> (a -> a -> Bool) -> (a -> a) -> a -> a
diff --git a/src/Data/Prd/Lattice.hs b/src/Data/Prd/Lattice.hs
index 445189c..7b2b07f 100644
--- a/src/Data/Prd/Lattice.hs
+++ b/src/Data/Prd/Lattice.hs
@@ -143,7 +143,7 @@ class Prd a => Lattice a where
   (/\) :: a -> a -> a
 
   -- | Lattice morphism.
-  fromSubset :: Min a => Set a -> a
+  fromSubset :: Minimal a => Set a -> a
   fromSubset = join
 
 -- | The partial ordering induced by the join-semilattice structure
@@ -153,10 +153,10 @@ joinLeq x y = x \/ y =~ y
 meetLeq :: Lattice a => a -> a -> Bool
 meetLeq x y = x /\ y =~ x
 
-join :: (Min a, Lattice a, Foldable f) => f a -> a
+join :: (Minimal a, Lattice a, Foldable f) => f a -> a
 join = foldr' (\/) minimal
 
-meet :: (Max a, Lattice a, Foldable f) => f a -> a
+meet :: (Maximal a, Lattice a, Foldable f) => f a -> a
 meet = foldr' (/\) maximal
 
 -- | The join of at a list of join-semilattice elements (of length at least one)
@@ -170,8 +170,6 @@ meet1 = unMeet . foldMap1 Meet
 
 -- | Birkhoff's self-dual ternary median operation.
 --
--- TODO: require a /Dioid/ instance.
---
 -- @ median x x y ≡ x @
 --
 -- @ median x y z ≡ median z x y @
@@ -183,7 +181,6 @@ meet1 = unMeet . foldMap1 Meet
 median :: Lattice a => a -> a -> a -> a
 median x y z = (x \/ y) /\ (y \/ z) /\ (z \/ x)
 
-
 ---------------------------------------------------------------------
 --  Instances
 ---------------------------------------------------------------------
@@ -225,20 +222,20 @@ instance Lattice All where
   All a \/ All b = All $ a \/ b
   All a /\ All b = All $ a /\ b
 
-instance Min All where
+instance Minimal All where
   minimal = All False
 
-instance Max All where
+instance Maximal All where
   maximal = All True
 
 instance Lattice Any where
   Any a \/ Any b = Any $ a \/ b
   Any a /\ Any b = Any $ a /\ b
 
-instance Min Any where
+instance Minimal Any where
   minimal = Any False
 
-instance Max Any where
+instance Maximal Any where
   maximal = Any True
 
 instance Lattice a => Lattice (Down a) where
@@ -275,7 +272,7 @@ newtype Join a = Join { unJoin :: a }
 instance Lattice a => Semigroup (Join a) where
   Join a <> Join b = Join (a \/ b)
 
-instance (Lattice a, Min a) => Monoid (Join a) where
+instance (Lattice a, Minimal a) => Monoid (Join a) where
   mempty = Join minimal
   Join a `mappend` Join b = Join (a \/ b)
 
@@ -288,6 +285,6 @@ newtype Meet a = Meet { unMeet :: a }
 instance Lattice a => Semigroup (Meet a) where
   Meet a <> Meet b = Meet (a /\ b)
 
-instance (Lattice a, Max a) => Monoid (Meet a) where
+instance (Lattice a, Maximal a) => Monoid (Meet a) where
   mempty = Meet maximal
   Meet a `mappend` Meet b = Meet (a /\ b)
diff --git a/test/Test/Data/Prd.hs b/test/Test/Data/Prd.hs
index 0a1e136..e2d2987 100644
--- a/test/Test/Data/Prd.hs
+++ b/test/Test/Data/Prd.hs
@@ -16,8 +16,8 @@ import qualified Hedgehog.Range as R
 rw :: Range Word
 rw = R.constant 0 100
 
-gen_min :: MonadGen m => m r -> m (Min r)
-gen_min g = maybe2Min id <$> G.maybe g
+gen_min :: MonadGen m => m r -> m (Minimal r)
+gen_min g = maybe2Minimal id <$> G.maybe g
 
 gen_min_plus :: Gen (MinPlus Word)
 gen_min_plus = gen_min $ Sum <$> G.word rw