diff --git a/src/Applicative.hs b/src/Applicative.hs
index fe2cbed97..063ba4abc 100644
--- a/src/Applicative.hs
+++ b/src/Applicative.hs
@@ -5,9 +5,16 @@ module Applicative (
   orAlt,
   orEmpty,
   eitherA,
+  guarded,
+  guardedA,
+  purer,
+  liftAA2,
+  (<<*>>),
 ) where
 
-import Data.Bool (Bool)
+import Data.Bool (Bool, bool)
+import Data.Function ((.))
+import Data.Functor (Functor)
 import Data.Either (Either(..))
 import Data.Monoid (Monoid(..))
 import Control.Applicative
@@ -20,3 +27,19 @@ orEmpty b a = if b then pure a else empty
 
 eitherA :: (Alternative f) => f a -> f b -> f (Either a b)
 eitherA a b = (Left <$> a) <|> (Right <$> b)
+
+guarded :: (Alternative f) => (a -> Bool) -> a -> f a
+guarded p x = bool empty (pure x) (p x)
+
+guardedA :: (Functor f, Alternative t) => (a -> f Bool) -> a -> f (t a)
+guardedA p x = bool empty (pure x) <$> p x
+
+purer :: (Applicative f, Applicative g) => a -> f (g a)
+purer = pure . pure
+
+liftAA2 :: (Applicative f, Applicative g) => (a -> b -> c) -> f (g a) -> f (g b) -> f (g c)
+liftAA2 = liftA2 . liftA2
+
+(<<*>>) :: (Applicative f, Applicative g)  => f (g (a -> b)) -> f (g a) -> f (g b)
+(<<*>>) = liftA2 (<*>)
+
diff --git a/src/Functor.hs b/src/Functor.hs
index 87d6bf349..03bbf01fe 100644
--- a/src/Functor.hs
+++ b/src/Functor.hs
@@ -29,6 +29,9 @@ infixl 4 $>
 ($>) :: Functor f => f a -> b -> f b
 ($>) = flip (<$)
 
+(<<$>>) :: (Functor f, Functor g) => (a -> b) -> f (g a) -> f (g b)
+(<<$>>) = fmap . fmap
+
 void :: Functor f => f a -> f ()
 void x = () <$ x
 #endif