Add applicative ListT transformer

Author: turion

monad-bayes.cabal

@@ -86,6 +86,7 @@ common test-deps
 library
   import:             deps
   exposed-modules:
+    Control.Applicative.List
     Control.Monad.Bayes.Class
     Control.Monad.Bayes.Density.Free
     Control.Monad.Bayes.Density.State
@@ -114,8 +115,11 @@ library
   other-modules:      Control.Monad.Bayes.Traced.Common
   default-language:   Haskell2010
   default-extensions:
+    ApplicativeDo
     BlockArguments
+    DerivingStrategies
     FlexibleContexts
+    GeneralizedNewtypeDeriving
     ImportQualifiedPost
     LambdaCase
     OverloadedStrings

src/Control/Applicative/List.hs

@@ -0,0 +1,17 @@
+module Control.Applicative.List where
+
+-- base
+
+import Control.Applicative
+import Data.Functor.Compose
+
+-- | _Applicative_ transformer adding a list/nondeterminism/choice effect.
+--   It is not a valid monad transformer, but it is a valid 'Applicative'.
+newtype ListT m a = ListT {getListT :: Compose [] m a}
+  deriving newtype (Functor, Applicative, Alternative)
+
+lift :: m a -> ListT m a
+lift = ListT . Compose . pure
+
+runListT :: ListT m a -> [m a]
+runListT = getCompose . getListT