WIP: Num class

src/Fcf.hs

@@ -150,7 +150,7 @@ module Fcf
 
   , type (+)
   , type (-)
-  , type (Fcf.Data.Nat.*)
+  , type (Fcf.Class.Num.*)
   , type (^)
   , type (<=)
   , type (>=)
@@ -180,7 +180,8 @@ import Fcf.Combinators
 import Fcf.Data.Bool
 import Fcf.Data.Common
 import Fcf.Data.List
-import Fcf.Data.Nat
+import Fcf.Class.Ord
 import Fcf.Class.Functor
 import Fcf.Class.Bifunctor
+import Fcf.Class.Num
 import Fcf.Utils

src/Fcf/Class/Num.hs

@@ -0,0 +1,86 @@
+{-# LANGUAGE
+    CPP,
+    DataKinds,
+    PolyKinds,
+    TypeFamilies,
+    TypeOperators,
+    UndecidableInstances #-}
+
+#if __GLASGOW_HASKELL__ >= 806
+{-# LANGUAGE NoStarIsType #-}
+#endif
+
+
+-- | Numeric operations.
+module Fcf.Class.Num
+  ( -- * Pure type families
+    -- | Nicer to use when applied explicitly.
+    type (:+)
+  , type (:-)
+  , type (:*)
+  , type (:^)
+
+    -- * First-class families
+    -- | Can be composed and passed to higher-order functions.
+  , type (+)
+  , type (-)
+  , type (Fcf.Class.Num.*)
+  , type (^)
+  ) where
+
+import Fcf.Core (Exp, Eval)
+
+#if __GLASGOW_HASKELL__ >= 802
+import qualified GHC.TypeLits as TL
+#endif
+
+-- | Type-level addition.
+--
+-- This is the fcf-encoding of @(':+')@.
+-- To define a new addition, add type instances to @(':+')@.
+data (+) :: a -> a -> Exp a
+type instance Eval (x + y) = x :+ y
+
+-- | Type-level semigroup composition @('Data.Semigroup.<>')@.
+type family (:+) (x :: a) (y :: a) :: a
+
+type instance (:+) (a :: TL.Nat) (b :: TL.Nat)= a TL.+ b
+
+-- | Type-level subtraction.
+--
+-- This is the fcf-encoding of @(':-')@.
+-- To define a new subtraction, add type instances to @(':-')@.
+data (-) :: a -> a -> Exp a
+type instance Eval (x - y) = x :- y
+
+-- | Type-level subtraction.
+type family (:-) (x :: a) (y :: a) :: a
+
+type instance (:-) (a :: TL.Nat) (b :: TL.Nat) = a TL.- b
+
+-- | Type-level multiplication.
+--
+-- This is the fcf-encoding of @('Fcf.Data.Nat.*')@.
+-- To define a new multiplication, add type instances to @('Fcf.Data.Nat.*')@.
+data (*) :: a -> a -> Exp a
+
+type instance Eval (x Fcf.Class.Num.* y) = x :* y
+
+-- | Type-level multiplication.
+type family (:*) (x :: a) (y :: a) :: a
+
+type instance (:*) (a :: TL.Nat) (b :: TL.Nat) = a TL.* b
+
+
+-- | Type-level exponentiation.
+--
+-- This is the fcf-encoding of @('^')@.
+-- To define a new exponentiation, add type instances to @('^')@.
+data (^) :: a -> b -> Exp a
+type instance Eval (x ^ y) = x :^ y
+
+-- | Type-level exponentiation.
+type family (:^) (x :: a) (y :: b) :: a
+
+type instance (:^) (a :: TL.Nat) (b :: TL.Nat) = a TL.^ b
+

src/Fcf/Data/Nat.hs

@@ -15,6 +15,7 @@
 -- Note that the operators from this module conflict with "GHC.TypeLits" and
 -- "GHC.TypeNats".
 module Fcf.Data.Nat
+  {-# DEPRECATED "Use Fcf.Class.Num or Fcf.Class.Ord instead." #-}
   ( -- * Reexported type
     -- | From "GHC.TypeNats".