diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -1,121 +1,147 @@
-# 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:
+      - "\x0313semigroupoids\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
+
 matrix:
   include:
-    - env: CABALVER=1.24 GHCVER=7.0.4
-      compiler: ": #GHC 7.0.4"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.0.4], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=7.2.2
-      compiler: ": #GHC 7.2.2"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.2.2], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=7.4.2
-      compiler: ": #GHC 7.4.2"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.4.2], 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], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=7.8.4
-      compiler: ": #GHC 7.8.4"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.8.4], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=7.10.3
-      compiler: ": #GHC 7.10.3"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.10.3], sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=8.0.2
-      compiler: ": #GHC 8.0.2"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.2], sources: [hvr-ghc]}}
-    - env: CABALVER=2.0 GHCVER=8.2.1
-      compiler: ": #GHC 8.2.1"
-      addons: {apt: {packages: [cabal-install-2.0,ghc-8.2.1], sources: [hvr-ghc]}}
-    - env: CABALVER=head GHCVER=head
-      compiler: ": #GHC head"
-      addons: {apt: {packages: [cabal-install-head,ghc-head], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.0.4"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-7.0.4], sources: [hvr-ghc]}}
+    - compiler: "ghc-7.2.2"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [*apt_packages,cabal-install-2.0,ghc-7.2.2], 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:
-    - env: CABALVER=1.24 GHCVER=7.0.4
-    - env: CABALVER=1.24 GHCVER=7.2.2
-    - env: CABALVER=head GHCVER=head
+    - compiler: "ghc-7.0.4"
+    - compiler: "ghc-7.2.2"
+    - compiler: "ghc-8.4.1"
+    - compiler: "ghc-head"
 
 before_install:
- - unset CC
- - export PATH=$HOME/.cabal/bin:/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$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 -v
- - sed -i 's/^jobs:/-- jobs:/' ${HOME}/.cabal/config
- - cabal install --only-dependencies --enable-tests --dry -v > installplan.txt
- - sed -i -e '1,/^Resolving /d' installplan.txt; cat installplan.txt
+  - cabal --version
+  - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
+  - BENCH=${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 -j --only-dependencies --enable-tests;
-   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.
+# 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:
- # -v2 provides useful information for debugging
- - cabal configure --enable-tests -v2
+  # test that source-distributions can be generated
+  - (cd "." && cabal sdist)
+  - mv "."/dist/semigroupoids-*.tar.gz ${DISTDIR}/
+  - cd ${DISTDIR} || false
+  - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - "printf 'packages: semigroupoids-*/*.cabal\\n' > cabal.project"
+  - cat cabal.project
 
- # this builds all libraries and executables
- # (including tests/benchmarks)
- - cabal build
 
- - cabal test
+  # 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
 
- # tests that a source-distribution can be generated
- - cabal sdist
+  # cabal check
+  - (cd semigroupoids-* && cabal check)
 
- # check that the generated source-distribution can be built & installed
- - export SRC_TGZ=$(cabal info . | awk '{print $2 ".tar.gz";exit}') ;
-   cd dist/;
-   if [ -f "$SRC_TGZ" ]; then
-      cabal install --force-reinstalls "$SRC_TGZ";
-   else
-      echo "expected '$SRC_TGZ' not found";
-      exit 1;
-   fi
+  # haddock
+  - rm -rf ./dist-newstyle
+  - if $HADDOCK; then cabal new-haddock -w ${HC} ${TEST} ${BENCH} all; else echo "Skipping haddock generation";fi
 
-notifications:
-  irc:
-    channels:
-      - "irc.freenode.org#haskell-lens"
-    skip_join: true
-    template:
-      - "\x0313semigroupoids\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"
+# 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 +1,15 @@
+5.2.2 [2018.01.18]
+------------------
+* Add `optional` to `Data.Functor.Alt` (analogous to the `optional` function
+  in `Control.Applicative`)
+* `liftF2` is now a class method of `Apply` (mirroring the fact that `liftA2`
+  is now a class method of `Applicative`). `liftF2` and `(<.>)` have default
+  definitions in terms of the other.
+* Allow building with GHC 8.4
+* `Apply` and `Bind` instances for `Q`, from the `template-haskell` package.
+* Add instances for `(:~:)` and `(:~~:)` from `Data.Type.Equality`, and
+  `Coercion` from `Data.Type.Coercion`
+
 5.2.1
 -----
 * Add the `toNonEmpty` method to `Foldable1`. Add `foldrM1` and `foldlM1`
diff --git a/semigroupoids.cabal b/semigroupoids.cabal
--- a/semigroupoids.cabal
+++ b/semigroupoids.cabal
@@ -1,6 +1,6 @@
 name:          semigroupoids
 category:      Control, Comonads
-version:       5.2.1
+version:       5.2.2
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
@@ -10,7 +10,15 @@
 homepage:      http://github.com/ekmett/semigroupoids
 bug-reports:   http://github.com/ekmett/semigroupoids/issues
 copyright:     Copyright (C) 2011-2015 Edward A. Kmett
-tested-with:   GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.1
+tested-with:   GHC == 7.0.4
+             , GHC == 7.2.2
+             , 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
 build-type:    Custom
 synopsis:      Semigroupoids: Category sans id
 extra-source-files:
@@ -132,13 +140,14 @@
     base-orphans        >= 0.5.4   && < 1,
     bifunctors          >= 5       && < 6,
     semigroups          >= 0.8.3.1 && < 1,
+    template-haskell,
     transformers        >= 0.2     && < 0.6,
     transformers-compat >= 0.5     && < 0.6
 
-  if impl(ghc >= 7.0 && < 7.4)
-    build-depends: generic-deriving >= 1.11 && < 1.12
+  if impl(ghc >= 7.0 && < 7.2)
+    build-depends: generic-deriving >= 1.11 && < 1.13
 
-  if impl(ghc >= 7.4 && < 7.6)
+  if impl(ghc >= 7.2 && < 7.6)
     build-depends: ghc-prim
 
   if flag(containers)
@@ -154,7 +163,7 @@
     build-depends: comonad >= 4.2.6 && < 6
 
   if flag(tagged)
-    build-depends: tagged >= 0.7.3 && < 1
+    build-depends: tagged >= 0.8.5 && < 1
 
   if flag(unordered-containers)
     build-depends: hashable >= 1.1  && < 1.3,
@@ -198,5 +207,5 @@
   else
     build-depends:
       base      >= 4      && < 5,
-      doctest   >= 0.11.1 && < 0.13,
+      doctest   >= 0.11.1 && < 0.14,
       semigroupoids
diff --git a/src/Data/Functor/Alt.hs b/src/Data/Functor/Alt.hs
--- a/src/Data/Functor/Alt.hs
+++ b/src/Data/Functor/Alt.hs
@@ -24,10 +24,11 @@
 ----------------------------------------------------------------------------
 module Data.Functor.Alt
   ( Alt(..)
+  , optional
   , module Data.Functor.Apply
   ) where
 
-import Control.Applicative hiding (some, many)
+import Control.Applicative hiding (some, many, optional)
 import Control.Applicative.Backwards
 import Control.Applicative.Lift
 import Control.Arrow
@@ -50,8 +51,8 @@
 import Data.Functor.Compose
 import Data.Functor.Product
 import Data.Functor.Reverse
-import Data.Semigroup hiding (Product)
 import Data.List.NonEmpty (NonEmpty(..))
+import Data.Semigroup (Option(..), Semigroup(..))
 import Prelude (($),Either(..),Maybe(..),const,IO,Ord,(++),(.),either,seq,undefined)
 import Unsafe.Coerce
 
@@ -61,6 +62,11 @@
 import Data.Sequence (Seq)
 import qualified Data.Map as Map
 import Data.Map (Map)
+# if MIN_VERSION_base(4,8,0)
+import Prelude (mappend)
+# else
+import Data.Monoid (mappend)
+# endif
 #endif
 
 #if defined(MIN_VERSION_tagged) || (MIN_VERSION_base(4,7,0))
@@ -73,6 +79,7 @@
 import GHC.Generics
 #endif
 
+
 infixl 3 <!>
 
 -- | Laws:
@@ -116,6 +123,10 @@
   many v = many_v
     where many_v = some_v <!> pure []
           some_v = (:) <$> v <*> many_v
+
+-- | One or none.
+optional :: (Alt f, Applicative f) => f a -> f (Maybe a)
+optional v = Just <$> v <!> pure Nothing
 
 instance (Alt f, Alt g) => Alt (f :*: g) where
   (as :*: bs) <!> (cs :*: ds) = (as <!> cs) :*: (bs <!> ds)
diff --git a/src/Data/Functor/Apply.hs b/src/Data/Functor/Apply.hs
--- a/src/Data/Functor/Apply.hs
+++ b/src/Data/Functor/Apply.hs
@@ -23,7 +23,6 @@
 
   , Apply(..)
   , (<..>)    -- :: Apply w => w a -> w (a -> b) -> w b
-  , liftF2    -- :: Apply w => (a -> b -> c) -> w a -> w b -> w c
   , liftF3    -- :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
 
   -- * Wrappers
@@ -41,10 +40,6 @@
 (<..>) = liftF2 (flip id)
 {-# INLINE (<..>) #-}
 
--- | Lift a binary function into a comonad with zipping
-liftF2 :: Apply w => (a -> b -> c) -> w a -> w b -> w c
-liftF2 f a b = f <$> a <.> b
-{-# INLINE liftF2 #-}
 
 -- | Lift a ternary function into a comonad with zipping
 liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
diff --git a/src/Data/Functor/Bind.hs b/src/Data/Functor/Bind.hs
--- a/src/Data/Functor/Bind.hs
+++ b/src/Data/Functor/Bind.hs
@@ -25,7 +25,6 @@
   -- * Applyable functors
   , Apply(..)
   , (<..>)    -- :: Apply w => w a -> w (a -> b) -> w b
-  , liftF2    -- :: Apply w => (a -> b -> c) -> w a -> w b -> w c
   , liftF3    -- :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
   -- * Wrappers
   , WrappedApplicative(..)
diff --git a/src/Data/Functor/Bind/Class.hs b/src/Data/Functor/Bind/Class.hs
--- a/src/Data/Functor/Bind/Class.hs
+++ b/src/Data/Functor/Bind/Class.hs
@@ -80,6 +80,7 @@
 import Data.Functor.Extend
 import Data.List.NonEmpty
 import Data.Orphans ()
+import Language.Haskell.TH (Q)
 import Prelude hiding (id, (.))
 
 #if MIN_VERSION_base(4,4,0)
@@ -144,6 +145,7 @@
 -- @
 class Functor f => Apply f where
   (<.>) :: f (a -> b) -> f a -> f b
+  (<.>) = liftF2 id
 
   -- | @ a '.>' b = 'const' 'id' '<$>' a '<.>' b @
   (.>) :: f a -> f b -> f b
@@ -153,6 +155,15 @@
   (<.) :: f a -> f b -> f a
   a <. b = const <$> a <.> b
 
+  -- | Lift a binary function into a comonad with zipping
+  liftF2 :: (a -> b -> c) -> f a -> f b -> f c
+  liftF2 f a b = f <$> a <.> b
+  {-# INLINE liftF2 #-}
+
+#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 708
+  {-# MINIMAL (<.>) | liftF2 #-}
+#endif
+
 #ifdef MIN_VERSION_tagged
 instance Apply (Tagged a) where
   (<.>) = (<*>)
@@ -269,6 +280,11 @@
   (a :+ b) <.> (c :+ d) = a c :+ b d
 #endif
 
+-- Applicative Q was only added in template-haskell 2.7 (GHC 7.4), so
+-- define in terms of Monad instead.
+instance Apply Q where
+  (<.>) = ap
+
 #ifdef MIN_VERSION_containers
 -- | A Map is not 'Applicative', but it is an instance of 'Apply'
 instance Ord k => Apply (Map k) where
@@ -495,6 +511,9 @@
   (>>-) = (>>=)
 
 instance Bind Identity where
+  (>>-) = (>>=)
+
+instance Bind Q where
   (>>-) = (>>=)
 
 instance Bind m => Bind (IdentityT m) where
diff --git a/src/Data/Functor/Bind/Trans.hs b/src/Data/Functor/Bind/Trans.hs
--- a/src/Data/Functor/Bind/Trans.hs
+++ b/src/Data/Functor/Bind/Trans.hs
@@ -31,7 +31,9 @@
 import qualified Control.Monad.Trans.Writer.Strict as Strict
 import Data.Functor.Bind
 import Data.Orphans ()
+#if !(MIN_VERSION_base(4,11,0))
 import Data.Semigroup hiding (Product)
+#endif
 import Prelude hiding (id, (.))
 
 -- | A subset of monad transformers can transform any 'Bind' as well.
diff --git a/src/Data/Groupoid.hs b/src/Data/Groupoid.hs
--- a/src/Data/Groupoid.hs
+++ b/src/Data/Groupoid.hs
@@ -1,5 +1,6 @@
 {-# LANGUAGE CPP #-}
 {-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE GADTs #-}
 #if __GLASGOW_HASKELL__ >= 706
 {-# LANGUAGE PolyKinds #-}
 #endif
@@ -22,9 +23,27 @@
 import Data.Semigroupoid
 import Data.Semigroupoid.Dual
 
+#if MIN_VERSION_base(4,7,0)
+import qualified Data.Type.Coercion as Co
+import qualified Data.Type.Equality as Eq
+#endif
+
 -- | semigroupoid with inverses. This technically should be a category with inverses, except we need to use Ob to define the valid objects for the category
 class Semigroupoid k => Groupoid k where
   inv :: k a b -> k b a
 
 instance Groupoid k => Groupoid (Dual k) where
   inv (Dual k) = Dual (inv k)
+
+#if MIN_VERSION_base(4,7,0)
+instance Groupoid Co.Coercion where
+  inv = Co.sym
+
+instance Groupoid (Eq.:~:) where
+  inv = Eq.sym
+#endif
+
+#if MIN_VERSION_base(4,10,0)
+instance Groupoid (Eq.:~~:) where
+  inv Eq.HRefl = Eq.HRefl
+#endif
diff --git a/src/Data/Semigroup/Bitraversable.hs b/src/Data/Semigroup/Bitraversable.hs
--- a/src/Data/Semigroup/Bitraversable.hs
+++ b/src/Data/Semigroup/Bitraversable.hs
@@ -15,7 +15,9 @@
   ) where
 
 import Control.Applicative
+#if !(MIN_VERSION_base(4,11,0))
 import Data.Semigroup
+#endif
 import Data.Semigroup.Traversable.Class
 
 bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m
diff --git a/src/Data/Semigroup/Traversable.hs b/src/Data/Semigroup/Traversable.hs
--- a/src/Data/Semigroup/Traversable.hs
+++ b/src/Data/Semigroup/Traversable.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE CPP #-}
 -----------------------------------------------------------------------------
 -- |
 -- Copyright   :  (C) 2011-2015 Edward Kmett
@@ -14,7 +15,9 @@
   ) where
 
 import Control.Applicative
+#if !(MIN_VERSION_base(4,11,0))
 import Data.Semigroup
+#endif
 import Data.Semigroup.Traversable.Class
 
 foldMap1Default :: (Traversable1 f, Semigroup m) => (a -> m) -> f a -> m
diff --git a/src/Data/Semigroupoid.hs b/src/Data/Semigroupoid.hs
--- a/src/Data/Semigroupoid.hs
+++ b/src/Data/Semigroupoid.hs
@@ -1,4 +1,5 @@
 {-# LANGUAGE CPP #-}
+{-# LANGUAGE GADTs #-}
 
 #if __GLASGOW_HASKELL__ >= 706
 {-# LANGUAGE PolyKinds #-}
@@ -47,6 +48,11 @@
 import Data.Tagged (Tagged (..))
 #endif
 
+#if MIN_VERSION_base(4,7,0)
+import qualified Data.Type.Coercion as Co
+import qualified Data.Type.Equality as Eq
+#endif
+
 -- | 'Control.Category.Category' sans 'Control.Category.id'
 class Semigroupoid c where
   o :: c j k -> c i j -> c i k
@@ -95,4 +101,17 @@
 #ifdef MIN_VERSION_tagged
 instance Semigroupoid Tagged where
   Tagged b `o` _ = Tagged b
+#endif
+
+#if MIN_VERSION_base(4,7,0)
+instance Semigroupoid Co.Coercion where
+  o = flip Co.trans
+
+instance Semigroupoid (Eq.:~:) where
+  o = flip Eq.trans
+#endif
+
+#if MIN_VERSION_base(4,10,0)
+instance Semigroupoid (Eq.:~~:) where
+  o Eq.HRefl Eq.HRefl = Eq.HRefl
 #endif