implement Lattice for Int and Nat

src/Data/Int.dcl

 definition module Data.Int
 
 from Algebra.Order import class Eq, class Ord
+from Algebra.Enum import class Enum
 from Algebra.Group import class Semigroup, class Monoid, class Group
 from Algebra.Ring import class Semiring, class Ring, class Domain
-from Algebra.Enum import class Enum
+from Algebra.Lattice import class MeetSemilattice, class JoinSemilattice, class UpperBounded, class LowerBounded
 
 /// # Definition
 
@@ -23,6 +24,11 @@ instance Semiring Int
 // instance Ring Int
 instance Domain Int
 
+instance MeetSemilattice Int
+instance JoinSemilattice Int
+instance UpperBounded Int
+instance LowerBounded Int
+
 /// # Helpers
 
 inc :: !Int -> Int

src/Data/Int.icl

@@ -3,9 +3,10 @@ implementation module Data.Int
 import Control.Function
 
 import Algebra.Order
+import Algebra.Enum
 import Algebra.Group
 import Algebra.Ring
-import Algebra.Enum
+import Algebra.Lattice
 
 import Clean.Prim
 
@@ -62,6 +63,7 @@ instance Monoid Int where
 
 instance Group Int where
     (-) x y = prim_subInt x y
+
     inverse x = prim_negInt x
 
 instance Semiring Int where
@@ -86,6 +88,18 @@ instance Domain Int where
 	lcm 0 _    = 0
 	lcm x y    = abs ((x `quot` gcd x y) * y)
 
+instance MeetSemilattice Int where
+    (/\) x y = prim_minInt x y
+
+instance JoinSemilattice Int where
+    (\/) x y = prim_maxInt x y
+
+instance UpperBounded Int where
+    top = undefined
+
+instance LowerBounded Int where
+    bottom = undefined
+
 /// # Helpers
 
 inc :: !Int -> Int

src/Data/Nat.dcl

@@ -2,7 +2,8 @@ definition module Data.Nat
 
 from Algebra.Order import class Eq, class Ord
 from Algebra.Group import class Semigroup, class Monoid
-from Algebra.Ring import class Semiring
+from Algebra.Ring import class Semiring, class Domain
+from Algebra.Lattice import class MeetSemilattice, class JoinSemilattice, class UpperBounded, class LowerBounded
 
 /// # Definition
 
@@ -20,6 +21,11 @@ instance Semigroup Nat
 instance Monoid Nat
 instance Semiring Nat
 
+instance MeetSemilattice Nat
+instance JoinSemilattice Nat
+instance UpperBounded Nat
+instance LowerBounded Nat
+
 /// # Special Algebra
 
 (.-) infixl 6 :: !Nat !Nat -> Nat

src/Data/Nat.icl

@@ -7,6 +7,7 @@ import Control.Function
 import Algebra.Order
 import Algebra.Group
 import Algebra.Ring
+import Algebra.Lattice
 
 import Clean.Prim
 
@@ -17,8 +18,8 @@ import Clean.Prim
 //TODO rewrite in inlined ABC (?)
 nat :: !Int -> Nat
 nat n
-    | prim_ltInt n 0 = abort "Data.Nat.nat: negative integer"
-    | otherwise      = n
+    | n < 0     = prim_abort "Data.Nat.nat: negative integer"
+    | otherwise = n
 
 int :: !Nat -> Int
 int n = prim_noop
@@ -48,10 +49,25 @@ instance Semiring Nat where
 
     unity = prim_oneInt
 
+
+/// ## Lattice
+
+instance MeetSemilattice Nat where
+    (/\) x y = prim_minInt x y
+
+instance JoinSemilattice Nat where
+    (\/) x y = prim_maxInt x y
+
+instance UpperBounded Nat where
+    top = prim_upperInt
+
+instance LowerBounded Nat where
+    bottom = prim_zeroInt
+
 /// # Special Algebra
 
 //TODO rewrite in inlined ABC (?)
 (.-) infixl 6 :: !Nat !Nat -> Nat
 (.-) n m
-    | prim_ltInt m n = prim_subInt n m
-    | otherwise      = 0
+    | m < n     = prim_subInt n m
+    | otherwise = prim_zeroInt