diff --git a/.ghci b/.ghci
deleted file mode 100644
--- a/.ghci
+++ /dev/null
@@ -1,1 +0,0 @@
-:set -isrc -idist/build/autogen -optP-include -optPdist/build/autogen/cabal_macros.h
diff --git a/.gitignore b/.gitignore
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 dist
+dist-newstyle
 docs
 wiki
 TAGS
@@ -11,3 +12,21 @@
 *.hi
 *~
 *#
+.stack-work/
+cabal-dev
+*.chi
+*.chs.h
+*.dyn_o
+*.dyn_hi
+.hpc
+.hsenv
+.cabal-sandbox/
+cabal.sandbox.config
+*.prof
+*.aux
+*.hp
+*.eventlog
+cabal.project.local
+cabal.project.local~
+.HTF/
+.ghc.environment.*
diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,97 +1,146 @@
-# This file has been generated -- see https://github.com/hvr/multi-ghc-travis
+# This Travis job script has been generated by a script via
+#
+#   runghc make_travis_yml_2.hs '-o' '.travis.yml' '--irc-channel=irc.freenode.org#haskell-lens' '--no-no-tests-no-bench' '--no-installed' 'cabal.project'
+#
+# For more information, see https://github.com/hvr/multi-ghc-travis
+#
 language: c
 sudo: false
 
+git:
+  submodules: false  # whether to recursively clone submodules
+
+notifications:
+  irc:
+    channels:
+      - "irc.freenode.org#haskell-lens"
+    skip_join: true
+    template:
+      - "\x0313adjunctions\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"
+
 cache:
   directories:
-    - $HOME/.cabsnap
     - $HOME/.cabal/packages
+    - $HOME/.cabal/store
 
 before_cache:
   - rm -fv $HOME/.cabal/packages/hackage.haskell.org/build-reports.log
-  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/00-index.tar
+  # remove files that are regenerated by 'cabal update'
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/00-index.*
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/*.json
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.cache
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.tar
+  - rm -fv $HOME/.cabal/packages/hackage.haskell.org/01-index.tar.idx
 
+  - rm -rfv $HOME/.cabal/packages/head.hackage
+
+addons:
+  apt:
+    packages: &apt_packages
+      - ghc-ppa-tools
+      - alex-3.1.7
+      - happy-1.19.5
+
 matrix:
   include:
-    - env: CABALVER=1.24 GHCVER=7.4.2
-      compiler: ": #GHC 7.4.2"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.4.2,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=7.6.3
-      compiler: ": #GHC 7.6.3"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.6.3,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.18 GHCVER=7.8.4
-      compiler: ": #GHC 7.8.4"
-      addons: {apt: {packages: [cabal-install-1.18,ghc-7.8.4,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.22 GHCVER=7.10.1
-      compiler: ": #GHC 7.10.1"
-      addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.1,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
-    - env: CABALVER=1.22 GHCVER=7.10.2
-      compiler: ": #GHC 7.10.2"
-      addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.2,alex-3.1.4,happy-1.19.5], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.4.2"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-7.4.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.6.3"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-7.6.3], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.8.4"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-7.8.4], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.10.3"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-7.10.3], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.0.2"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-8.0.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.2.2"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-8.2.2], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.4.1"
+      env: GHCHEAD=true
+      addons: {apt: {packages: [*apt_packages,cabal-install-head,ghc-8.4.1], sources: [hvr-ghc]}}
+    - compiler: "ghc-head"
+      env: GHCHEAD=true
+      addons: {apt: {packages: [*apt_packages,cabal-install-head,ghc-head], sources: [hvr-ghc]}}
 
+  allow_failures:
+    - compiler: "ghc-8.4.1"
+    - compiler: "ghc-head"
+
 before_install:
- - unset CC
- - export HAPPYVER=1.19.5
- - export ALEXVER=3.1.4
- - export PATH=~/.cabal/bin:/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:/opt/happy/$HAPPYVER/bin:/opt/alex/$ALEXVER/bin:$PATH
+  - HC=${CC}
+  - HCPKG=${HC/ghc/ghc-pkg}
+  - unset CC
+  - ROOTDIR=$(pwd)
+  - mkdir -p $HOME/.local/bin
+  - "PATH=/opt/ghc/bin:/opt/ghc-ppa-tools/bin:$HOME/local/bin:$PATH"
+  - HCNUMVER=$(( $(${HC} --numeric-version|sed -E 's/([0-9]+)\.([0-9]+)\.([0-9]+).*/\1 * 10000 + \2 * 100 + \3/') ))
+  - echo $HCNUMVER
 
 install:
- - cabal --version
- - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"
- - if [ -f $HOME/.cabal/packages/hackage.haskell.org/00-index.tar.gz ];
-   then
-     zcat $HOME/.cabal/packages/hackage.haskell.org/00-index.tar.gz >
-          $HOME/.cabal/packages/hackage.haskell.org/00-index.tar;
-   fi
- - travis_retry cabal update
- - "sed -i  's/^jobs:.*$/jobs: 2/' $HOME/.cabal/config"
- - cabal install --only-dependencies --enable-tests --enable-benchmarks --dry -v > installplan.txt
- - sed -i -e '1,/^Resolving /d' installplan.txt; cat installplan.txt
+  - cabal --version
+  - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
+  - BENCH=${BENCH---enable-benchmarks}
+  - TEST=${TEST---enable-tests}
+  - HADDOCK=${HADDOCK-true}
+  - INSTALLED=${INSTALLED-true}
+  - GHCHEAD=${GHCHEAD-false}
+  - travis_retry cabal update -v
+  - "sed -i.bak 's/^jobs:/-- jobs:/' ${HOME}/.cabal/config"
+  - rm -fv cabal.project cabal.project.local
+  # Overlay Hackage Package Index for GHC HEAD: https://github.com/hvr/head.hackage
+  - |
+    if $GHCHEAD; then
+      sed -i.bak 's/-- allow-newer:.*/allow-newer: *:base, *:template-haskell, *:ghc, *:Cabal/' ${HOME}/.cabal/config
 
-# check whether current requested install-plan matches cached package-db snapshot
- - if diff -u installplan.txt $HOME/.cabsnap/installplan.txt;
-   then
-     echo "cabal build-cache HIT";
-     rm -rfv .ghc;
-     cp -a $HOME/.cabsnap/ghc $HOME/.ghc;
-     cp -a $HOME/.cabsnap/lib $HOME/.cabsnap/share $HOME/.cabsnap/bin $HOME/.cabal/;
-   else
-     echo "cabal build-cache MISS";
-     rm -rf $HOME/.cabsnap;
-     mkdir -p $HOME/.ghc $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin;
-     cabal install --only-dependencies --enable-tests --enable-benchmarks;
-     if [ "$GHCVER" = "7.10.1" ]; then cabal install Cabal-1.22.4.0; fi;
-   fi
+      echo 'repository head.hackage'                                                        >> ${HOME}/.cabal/config
+      echo '   url: http://head.hackage.haskell.org/'                                       >> ${HOME}/.cabal/config
+      echo '   secure: True'                                                                >> ${HOME}/.cabal/config
+      echo '   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740' >> ${HOME}/.cabal/config
+      echo '              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb' >> ${HOME}/.cabal/config
+      echo '              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e' >> ${HOME}/.cabal/config
+      echo '   key-threshold: 3'                                                            >> ${HOME}/.cabal.config
 
-# snapshot package-db on cache miss
- - if [ ! -d $HOME/.cabsnap ];
-   then
-      echo "snapshotting package-db to build-cache";
-      mkdir $HOME/.cabsnap;
-      cp -a $HOME/.ghc $HOME/.cabsnap/ghc;
-      cp -a $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin installplan.txt $HOME/.cabsnap/;
-   fi
+      cabal new-update head.hackage -v
+    fi
+  - grep -Ev -- '^\s*--' ${HOME}/.cabal/config | grep -Ev '^\s*$'
+  - "printf 'packages: \".\"\\n' > cabal.project"
+  - cat cabal.project
+  - if [ -f "./configure.ac" ]; then
+      (cd "." && autoreconf -i);
+    fi
+  - rm -f cabal.project.freeze
+  - cabal new-build -w ${HC} ${TEST} ${BENCH} --project-file="cabal.project" --dep -j2 all
+  - rm -rf "."/.ghc.environment.* "."/dist
+  - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
 
 # Here starts the actual work to be performed for the package under test;
 # any command which exits with a non-zero exit code causes the build to fail.
 script:
- - cabal configure --enable-tests -v2  # -v2 provides useful information for debugging
- - cabal build   # this builds all libraries and executables (including tests)
- - cabal test
- - cabal bench || true  # expected result: these will crash
- - cabal sdist || true  # tests that a source-distribution can be generated
+  # test that source-distributions can be generated
+  - (cd "." && cabal sdist)
+  - mv "."/dist/adjunctions-*.tar.gz ${DISTDIR}/
+  - cd ${DISTDIR} || false
+  - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - "printf 'packages: adjunctions-*/*.cabal\\n' > cabal.project"
+  - cat cabal.project
 
-# Check that the resulting source distribution can be built & installed.
-# If there are no other `.tar.gz` files in `dist`, this can be even simpler:
-# `cabal install --force-reinstalls dist/*-*.tar.gz`
- - SRC_TGZ=$(cabal info . | awk '{print $2;exit}').tar.gz &&
-   (cd dist && cabal install --force-reinstalls "$SRC_TGZ")
 
-notifications:
-  irc:
-    channels:
-      - "irc.freenode.org#haskell-lens"
-    skip_join: true
-    template:
-      - "\x0313adjunctions\x0f/\x0306%{branch}\x0f \x0314%{commit}\x0f %{message} \x0302\x1f%{build_url}\x0f"
+  # build & run tests, build benchmarks
+  - cabal new-build -w ${HC} ${TEST} ${BENCH} all
+  - if [ "x$TEST" = "x--enable-tests" ]; then cabal new-test -w ${HC} ${TEST} ${BENCH} all; fi
+
+  # cabal check
+  - (cd adjunctions-* && cabal check)
+
+  # haddock
+  - rm -rf ./dist-newstyle
+  - if $HADDOCK; then cabal new-haddock -w ${HC} ${TEST} ${BENCH} all; else echo "Skipping haddock generation";fi
+
+# REGENDATA ["-o",".travis.yml","--irc-channel=irc.freenode.org#haskell-lens","--no-no-tests-no-bench","--no-installed","cabal.project"]
 # EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,14 @@
+4.4 [2018.01.28]
+----------------
+* Added `imapRep`, `ifoldMapRep`, `itraverseRep` to make it easier to define representable `FunctorWithIndex`, `FoldableWithIndex`, `TraversableWithIndex` instances from the `lens` package.
+* Add `GHC.Generics`-based default implementation for `Data.Functor.Rep.Representable` instances
+* Add `Data.Functor.Rep.Representable` instances for `Backwards`, `Reverse`, and the datatypes in `GHC.Generics`.
+* Add `Data.Functor.Adjunction.Adjunction` instances for some datatypes in `GHC.Generics`
+* Add `Data.Functor.Contravariant.Rep.Representable` instances for `U1` and `(:*:)` from `GHC.Generics`
+* Add `collectRep` and `imapRep` functions to `Data.Functor.Rep`.
+* Add `MINIMAL` pragmas to the `Adjunction` classes.
+* Allow `free-5`.
+
 4.3
 ---
 * Removed a spurious superclass constraint for `Applicative (StoreT g w)`
diff --git a/adjunctions.cabal b/adjunctions.cabal
--- a/adjunctions.cabal
+++ b/adjunctions.cabal
@@ -1,8 +1,8 @@
 name:          adjunctions
 category:      Data Structures, Adjunctions
-version:       4.3
+version:       4.4
 license:       BSD3
-cabal-version: >= 1.6
+cabal-version: >= 1.8
 license-file:  LICENSE
 author:        Edward A. Kmett
 maintainer:    Edward A. Kmett <ekmett@gmail.com>
@@ -11,10 +11,9 @@
 bug-reports:   http://github.com/ekmett/adjunctions/issues
 copyright:     Copyright (C) 2011-2014 Edward A. Kmett
 synopsis:      Adjunctions and representable functors
-description:   Adjunctions and representable functors
+description:   Adjunctions and representable functors.
 build-type:    Simple
 extra-source-files:
-  .ghci
   .gitignore
   .travis.yml
   .vim.custom
@@ -23,6 +22,13 @@
   HLint.hs
   CHANGELOG.markdown
   README.markdown
+tested-with:   GHC == 7.4.2
+             , GHC == 7.6.3
+             , GHC == 7.8.4
+             , GHC == 7.10.3
+             , GHC == 8.0.2
+             , GHC == 8.2.2
+             , GHC == 8.4.1
 
 source-repository head
   type: git
@@ -45,8 +51,8 @@
     comonad             >= 4       && < 6,
     containers          >= 0.3     && < 0.6,
     contravariant       >= 1       && < 2,
-    distributive        >= 0.4     && < 1,
-    free                >= 4       && < 5,
+    distributive        >= 0.5.1   && < 1,
+    free                >= 4       && < 6,
     mtl                 >= 2.0.1   && < 2.3,
     profunctors         >= 4       && < 6,
     tagged              >= 0.7     && < 1,
@@ -56,6 +62,9 @@
     transformers-compat >= 0.3     && < 1,
     void                >= 0.5.5.1 && < 1
 
+  if impl(ghc < 7.6)
+    build-depends: ghc-prim
+
   exposed-modules:
     Control.Comonad.Representable.Store
     Control.Comonad.Trans.Adjoint
@@ -70,3 +79,24 @@
     Data.Functor.Rep
 
   ghc-options: -Wall
+
+  -- See https://ghc.haskell.org/trac/ghc/wiki/Migration/8.0#base-4.9.0.0
+  if impl(ghc >= 8.0)
+    ghc-options: -Wcompat -Wnoncanonical-monad-instances -Wnoncanonical-monadfail-instances
+
+test-suite spec
+  type:           exitcode-stdio-1.0
+  hs-source-dirs: tests
+
+  build-tool-depends: hspec-discover:hspec-discover >=2 && <3
+  build-depends:
+    adjunctions,
+    base             >= 4     && < 5,
+    distributive     >= 0.5.1 && < 1,
+    generic-deriving >= 1.11  && < 2,
+    hspec            >= 2     && < 3
+
+  main-is: Spec.hs
+  other-modules: GenericsSpec
+
+  ghc-options: -Wall -threaded -rtsopts
diff --git a/src/Control/Monad/Representable/State.hs b/src/Control/Monad/Representable/State.hs
--- a/src/Control/Monad/Representable/State.hs
+++ b/src/Control/Monad/Representable/State.hs
@@ -147,7 +147,7 @@
   StateT m >>- f = StateT $ fmap (>>- rightAdjunctRep (runStateT . f)) m
 
 instance (Representable g, Monad m) => Monad (StateT g m) where
-#if __GLASGOW_VERSION__ < 710
+#if __GLASGOW_HASKELL__ < 710
   return = StateT . leftAdjunctRep return
 #endif
   StateT m >>= f = StateT $ fmap (>>= rightAdjunctRep (runStateT . f)) m
diff --git a/src/Data/Functor/Adjunction.hs b/src/Data/Functor/Adjunction.hs
--- a/src/Data/Functor/Adjunction.hs
+++ b/src/Data/Functor/Adjunction.hs
@@ -1,12 +1,16 @@
 {-# LANGUAGE Rank2Types
            , MultiParamTypeClasses
            , FunctionalDependencies
+           , TypeOperators
            , UndecidableInstances #-}
 
 {-# LANGUAGE CPP #-}
 #if __GLASGOW_HASKELL__ >= 702
 {-# LANGUAGE Trustworthy #-}
 #endif
+#if __GLASGOW_HASKELL__ >= 708
+{-# LANGUAGE EmptyCase #-}
+#endif
 
 -------------------------------------------------------------------------------------------
 -- |
@@ -54,6 +58,7 @@
 import Data.Functor.Sum
 import Data.Profunctor
 import Data.Void
+import GHC.Generics
 
 -- | An adjunction between Hask and Hask.
 --
@@ -74,6 +79,9 @@
 -- > leftAdjunct counit = id
 class (Functor f, Representable u) =>
       Adjunction f u | f -> u, u -> f where
+#if __GLASGOW_HASKELL__ >= 708
+  {-# MINIMAL (unit, counit) | (leftAdjunct, rightAdjunct) #-}
+#endif
   unit         :: a -> u (f a)
   counit       :: f (u a) -> a
   leftAdjunct  :: (f a -> b) -> a -> u b
@@ -191,3 +199,39 @@
   unit a = return a :< tabulateAdjunction (\k -> leftAdjunct (wrap . flip unsplitL k) a)
   counit (Pure a) = extract a
   counit (Free k) = rightAdjunct (flip indexAdjunction k . unwrap) (extractL k)
+
+instance Adjunction V1 U1 where
+  unit _ = U1
+  counit = absurdV1
+
+absurdV1 :: V1 a -> b
+#if __GLASGOW_HASKELL__ >= 708
+absurdV1 x = case x of {}
+#else
+absurdV1 x = x `seq` undefined
+#endif
+
+instance Adjunction Par1 Par1 where
+  leftAdjunct f = Par1 . f . Par1
+  rightAdjunct f = unPar1 . f . unPar1
+
+instance Adjunction f g => Adjunction (Rec1 f) (Rec1 g) where
+  unit   = Rec1 . leftAdjunct Rec1
+  counit = rightAdjunct unRec1 . unRec1
+
+-- @i@ and @c@ indexes have to be the same due functional dependency.
+-- But we want them to be different, therefore we rather not define this instance
+{-
+instance Adjunction f g => Adjunction (M1 i c f) (M1 i c g) where
+  unit   = M1 . leftAdjunct M1
+  counit = rightAdjunct unM1 . unM1
+-}
+
+instance (Adjunction f g, Adjunction f' g') => Adjunction (f' :.: f) (g :.: g') where
+  unit   = Comp1 . leftAdjunct (leftAdjunct Comp1)
+  counit = rightAdjunct (rightAdjunct unComp1) . unComp1
+
+instance (Adjunction f g, Adjunction f' g') => Adjunction (f :+: f') (g :*: g') where
+  unit a = leftAdjunct L1 a :*: leftAdjunct R1 a
+  counit (L1 l) = rightAdjunct (\(x :*: _) -> x) l
+  counit (R1 r) = rightAdjunct (\(_ :*: x) -> x) r
diff --git a/src/Data/Functor/Contravariant/Adjunction.hs b/src/Data/Functor/Contravariant/Adjunction.hs
--- a/src/Data/Functor/Contravariant/Adjunction.hs
+++ b/src/Data/Functor/Contravariant/Adjunction.hs
@@ -41,6 +41,9 @@
 -- permit @unsafePerformIO@, and therefore does not exist.
 
 class (Contravariant f, Representable g) => Adjunction f g | f -> g, g -> f where
+#if __GLASGOW_HASKELL__ >= 708
+  {-# MINIMAL (unit, counit) | (leftAdjunct, rightAdjunct) #-}
+#endif
   unit :: a -> g (f a) -- monad in Hask
   counit :: a -> f (g a) -- comonad in Hask^op
   leftAdjunct  :: (b -> f a) -> a -> g b
diff --git a/src/Data/Functor/Contravariant/Rep.hs b/src/Data/Functor/Contravariant/Rep.hs
--- a/src/Data/Functor/Contravariant/Rep.hs
+++ b/src/Data/Functor/Contravariant/Rep.hs
@@ -1,4 +1,7 @@
-{-# LANGUAGE TypeFamilies, FlexibleContexts, FlexibleInstances #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
 {-# OPTIONS_GHC -fenable-rewrite-rules #-}
 ----------------------------------------------------------------------
 -- |
@@ -26,6 +29,7 @@
 import Data.Functor.Product
 import Data.Profunctor
 import Data.Proxy
+import GHC.Generics hiding (Rep)
 import Prelude hiding (lookup)
 
 -- | A 'Contravariant' functor @f@ is 'Representable' if 'tabulate' and 'index' witness an isomorphism to @(_ -> Rep f)@.
@@ -59,7 +63,7 @@
 -- This can be used with the combinators from the @lens@ package.
 --
 -- @'tabulated' :: 'Representable' f => 'Iso'' (a -> 'Rep' f) (f a)@
-tabulated :: (Representable f, Representable g, Profunctor p, Functor h) 
+tabulated :: (Representable f, Representable g, Profunctor p, Functor h)
           => p (f a) (h (g b)) -> p (a -> Rep f) (h (b -> Rep g))
 tabulated = dimap tabulate (fmap index)
 {-# INLINE tabulated #-}
@@ -90,3 +94,16 @@
   contramapWithRep h (Pair f g) = Pair
       (contramapWithRep (fmap fst . h) f)
       (contramapWithRep (fmap snd . h) g)
+
+instance Representable U1 where
+  type Rep U1 = ()
+  tabulate _ = U1
+  index U1 _ = ()
+  contramapWithRep _ U1 = U1
+
+instance (Representable f, Representable g) => Representable (f :*: g) where
+  type Rep (f :*: g) = (Rep f, Rep g)
+  tabulate f = tabulate (fst . f) :*: tabulate (snd . f)
+  index (f :*: g) a = (index f a, index g a)
+  contramapWithRep h (f :*: g) =
+    contramapWithRep (fmap fst . h) f :*: contramapWithRep (fmap snd . h) g
diff --git a/src/Data/Functor/Rep.hs b/src/Data/Functor/Rep.hs
--- a/src/Data/Functor/Rep.hs
+++ b/src/Data/Functor/Rep.hs
@@ -1,10 +1,16 @@
 {-# LANGUAGE CPP #-}
 {-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE TypeOperators #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE UndecidableInstances #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE DeriveFunctor #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE DefaultSignatures #-}
+{-# LANGUAGE Trustworthy #-}
+{-# LANGUAGE TypeOperators #-}
 {-# OPTIONS_GHC -fenable-rewrite-rules #-}
 ----------------------------------------------------------------------
 -- |
@@ -31,6 +37,7 @@
   , fmapRep
   -- ** Distributive
   , distributeRep
+  , collectRep
   -- ** Apply/Applicative
   , apRep
   , pureRep
@@ -57,10 +64,24 @@
   , duplicateRepBy
   , extendRepBy
   , extractRepBy
+  -- ** WithIndex
+  , imapRep
+  , ifoldMapRep
+  , itraverseRep
+
+  -- ** Generics
+  , GRep
+  , gindex
+  , gtabulate
+  , WrappedRep(..)
   ) where
 
 import Control.Applicative
+import Control.Applicative.Backwards
 import Control.Arrow ((&&&))
+#if __GLASGOW_HASKELL__ >= 708
+import Data.Coerce
+#endif
 import Control.Comonad
 import Control.Comonad.Trans.Class
 import Control.Comonad.Trans.Traced
@@ -71,19 +92,23 @@
 import Data.Complex
 #endif
 import Data.Distributive
+import Data.Foldable (Foldable(fold))
 import Data.Functor.Bind
 import Data.Functor.Identity
 import Data.Functor.Compose
 import Data.Functor.Extend
 import Data.Functor.Product
+import Data.Functor.Reverse
 import qualified Data.Monoid as Monoid
-import Data.Profunctor
+import Data.Profunctor.Unsafe
 import Data.Proxy
 import Data.Sequence (Seq)
 import qualified Data.Sequence as Seq
 import Data.Semigroup hiding (Product)
 import Data.Tagged
+import Data.Traversable (Traversable(sequenceA))
 import Data.Void
+import GHC.Generics hiding (Rep)
 import Prelude hiding (lookup)
 
 -- | A 'Functor' @f@ is 'Representable' if 'tabulate' and 'index' witness an isomorphism to @(->) x@.
@@ -99,14 +124,128 @@
 -- @
 
 class Distributive f => Representable f where
+  -- | If no definition is provided, this will default to 'GRep'.
   type Rep f :: *
+  type Rep f = GRep f
+
   -- |
   -- @
   -- 'fmap' f . 'tabulate' ≡ 'tabulate' . 'fmap' f
   -- @
+  --
+  -- If no definition is provided, this will default to 'gtabulate'.
   tabulate :: (Rep f -> a) -> f a
+  default tabulate :: (Generic1 f, GRep f ~ Rep f, GTabulate (Rep1 f))
+                   => (Rep f -> a) -> f a
+  tabulate = gtabulate
+
+  -- | If no definition is provided, this will default to 'gindex'.
   index    :: f a -> Rep f -> a
+  default index :: (Generic1 f, GRep f ~ Rep f, GIndex (Rep1 f))
+                => f a -> Rep f -> a
+  index = gindex
 
+-- | A default implementation of 'Rep' for a datatype that is an instance of
+-- 'Generic1'. This is usually composed of 'Either', tuples, unit tuples, and
+-- underlying 'Rep' values. For instance, if you have:
+--
+-- @
+-- data Foo a = MkFoo a (Bar a) (Baz (Quux a)) deriving ('Functor', 'Generic1')
+-- instance 'Representable' Foo
+-- @
+--
+-- Then you'll get:
+--
+-- @
+-- 'GRep' Foo = Either () (Either ('WrappedRep' Bar) ('WrappedRep' Baz, 'WrappedRep' Quux))
+-- @
+--
+-- (See the Haddocks for 'WrappedRep' for an explanation of its purpose.)
+type GRep f = GRep' (Rep1 f)
+
+-- | A default implementation of 'tabulate' in terms of 'GRep'.
+gtabulate :: (Generic1 f, GRep f ~ Rep f, GTabulate (Rep1 f))
+          => (Rep f -> a) -> f a
+gtabulate = to1 . gtabulate'
+
+-- | A default implementation of 'index' in terms of 'GRep'.
+gindex :: (Generic1 f, GRep f ~ Rep f, GIndex (Rep1 f))
+       => f a -> Rep f -> a
+gindex = gindex' . from1
+
+type family GRep' (f :: * -> *) :: *
+class GTabulate f where
+  gtabulate' :: (GRep' f -> a) -> f a
+class GIndex f where
+  gindex' :: f a -> GRep' f -> a
+
+type instance GRep' (f :*: g) = Either (GRep' f) (GRep' g)
+instance (GTabulate f, GTabulate g) => GTabulate (f :*: g) where
+  gtabulate' f = gtabulate' (f . Left) :*: gtabulate' (f . Right)
+instance (GIndex f, GIndex g) => GIndex (f :*: g) where
+  gindex' (a :*: _) (Left  i) = gindex' a i
+  gindex' (_ :*: b) (Right j) = gindex' b j
+
+type instance GRep' (f :.: g) = (WrappedRep f, GRep' g)
+instance (Representable f, GTabulate g) => GTabulate (f :.: g) where
+  gtabulate' f = Comp1 $ tabulate $ fmap gtabulate' $ fmap (curry f) WrapRep
+instance (Representable f, GIndex g) => GIndex (f :.: g) where
+  gindex' (Comp1 fg) (i, j) = gindex' (index fg (unwrapRep i)) j
+
+type instance GRep' Par1 = ()
+instance GTabulate Par1 where
+  gtabulate' f = Par1 (f ())
+instance GIndex Par1 where
+  gindex' (Par1 a) () = a
+
+type instance GRep' (Rec1 f) = WrappedRep f
+#if __GLASGOW_HASKELL__ >= 708
+-- Using coerce explicitly here seems a bit more readable, and
+-- likely a drop easier on the simplifier.
+instance Representable f => GTabulate (Rec1 f) where
+  gtabulate' = coerce (tabulate :: (Rep f -> a) -> f a)
+                 :: forall a . (WrappedRep f -> a) -> Rec1 f a
+instance Representable f => GIndex (Rec1 f) where
+  gindex' = coerce (index :: f a -> Rep f -> a)
+                 :: forall a . Rec1 f a -> WrappedRep f -> a
+#else
+instance Representable f => GTabulate (Rec1 f) where
+  gtabulate' = Rec1 #. tabulate .# (. WrapRep)
+instance Representable f => GIndex (Rec1 f) where
+  gindex' = (. unwrapRep) #. index .# unRec1
+#endif
+
+type instance GRep' (M1 i c f) = GRep' f
+instance GTabulate f => GTabulate (M1 i c f) where
+  gtabulate' = M1 #. gtabulate'
+instance GIndex f => GIndex (M1 i c f) where
+  gindex' = gindex' .# unM1
+
+-- | On the surface, 'WrappedRec' is a simple wrapper around 'Rep'. But it plays
+-- a very important role: it prevents generic 'Representable' instances for
+-- recursive types from sending the typechecker into an infinite loop. Consider
+-- the following datatype:
+--
+-- @
+-- data Stream a = a :< Stream a deriving ('Functor', 'Generic1')
+-- instance 'Representable' Stream
+-- @
+--
+-- With 'WrappedRep', we have its 'Rep' being:
+--
+-- @
+-- 'Rep' Stream = 'Either' () ('WrappedRep' Stream)
+-- @
+--
+-- If 'WrappedRep' didn't exist, it would be:
+--
+-- @
+-- 'Rep' Stream = Either () (Either () (Either () ...))
+-- @
+--
+-- An infinite type! 'WrappedRep' breaks the potentially infinite loop.
+newtype WrappedRep f = WrapRep { unwrapRep :: Rep f }
+
 {-# RULES
 "tabulate/index" forall t. tabulate (index t) = t #-}
 
@@ -152,6 +291,9 @@
 distributeRep :: (Representable f, Functor w) => w (f a) -> f (w a)
 distributeRep wf = tabulate (\k -> fmap (`index` k) wf)
 
+collectRep :: (Representable f, Functor w) => (a -> f b) -> w a -> f (w b)
+collectRep f w = tabulate (\k -> (`index` k) . f <$> w)
+
 duplicateRepBy :: Representable f => (Rep f -> Rep f -> Rep f) -> f a -> f (f a)
 duplicateRepBy plus w = tabulate (\m -> tabulate (index w . plus m))
 
@@ -176,6 +318,17 @@
 extractRep :: (Representable f, Monoid (Rep f)) => f a -> a
 extractRep = extractRepBy mempty
 
+imapRep :: Representable r => (Rep r -> a -> a') -> (r a -> r a')
+imapRep f xs = tabulate (f <*> index xs)
+
+ifoldMapRep :: forall r m a. (Representable r, Foldable r, Monoid m)
+            => (Rep r -> a -> m) -> (r a -> m)
+ifoldMapRep ix xs = fold (tabulate (\(i :: Rep r) -> ix i $ index xs i) :: r m)
+
+itraverseRep :: forall r f a a'. (Representable r, Traversable r, Applicative f)
+             => (Rep r -> a -> f a') -> (r a -> f (r a'))
+itraverseRep ix xs = sequenceA $ tabulate (ix <*> index xs)
+
 -- * Instances
 
 instance Representable Proxy where
@@ -195,8 +348,8 @@
 
 instance Representable m => Representable (IdentityT m) where
   type Rep (IdentityT m) = Rep m
-  index (IdentityT m) i = index m i
-  tabulate = IdentityT . tabulate
+  index = index .# runIdentityT
+  tabulate = IdentityT #. tabulate
 
 instance Representable ((->) e) where
   type Rep ((->) e) = e
@@ -216,7 +369,7 @@
 instance Representable w => Representable (TracedT s w) where
   type Rep (TracedT s w) = (s, Rep w)
   index (TracedT w) (e,k) = index w k e
-  tabulate = TracedT . unCo . collect (Co . tabulate) . curry
+  tabulate = TracedT . unCo . collect (Co #. tabulate) . curry
 
 instance (Representable f, Representable g) => Representable (Product f g) where
   type Rep (Product f g) = Either (Rep f) (Rep g)
@@ -231,6 +384,16 @@
       k Seq.:< ks -> index (index as k) ks
   tabulate f = f Seq.empty :< tabulate (\k -> tabulate (f . (k Seq.<|)))
 
+instance Representable f => Representable (Backwards f) where
+  type Rep (Backwards f) = Rep f
+  index = index .# forwards
+  tabulate = Backwards #. tabulate
+
+instance Representable f => Representable (Reverse f) where
+  type Rep (Reverse f) = Rep f
+  index = index .# getReverse
+  tabulate = Reverse #. tabulate
+
 instance Representable Monoid.Dual where
   type Rep Monoid.Dual = ()
   index (Monoid.Dual d) () = d
@@ -253,12 +416,43 @@
   tabulate f = f False :+ f True
 #endif
 
+instance Representable U1 where
+  type Rep U1 = Void
+  index U1 = absurd
+  tabulate _ = U1
+
+instance (Representable f, Representable g) => Representable (f :*: g) where
+  type Rep (f :*: g) = Either (Rep f) (Rep g)
+  index (a :*: _) (Left  i) = index a i
+  index (_ :*: b) (Right j) = index b j
+  tabulate f = tabulate (f . Left) :*: tabulate (f . Right)
+
+instance (Representable f, Representable g) => Representable (f :.: g) where
+  type Rep (f :.: g) = (Rep f, Rep g)
+  index (Comp1 fg) (i, j) = index (index fg i) j
+  tabulate = Comp1 . tabulate . fmap tabulate . curry
+
+instance Representable Par1 where
+  type Rep Par1 = ()
+  index (Par1 a) () = a
+  tabulate f = Par1 (f ())
+
+instance Representable f => Representable (Rec1 f) where
+  type Rep (Rec1 f) = Rep f
+  index = index .# unRec1
+  tabulate = Rec1 #. tabulate
+
+instance Representable f => Representable (M1 i c f) where
+  type Rep (M1 i c f) = Rep f
+  index = index .# unM1
+  tabulate = M1 #. tabulate
+
 newtype Co f a = Co { unCo :: f a } deriving Functor
 
 instance Representable f => Representable (Co f) where
   type Rep (Co f) = Rep f
-  tabulate = Co . tabulate
-  index (Co f) i = index f i
+  tabulate = Co #. tabulate
+  index = index .# unCo
 
 instance Representable f => Apply (Co f) where
   (<.>) = apRep
@@ -269,6 +463,7 @@
 
 instance Representable f => Distributive (Co f) where
   distribute = distributeRep
+  collect = collectRep
 
 instance Representable f => Bind (Co f) where
   (>>-) = bindRep
diff --git a/tests/GenericsSpec.hs b/tests/GenericsSpec.hs
new file mode 100644
--- /dev/null
+++ b/tests/GenericsSpec.hs
@@ -0,0 +1,112 @@
+{-# LANGUAGE CPP #-}
+{-# LANGUAGE DeriveFunctor #-}
+{-# LANGUAGE DeriveGeneric #-}
+{-# LANGUAGE EmptyDataDecls #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TemplateHaskell #-}
+{-# LANGUAGE TypeFamilies #-}
+----------------------------------------------------------------------
+-- |
+-- Copyright   :  (c) Edward Kmett 2011-2014
+-- License     :  BSD3
+--
+-- Maintainer  :  ekmett@gmail.com
+-- Stability   :  experimental
+--
+-- Tests for generically derived 'Representable' instances.
+----------------------------------------------------------------------
+module GenericsSpec (main, spec) where
+
+import           Data.Distributive (Distributive(..))
+import           Data.Functor.Rep (Representable(..), WrappedRep(..))
+
+#if __GLASGOW_HASKELL__ >= 706
+import           Generics.Deriving.Base hiding (Rep)
+#else
+import qualified Generics.Deriving.TH as Generics (deriveAll1)
+#endif
+
+import           Test.Hspec
+
+main :: IO ()
+main = hspec spec
+
+spec :: Spec
+spec = do
+  describe "Id" $
+    itIndexes "idExample" "idRep" idExample idRep 42
+  describe "Stream" $ do
+    let streamIndexes :: String -> Rep Stream -> Int -> Spec
+        streamIndexes repNum = itIndexes "streamExample" ("streamRep" ++ repNum) streamExample
+    streamIndexes "1" streamRep1 0
+    streamIndexes "2" streamRep2 1
+    streamIndexes "3" streamRep3 2
+  describe "PolyRec" $ do
+    let polyRecIndexes :: String -> Rep PolyRec -> Int -> Spec
+        polyRecIndexes repNum = itIndexes "polyRecExample" ("polyRecRep" ++ repNum)
+                                          polyRecExample
+    polyRecIndexes "1" polyRecRep1 1
+    polyRecIndexes "2" polyRecRep2 2
+    polyRecIndexes "3" polyRecRep3 0
+
+itIndexes :: (Eq a, Representable f, Show a)
+          => String -> String -> f a -> Rep f -> a -> Spec
+itIndexes exampleStr repStr exampleVal rep res =
+  it ("index " ++ exampleStr ++ " " ++ repStr ++ " = " ++ show res) $
+    index exampleVal rep `shouldBe` res
+
+-------------------------------------------------------------------------------
+
+newtype Id a = Id { runId :: a }
+  deriving Functor
+instance Distributive Id where
+  collect f  = Id . fmap (runId . f)
+  distribute = Id . fmap runId
+instance Representable Id
+  -- type Rep Id = ()
+
+idExample :: Id Int
+idExample = Id 42
+
+idRep :: Rep Id
+idRep = ()
+
+data Stream a = (:>) { shead :: a, stail :: Stream a }
+  deriving Functor
+instance Distributive Stream where
+  distribute w = fmap shead w :> distribute (fmap stail w)
+instance Representable Stream
+  -- type Rep Stream = Either () (WrappedRep Stream)
+
+streamExample :: Stream Int
+streamExample = let s = 0 :> fmap (+1) s in s
+
+streamRep1, streamRep2, streamRep3 :: Rep Stream
+streamRep1 = Left ()
+streamRep2 = Right $ WrapRep $ Left ()
+streamRep3 = Right $ WrapRep $ Right $ WrapRep $ Left ()
+
+data PolyRec a = PolyRec (Id (PolyRec a)) a
+  deriving Functor
+instance Distributive PolyRec where
+  distribute fpa = PolyRec (Id $ distribute fpa) (fmap (\(PolyRec _ a) -> a) fpa)
+instance Representable PolyRec
+  -- type Rep PolyRec = Either (WrappedRep Id, WrappedRep PolyRec) ()
+
+polyRecExample :: PolyRec Int
+polyRecExample = let p = PolyRec (Id (fmap (+1) p)) 0 in p
+
+polyRecRep1, polyRecRep2, polyRecRep3 :: Rep PolyRec
+polyRecRep1 = Left (WrapRep (), WrapRep $ Right ())
+polyRecRep2 = Left (WrapRep (), WrapRep $ Left (WrapRep (), WrapRep $ Right ()))
+polyRecRep3 = Right ()
+
+#if __GLASGOW_HASKELL__ >= 706
+deriving instance Generic1 Id
+deriving instance Generic1 Stream
+deriving instance Generic1 PolyRec
+#else
+$(Generics.deriveAll1 ''Id)
+$(Generics.deriveAll1 ''Stream)
+$(Generics.deriveAll1 ''PolyRec)
+#endif
diff --git a/tests/Spec.hs b/tests/Spec.hs
new file mode 100644
--- /dev/null
+++ b/tests/Spec.hs
@@ -0,0 +1,1 @@
+{-# OPTIONS_GHC -F -pgmF hspec-discover #-}
