Add various instances to newtypes in Data.Monoid

Summary:
Add Functor instances for Dual, Sum and Product
Add Foldable instances for Dual, Sum and Product
Add Traversable instances for Dual, Sum and Product
Add Foldable and Traversable instances for First and Last
Add Applicative, Monad instances to Dual, Sum, Product
Add MonadFix to Data.Monoid wrappers
Derive Data for Identity
Add Data instances to Data.Monoid wrappers
Add Data (Alt f a) instance

Reviewers: ekmett, dfeuer, hvr, austin

Reviewed By: dfeuer, austin

Subscribers: thomie

Differential Revision: https://phabricator.haskell.org/D673

GHC Trac Issues: #10107

1 files changed, 60 insertions, 0 deletions

diff --git a/libraries/base/Data/Foldable.hs b/libraries/base/Data/Foldable.hs
index a745f66092..1f20261943 100644
--- a/libraries/base/Data/Foldable.hs
+++ b/libraries/base/Data/Foldable.hs
@@ -282,6 +282,66 @@ instance Foldable Proxy where
     sum _      = 0
     product _  = 1
 
+instance Foldable Dual where
+    foldMap            = coerce
+
+    elem               = (. getDual) #. (==)
+    foldl              = coerce
+    foldl'             = coerce
+    foldl1 _           = getDual
+    foldr f z (Dual x) = f x z
+    foldr'             = foldr
+    foldr1 _           = getDual
+    length _           = 1
+    maximum            = getDual
+    minimum            = getDual
+    null _             = False
+    product            = getDual
+    sum                = getDual
+    toList (Dual x)    = [x]
+
+instance Foldable Sum where
+    foldMap            = coerce
+
+    elem               = (. getSum) #. (==)
+    foldl              = coerce
+    foldl'             = coerce
+    foldl1 _           = getSum
+    foldr f z (Sum x)  = f x z
+    foldr'             = foldr
+    foldr1 _           = getSum
+    length _           = 1
+    maximum            = getSum
+    minimum            = getSum
+    null _             = False
+    product            = getSum
+    sum                = getSum
+    toList (Sum x)     = [x]
+
+instance Foldable Product where
+    foldMap               = coerce
+
+    elem                  = (. getProduct) #. (==)
+    foldl                 = coerce
+    foldl'                = coerce
+    foldl1 _              = getProduct
+    foldr f z (Product x) = f x z
+    foldr'                = foldr
+    foldr1 _              = getProduct
+    length _              = 1
+    maximum               = getProduct
+    minimum               = getProduct
+    null _                = False
+    product               = getProduct
+    sum                   = getProduct
+    toList (Product x)    = [x]
+
+instance Foldable First where
+    foldMap f = foldMap f . getFirst
+
+instance Foldable Last where
+    foldMap f = foldMap f . getLast
+
 -- We don't export Max and Min because, as Edward Kmett pointed out to me,
 -- there are two reasonable ways to define them. One way is to use Maybe, as we
 -- do here; the other way is to impose a Bounded constraint on the Monoid