lude

Haskell prelude alternative
git clone git://git.rr3.xyz/lude | git clone gits://git.rr3.xyz/lude
Log | Files | Refs | README | LICENSE

Lattice.hs (2185B)

      1 module Lude.Order.Lattice (
      2     GlbLatticed (..),
      3     LubLatticed (..),
      4     Latticed,
      5     BoundedGlbLatticed,
      6     BoundedLubLatticed,
      7     BoundedLatticed,
      8 ) where
      9 
     10 import Data.Coerce
     11 import Numeric.Natural qualified as Base
     12 import Prelude qualified as Base
     13 
     14 import Lude.Haskell
     15 import Lude.Order.Bound
     16 import Lude.Order.Partial
     17 
     18 -- TODO: Infix operators for glb and lub?
     19 
     20 --------------------------------------------------------------------------------
     21 
     22 type GlbLatticed :: forall {r :: Repr}. Type# r -> Constraint
     23 class (PartiallyOrdered a) => GlbLatticed a where
     24     glb :: Biendo a
     25 
     26 type LubLatticed :: forall {r :: Repr}. Type# r -> Constraint
     27 class (PartiallyOrdered a) => LubLatticed a where
     28     lub :: Biendo a
     29 
     30 type Latticed :: forall {r :: Repr}. Type# r -> Constraint
     31 class (GlbLatticed a, LubLatticed a) => Latticed a
     32 instance (GlbLatticed a, LubLatticed a) => Latticed a
     33 
     34 type BoundedGlbLatticed :: forall {r :: Repr}. Type# r -> Constraint
     35 class (BoundedAbove a, GlbLatticed a) => BoundedGlbLatticed a
     36 instance (BoundedAbove a, GlbLatticed a) => BoundedGlbLatticed a
     37 
     38 type BoundedLubLatticed :: forall {r :: Repr}. Type# r -> Constraint
     39 class (BoundedBelow a, LubLatticed a) => BoundedLubLatticed a
     40 instance (BoundedBelow a, LubLatticed a) => BoundedLubLatticed a
     41 
     42 type BoundedLatticed :: forall {r :: Repr}. Type# r -> Constraint
     43 class (BoundedGlbLatticed a, BoundedLubLatticed a) => BoundedLatticed a
     44 instance (BoundedGlbLatticed a, BoundedLubLatticed a) => BoundedLatticed a
     45 
     46 --------------------------------------------------------------------------------
     47 -- Interop
     48 
     49 instance (Base.Ord a) => GlbLatticed (BaseInterop a) where glb = coerce Base.min
     50 instance (Base.Ord a) => LubLatticed (BaseInterop a) where lub = coerce Base.max
     51 
     52 deriving via BaseInterop Base.Natural instance GlbLatticed Base.Natural
     53 deriving via BaseInterop Base.Natural instance LubLatticed Base.Natural
     54 deriving via BaseInterop Base.Integer instance GlbLatticed Base.Integer
     55 deriving via BaseInterop Base.Integer instance LubLatticed Base.Integer
     56 deriving via BaseInterop Base.Rational instance GlbLatticed Base.Rational
     57 deriving via BaseInterop Base.Rational instance LubLatticed Base.Rational