freer

src/Control/Monad/Trans/Indexed/Free.hs

@@ -11,7 +11,7 @@
 
 module Control.Monad.Trans.Indexed.Free
   ( IxFree (ixlift, ixhoist, ixfoldMap), coerceIxFree
-  , IxFunctor, IxMap (IxMap), hoistIxMap, liftIxMap, lowerIxMap
+  , IxFunctor, IxMap (IxMap), ixliftFreer, ixhoistFreer
   ) where
 
 import Control.Monad.Free
@@ -24,8 +24,9 @@ is characterized by the `IxFree` class
 up to the isomorphism `coerceIxFree`.
 
 `IxFree` and `IxMap`, the free `IndexedMonadTrans` and
-the free `IxFunctor` can be used as a DSL
-generated by primitive commands like [this Conor McBride example]
+the free `IxFunctor`, can be combined as a "freer" `IndexedMonadTrans`
+and used as a DSL generated by primitive commands like
+[this Conor McBride example]
 (https://stackoverflow.com/questions/28690448/what-is-indexed-monad).
 
 >>> :set -XGADTs -XDataKinds
@@ -45,14 +46,14 @@ data DVDCommand
 insert
   :: (IxFree free, Monad m)
   => DVD -> free (IxMap DVDCommand) 'False 'True m ()
-insert dvd = ixlift (liftIxMap (Insert dvd))
+insert dvd = ixliftFreer (Insert dvd)
 :}
 
 >>> :{
 eject
   :: (IxFree free, Monad m)
   => free (IxMap DVDCommand) 'True 'False m DVD
-eject = ixlift (liftIxMap Eject)
+eject = ixliftFreer Eject
 :}
 
 >>> :set -XQualifiedDo
@@ -101,17 +102,24 @@ type IxFunctor
 type IxFunctor f = forall i j. Functor (f i j)
 
 {- |
-
+`IxMap` is the free `IxFunctor`. It's a left Kan extension.
+Combining `IxFree` with `IxMap` as demonstrated in the above example,
+gives the "freer" `IndexedMonadTrans`, modeled on a definition of
+[Oleg Kiselyov]
+(https://okmij.org/ftp/Computation/free-monad.html#freer)
 -}
 data IxMap f i j x where
   IxMap :: (x -> y) -> f i j x -> IxMap f i j y
 instance Functor (IxMap f i j) where
   fmap g (IxMap f x) = IxMap (g . f) x
-hoistIxMap
-  :: (forall x. f i j x -> g i j x)
-  -> IxMap f i j x -> IxMap g i j x
-hoistIxMap g (IxMap f x) = IxMap f (g x)
-liftIxMap :: g i j x -> IxMap g i j x
-liftIxMap = IxMap id
-lowerIxMap :: Functor (g i j) => IxMap g i j x -> g i j x
-lowerIxMap (IxMap f x) = fmap f x
+
+ixliftFreer
+  :: (IxFree free, Monad m)
+  => f i j x -> free (IxMap f) i j m x
+ixliftFreer x = ixlift (IxMap id x)
+
+ixhoistFreer
+  :: (IxFree free, Monad m)
+  => (forall i j x. f i j x -> g i j x)
+  -> free (IxMap f) i j m x -> free (IxMap g) i j m x
+ixhoistFreer f = ixhoist (\(IxMap g x) -> IxMap g (f x))