diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,11 +2,17 @@
 #
 #   haskell-ci '--output=.travis.yml' '--config=cabal.haskell-ci' 'cabal.project'
 #
+# To regenerate the script (for example after adjusting tested-with) run
+#
+#   haskell-ci regenerate
+#
 # For more information, see https://github.com/haskell-CI/haskell-ci
 #
-# version: 0.3.20190425
+# version: 0.10
 #
+version: ~> 1.0
 language: c
+os: linux
 dist: xenial
 git:
   # whether to recursively clone submodules
@@ -17,11 +23,12 @@
       - irc.freenode.org#haskell-lens
     skip_join: true
     template:
-      - "\"\\x0313machines\\x03/\\x0306%{branch}\\x03 \\x0314%{commit}\\x03 %{build_url} %{message}\""
+      - "\x0313machines\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"
 cache:
   directories:
     - $HOME/.cabal/packages
     - $HOME/.cabal/store
+    - $HOME/.hlint
 before_cache:
   - rm -fv $CABALHOME/packages/hackage.haskell.org/build-reports.log
   # remove files that are regenerated by 'cabal update'
@@ -31,74 +38,61 @@
   - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.tar
   - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.tar.idx
   - rm -rfv $CABALHOME/packages/head.hackage
-matrix:
+jobs:
   include:
-    - compiler: ghc-8.8.1
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.8.1","cabal-install-3.0"]}}
-      env: GHCHEAD=true
+    - compiler: ghc-8.10.1
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.10.1","cabal-install-3.2"]}}
+      os: linux
+    - compiler: ghc-8.8.3
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.8.3","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-8.6.5
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.6.5","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.6.5","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-8.4.4
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.4.4","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.4.4","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-8.2.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.2.2","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.2.2","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-8.0.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.0.2","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.0.2","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-7.10.3
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.10.3","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.10.3","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-7.8.4
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.8.4","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.8.4","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-7.6.3
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.6.3","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.6.3","cabal-install-3.2"]}}
+      os: linux
     - compiler: ghc-7.4.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.4.2","cabal-install-2.4"]}}
-    - compiler: ghc-head
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-head","cabal-install-head"]}}
-      env: GHCHEAD=true
-  allow_failures:
-    - compiler: ghc-head
-    - compiler: ghc-8.8.1
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.4.2","cabal-install-3.2"]}}
+      os: linux
 before_install:
   - HC=$(echo "/opt/$CC/bin/ghc" | sed 's/-/\//')
+  - WITHCOMPILER="-w $HC"
+  - HADDOCK=$(echo "/opt/$CC/bin/haddock" | sed 's/-/\//')
   - HCPKG="$HC-pkg"
   - unset CC
   - CABAL=/opt/ghc/bin/cabal
   - CABALHOME=$HOME/.cabal
   - export PATH="$CABALHOME/bin:$PATH"
   - TOP=$(pwd)
-  - HCNUMVER=$(( $(${HC} --numeric-version|sed -E 's/([0-9]+)\.([0-9]+)\.([0-9]+).*/\1 * 10000 + \2 * 100 + \3/') ))
+  - "HCNUMVER=$(${HC} --numeric-version|perl -ne '/^(\\d+)\\.(\\d+)\\.(\\d+)(\\.(\\d+))?$/; print(10000 * $1 + 100 * $2 + ($3 == 0 ? $5 != 1 : $3))')"
   - echo $HCNUMVER
-  - CABAL="$CABAL -vnormal+nowrap+markoutput"
+  - CABAL="$CABAL -vnormal+nowrap"
   - set -o pipefail
-  - |
-    echo 'function blue(s) { printf "\033[0;34m" s "\033[0m " }'           >> .colorful.awk
-    echo 'BEGIN { state = "output"; }'                                     >> .colorful.awk
-    echo '/^-----BEGIN CABAL OUTPUT-----$/ { state = "cabal" }'            >> .colorful.awk
-    echo '/^-----END CABAL OUTPUT-----$/ { state = "output" }'             >> .colorful.awk
-    echo '!/^(-----BEGIN CABAL OUTPUT-----|-----END CABAL OUTPUT-----)/ {' >> .colorful.awk
-    echo '  if (state == "cabal") {'                                       >> .colorful.awk
-    echo '    print blue($0)'                                              >> .colorful.awk
-    echo '  } else {'                                                      >> .colorful.awk
-    echo '    print $0'                                                    >> .colorful.awk
-    echo '  }'                                                             >> .colorful.awk
-    echo '}'                                                               >> .colorful.awk
-  - cat .colorful.awk
-  - |
-    color_cabal_output () {
-      awk -f $TOP/.colorful.awk
-    }
-  - echo text | color_cabal_output
-install:
-  - ${CABAL} --version
-  - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
   - TEST=--enable-tests
   - BENCH=--enable-benchmarks
   - if [ $HCNUMVER -lt 80000 ] ; then BENCH=--disable-benchmarks ; fi
-  - GHCHEAD=${GHCHEAD-false}
+  - HEADHACKAGE=false
   - rm -f $CABALHOME/config
   - |
     echo "verbose: normal +nowrap +markoutput"          >> $CABALHOME/config
     echo "remote-build-reporting: anonymous"            >> $CABALHOME/config
+    echo "write-ghc-environment-files: always"          >> $CABALHOME/config
     echo "remote-repo-cache: $CABALHOME/packages"       >> $CABALHOME/config
     echo "logs-dir:          $CABALHOME/logs"           >> $CABALHOME/config
     echo "world-file:        $CABALHOME/world"          >> $CABALHOME/config
@@ -111,18 +105,12 @@
     echo "  prefix: $CABALHOME"                         >> $CABALHOME/config
     echo "repository hackage.haskell.org"               >> $CABALHOME/config
     echo "  url: http://hackage.haskell.org/"           >> $CABALHOME/config
+install:
+  - ${CABAL} --version
+  - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
   - |
-    if $GHCHEAD; then
-    echo "allow-newer: $($HCPKG list --simple-output | sed -E 's/([a-zA-Z-]+)-[0-9.]+/*:\1/g')" >> $CABALHOME/config
-    
-    echo "repository head.hackage"                                                        >> $CABALHOME/config
-    echo "   url: http://head.hackage.haskell.org/"                                       >> $CABALHOME/config
-    echo "   secure: True"                                                                >> $CABALHOME/config
-    echo "   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740" >> $CABALHOME/config
-    echo "              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb" >> $CABALHOME/config
-    echo "              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e" >> $CABALHOME/config
-    echo "   key-threshold: 3"                                                            >> $CABALHOME/config
-    fi
+    echo "program-default-options"                >> $CABALHOME/config
+    echo "  ghc-options: $GHCJOBS +RTS -M6G -RTS" >> $CABALHOME/config
   - cat $CABALHOME/config
   - rm -fv cabal.project cabal.project.local cabal.project.freeze
   - travis_retry ${CABAL} v2-update -v
@@ -130,48 +118,57 @@
   - rm -rf cabal.project cabal.project.local cabal.project.freeze
   - touch cabal.project
   - |
-    echo 'packages: "."' >> cabal.project
-    echo 'packages: "./examples"' >> cabal.project
+    echo "packages: ." >> cabal.project
+    echo "packages: ./examples" >> cabal.project
+  - if [ $HCNUMVER -ge 80200 ] ; then echo 'package machines' >> cabal.project ; fi
+  - "if [ $HCNUMVER -ge 80200 ] ; then echo '  ghc-options: -Werror=missing-methods' >> cabal.project ; fi"
+  - if [ $HCNUMVER -ge 80200 ] ; then echo 'package machines-examples' >> cabal.project ; fi
+  - "if [ $HCNUMVER -ge 80200 ] ; then echo '  ghc-options: -Werror=missing-methods' >> cabal.project ; fi"
   - |
-    echo "write-ghc-environment-files: always" >> cabal.project
-  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | grep -vE -- '^(machines|machines-examples)$' | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
+  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | (grep -vE -- '^(machines|machines-examples)$' || true) | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
   - cat cabal.project || true
   - cat cabal.project.local || true
   - if [ -f "./configure.ac" ]; then (cd "." && autoreconf -i); fi
   - if [ -f "./examples/configure.ac" ]; then (cd "./examples" && autoreconf -i); fi
-  - ${CABAL} v2-freeze -w ${HC} ${TEST} ${BENCH} | color_cabal_output
+  - ${CABAL} v2-freeze $WITHCOMPILER ${TEST} ${BENCH}
   - "cat cabal.project.freeze | sed -E 's/^(constraints: *| *)//' | sed 's/any.//'"
   - rm  cabal.project.freeze
-  - ${CABAL} v2-build -w ${HC} ${TEST} ${BENCH} --dep -j2 all | color_cabal_output
+  - travis_wait 40 ${CABAL} v2-build $WITHCOMPILER ${TEST} ${BENCH} --dep -j2 all
 script:
   - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
   # Packaging...
-  - ${CABAL} v2-sdist all | color_cabal_output
+  - ${CABAL} v2-sdist all
   # Unpacking...
   - mv dist-newstyle/sdist/*.tar.gz ${DISTDIR}/
   - cd ${DISTDIR} || false
-  - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - find . -maxdepth 1 -type f -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - find . -maxdepth 1 -type f -name '*.tar.gz' -exec rm       '{}' \;
+  - PKGDIR_machines="$(find . -maxdepth 1 -type d -regex '.*/machines-[0-9.]*')"
+  - PKGDIR_machines_examples="$(find . -maxdepth 1 -type d -regex '.*/machines-examples-[0-9.]*')"
   # Generate cabal.project
   - rm -rf cabal.project cabal.project.local cabal.project.freeze
   - touch cabal.project
   - |
-    echo 'packages: "machines-*/*.cabal"' >> cabal.project
-    echo 'packages: "machines-examples-*/*.cabal"' >> cabal.project
+    echo "packages: ${PKGDIR_machines}" >> cabal.project
+    echo "packages: ${PKGDIR_machines_examples}" >> cabal.project
+  - if [ $HCNUMVER -ge 80200 ] ; then echo 'package machines' >> cabal.project ; fi
+  - "if [ $HCNUMVER -ge 80200 ] ; then echo '  ghc-options: -Werror=missing-methods' >> cabal.project ; fi"
+  - if [ $HCNUMVER -ge 80200 ] ; then echo 'package machines-examples' >> cabal.project ; fi
+  - "if [ $HCNUMVER -ge 80200 ] ; then echo '  ghc-options: -Werror=missing-methods' >> cabal.project ; fi"
   - |
-    echo "write-ghc-environment-files: always" >> cabal.project
-  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | grep -vE -- '^(machines|machines-examples)$' | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
+  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | (grep -vE -- '^(machines|machines-examples)$' || true) | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
   - cat cabal.project || true
   - cat cabal.project.local || true
   # Building with tests and benchmarks...
   # build & run tests, build benchmarks
-  - ${CABAL} v2-build -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  - ${CABAL} v2-build $WITHCOMPILER ${TEST} ${BENCH} all
   # Testing...
-  - ${CABAL} v2-test -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  - ${CABAL} v2-test $WITHCOMPILER ${TEST} ${BENCH} all
   # cabal check...
-  - (cd machines-* && ${CABAL} -vnormal check)
-  - (cd machines-examples-* && ${CABAL} -vnormal check)
+  - (cd ${PKGDIR_machines} && ${CABAL} -vnormal check)
+  - (cd ${PKGDIR_machines_examples} && ${CABAL} -vnormal check)
   # haddock...
-  - ${CABAL} v2-haddock -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  - ${CABAL} v2-haddock $WITHCOMPILER --with-haddock $HADDOCK ${TEST} ${BENCH} all
 
-# REGENDATA ["--output=.travis.yml","--config=cabal.haskell-ci","cabal.project"]
+# REGENDATA ("0.10",["--output=.travis.yml","--config=cabal.haskell-ci","cabal.project"])
 # EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,11 @@
+0.7.1 [2020.10.02]
+------------------
+* Allow building with GHC 9.0.
+* Add a `Data.Machine.MooreT` module.
+* Tweak the `Corepresentable Moore` instance's implementation of `cotabulate`
+  to ensure that `index . tabulate ≡ id` (note that for `Moore`,
+  `tabulate = cotabulate`).
+
 0.7 [2019.05.10]
 ----------------
 * Remove the `Monad` instances for `Mealy` and `MealyT`, as they were
diff --git a/examples/Examples.hs b/examples/Examples.hs
--- a/examples/Examples.hs
+++ b/examples/Examples.hs
@@ -31,11 +31,15 @@
 
 -- | bad slurping machine
 crashes :: Handle -> MachineT IO k String
-crashes h = repeatedly $ lift (hGetLine h) >>= yield
+crashes h = repeatedly $ do
+  x <- lift (hGetLine h)
+  yield x
 
 -- | here is a plan that yields all the lines at once.
 slurpHandlePlan :: Handle -> PlanT k [String] IO ()
-slurpHandlePlan h = lift (slurpHandle h) >>= yield
+slurpHandlePlan h = do
+  x <- lift (slurpHandle h)
+  yield x
 
 {-
  - but we want a plan that will yield one line at a time
@@ -68,7 +72,7 @@
 
 -- | A Process that takes in a String and outputs all the words in that String
 wordsProc :: Process String String
-wordsProc = repeatedly $ do { s <- await; mapM_ yield (words s) }
+wordsProc = repeatedly $ do { s <- await; mapM_ (\x -> yield x) (words s) }
 
 -- | A Plan to print all input.
 printPlan :: PlanT (Is String) () IO ()
diff --git a/examples/machines-examples.cabal b/examples/machines-examples.cabal
--- a/examples/machines-examples.cabal
+++ b/examples/machines-examples.cabal
@@ -24,7 +24,8 @@
              , GHC == 8.2.2
              , GHC == 8.4.4
              , GHC == 8.6.5
-             , GHC == 8.8.1
+             , GHC == 8.8.3
+             , GHC == 8.10.1
 
 source-repository head
   type: git
diff --git a/machines.cabal b/machines.cabal
--- a/machines.cabal
+++ b/machines.cabal
@@ -1,6 +1,6 @@
 name:          machines
 category:      Control, Enumerator
-version:       0.7
+version:       0.7.1
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
@@ -25,7 +25,8 @@
              , GHC == 8.2.2
              , GHC == 8.4.4
              , GHC == 8.6.5
-             , GHC == 8.8.1
+             , GHC == 8.8.3
+             , GHC == 8.10.1
 extra-source-files:
   .travis.yml
   .gitignore
@@ -72,6 +73,7 @@
     Data.Machine.Mealy
     Data.Machine.MealyT
     Data.Machine.Moore
+    Data.Machine.MooreT
     Data.Machine.Process
     Data.Machine.Plan
     Data.Machine.Runner
@@ -111,7 +113,7 @@
   default-language: Haskell2010
   build-depends:
     base    == 4.*,
-    doctest >= 0.11.1 && < 0.17,
+    doctest >= 0.11.1 && < 0.18,
     machines
   ghc-options: -Wall -threaded
   hs-source-dirs: tests
diff --git a/src/Data/Machine/Mealy.hs b/src/Data/Machine/Mealy.hs
--- a/src/Data/Machine/Mealy.hs
+++ b/src/Data/Machine/Mealy.hs
@@ -105,7 +105,7 @@
 #endif
 
 instance Automaton Mealy where
-  auto = construct . go where
+  auto x = construct $ go x where
     go (Mealy f) = await >>= \a -> case f a of
       (b, m) -> do
          yield b
diff --git a/src/Data/Machine/MealyT.hs b/src/Data/Machine/MealyT.hs
--- a/src/Data/Machine/MealyT.hs
+++ b/src/Data/Machine/MealyT.hs
@@ -3,7 +3,7 @@
 
 -----------------------------------------------------------------------------
 -- |
--- Module      :  Data.Machine.Mealy
+-- Module      :  Data.Machine.MealyT
 -- License     :  BSD-style (see the file LICENSE)
 --
 -- <http://en.wikipedia.org/wiki/Mealy_machine>
diff --git a/src/Data/Machine/Moore.hs b/src/Data/Machine/Moore.hs
--- a/src/Data/Machine/Moore.hs
+++ b/src/Data/Machine/Moore.hs
@@ -59,7 +59,7 @@
 {-# INLINE unfoldMoore #-}
 
 instance Automaton Moore where
-  auto = construct . go where
+  auto x = construct $ go x where
     go (Moore b f) = do
       yield b
       await >>= go . f
@@ -139,8 +139,7 @@
 
 instance Profunctor.Corepresentable Moore where
   type Corep Moore = []
-  cotabulate f0 = go (f0 . reverse) where
-    go f = Moore (f []) $ \a -> go (f.(a:))
+  cotabulate f = Moore (f []) $ \a -> cotabulate (f.(a:))
 
 instance MonadFix (Moore a) where
   mfix = mfixRep
diff --git a/src/Data/Machine/MooreT.hs b/src/Data/Machine/MooreT.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Machine/MooreT.hs
@@ -0,0 +1,141 @@
+{-# LANGUAGE CPP        #-}
+{-# LANGUAGE RankNTypes #-}
+
+#ifndef MIN_VERSION_profunctors
+#define MIN_VERSION_profunctors(x,y,z) 0
+#endif
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.Machine.MooreT
+-- Copyright   :  (C) 2012 Edward Kmett
+-- License     :  BSD-style (see the file LICENSE)
+--
+-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Stability   :  provisional
+-- Portability :  portable
+--
+-- <http://en.wikipedia.org/wiki/Moore_machine>
+----------------------------------------------------------------------------
+module Data.Machine.MooreT
+  ( MooreT(..)
+  , unfoldMooreT
+  , upgrade
+  , hoist
+  , couple
+  , firstM
+  , secondM
+  ) where
+
+import Control.Monad.Trans (lift)
+import Data.Distributive   (Distributive(..), cotraverse)
+import Data.Machine
+import Data.Machine.MealyT (MealyT(runMealyT))
+import Data.Pointed        (Pointed(..))
+import Data.Profunctor     (Costrong(..), Profunctor(..))
+
+#if !(MIN_VERSION_base(4,8,0))
+import Control.Applicative
+import Data.Monoid         (Monoid(..))
+#endif
+
+#if !(MIN_VERSION_base(4,11,0))
+import Data.Semigroup      (Semigroup(..))
+#endif
+
+-- | 'Moore' machine, with applicative effects
+newtype MooreT m a b = MooreT { runMooreT :: m (b, a -> MooreT m a b) }
+
+-- | Construct a MooreT machine from a state valuation and transition action
+unfoldMooreT :: Functor m => (s -> m (b, a -> s)) -> s -> MooreT m a b
+unfoldMooreT f = go where
+  go s = MooreT $ (\(b, k) -> (b, go . k)) <$> f s
+{-# INLINE unfoldMooreT #-}
+
+upgrade :: Applicative m => Moore a b -> MooreT m a b
+upgrade (Moore b f) = MooreT $ pure (b, upgrade . f)
+{-# INLINE upgrade #-}
+
+firstM :: (Functor m, Monad m) => (a' -> m a) -> MooreT m a b -> MooreT m a' b
+firstM f = MooreT .  fmap (fmap go) . runMooreT
+  where
+    go m x = MooreT $ f x >>= fmap (fmap go) . runMooreT . m
+{-# INLINE firstM #-}
+
+secondM :: Monad m => (b -> m b') -> MooreT m a b -> MooreT m a b'
+secondM f m = MooreT $ do
+  (b, m') <- runMooreT m
+  b' <- f b
+  return (b', secondM f . m')
+{-# INLINE secondM #-}
+
+hoist :: Functor n => (forall x. m x -> n x) -> MooreT m a b -> MooreT n a b
+hoist f = let go = MooreT . fmap (\(b, m') -> (b, go . m')) . f . runMooreT in go
+{-# INLINE hoist #-}
+
+couple :: Monad m => MooreT m a b -> MealyT m b a -> m c
+couple x y = do
+  (b, x') <- runMooreT x
+  (a, y') <- runMealyT y b
+  couple (x' a) y'
+{-# INLINE couple #-}
+
+instance AutomatonM MooreT where
+  autoT = construct . go where
+    go m = do
+      (b, m') <- lift (runMooreT m)
+      yield b
+      await >>= go . m'
+  {-# INLINE autoT #-}
+
+instance Functor m => Functor (MooreT m a) where
+  fmap f = let go = MooreT . fmap (\(b, m') -> (f b, go . m')) . runMooreT in go
+  {-# INLINE fmap #-}
+
+instance Functor m => Profunctor (MooreT m) where
+  rmap = fmap
+  {-# INLINE rmap #-}
+  lmap f = let go = MooreT . fmap (\(b, m') -> (b, go . m' . f)) . runMooreT in go
+  {-# INLINE lmap #-}
+#if MIN_VERSION_profunctors(3,1,1)
+  dimap f g = let go = MooreT . fmap (\(b, m') -> (g b, go . m' . f)) . runMooreT in go
+  {-# INLINE dimap #-}
+#endif
+
+instance Applicative m => Applicative (MooreT m a) where
+  pure x = let r = MooreT $ pure (x, const r) in r
+  {-# INLINE pure #-}
+  fm <*> xm = MooreT $
+    (\(f, fm') (x, xm') -> (f x, \a -> fm' a <*> xm' a)) <$> runMooreT fm <*> runMooreT xm
+  {-# INLINE (<*>) #-}
+
+instance Applicative m => Pointed (MooreT m a) where
+  point = pure
+  {-# INLINE point #-}
+
+instance (Functor m, Monad m) => Costrong (MooreT m) where
+  unfirst m = MooreT $ do
+    ((b, d), m') <- runMooreT m
+    return (b, \a -> unfirst $ m' (a, d))
+  {-# INLINE unfirst #-}
+  unsecond m = MooreT $ do
+    ((d, b), m') <- runMooreT m
+    return (b, \a -> unsecond $ m' (d, a))
+  {-# INLINE unsecond #-}
+
+instance (Distributive m, Applicative m) => Distributive (MooreT m a) where
+  distribute m = MooreT $
+    cotraverse (\x -> (fmap fst x, fmap distribute $ distribute $ fmap snd x))
+    $ fmap runMooreT m
+  {-# INLINE distribute #-}
+
+instance (Applicative m, Semigroup b) => Semigroup (MooreT m a b) where
+  a <> b = (<>) <$> a <*> b
+  {-# INLINE (<>) #-}
+
+instance (Applicative m, Monoid b) => Monoid (MooreT m a b) where
+  mempty = pure mempty
+  {-# INLINE mempty #-}
+#if !(MIN_VERSION_base(4,11,0))
+  mappend a b = mappend <$> a <*> b
+  {-# INLINE mappend #-}
+#endif
diff --git a/src/Data/Machine/Plan.hs b/src/Data/Machine/Plan.hs
--- a/src/Data/Machine/Plan.hs
+++ b/src/Data/Machine/Plan.hs
@@ -176,7 +176,7 @@
 
 -- | Like yield, except stops if there is no value to yield.
 maybeYield :: Maybe o -> Plan k o ()
-maybeYield = maybe stop yield
+maybeYield m = maybe stop (\x -> yield x) m
 
 -- | Wait for input.
 --
@@ -200,4 +200,7 @@
 
 -- | Run a monadic action repeatedly yielding its results, until it returns Nothing.
 exhaust :: Monad m => m (Maybe a) -> PlanT k a m ()
-exhaust f = do (lift f >>= maybeYield); exhaust f
+exhaust f = do
+  x <- lift f
+  maybeYield x
+  exhaust f
diff --git a/src/Data/Machine/Process.hs b/src/Data/Machine/Process.hs
--- a/src/Data/Machine/Process.hs
+++ b/src/Data/Machine/Process.hs
@@ -113,6 +113,7 @@
 -- | The trivial 'Process' that simply repeats each input it receives.
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- echo :: Process a a
 -- echo = repeatedly $ do
@@ -134,11 +135,12 @@
 
 -- | A 'Process' that prepends the elements of a 'Foldable' onto its input, then repeats its input from there.
 prepended :: Foldable f => f a -> Process a a
-prepended = before echo . traverse_ yield
+prepended f = before echo $ traverse_ (\x -> yield x) f
 
 -- | A 'Process' that only passes through inputs that match a predicate.
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- filtered :: (a -> Bool) -> Process a a
 -- filtered p = repeatedly $ do
@@ -164,6 +166,7 @@
 -- | A 'Process' that drops the first @n@, then repeats the rest.
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- dropping n = before echo $ replicateM_ n await
 -- @
@@ -174,8 +177,8 @@
 -- [4,5]
 --
 dropping :: Int -> Process a a
-dropping =
-    loop
+dropping i =
+    loop i
   where
     loop cnt
       | cnt <= 0
@@ -187,6 +190,7 @@
 -- | A 'Process' that passes through the first @n@ elements from its input then stops
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- taking n = construct . replicateM_ n $ await >>= yield
 -- @
@@ -197,8 +201,8 @@
 -- [1,2,3]
 --
 taking :: Int -> Process a a
-taking =
-    loop
+taking i =
+    loop i
   where
     loop cnt
       | cnt <= 0
@@ -210,6 +214,7 @@
 -- | A 'Process' that passes through elements until a predicate ceases to hold, then stops
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- takingWhile :: (a -> Bool) -> Process a a
 -- takingWhile p = repeatedly $ await >>= \v -> if p v then yield v else stop
@@ -234,6 +239,7 @@
 -- 'Nothing' is found, then stops.
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- takingJusts :: Process (Maybe a) a
 -- takingJusts = repeatedly $ await >>= maybe stop yield
@@ -256,6 +262,7 @@
 -- | A 'Process' that drops elements while a predicate holds
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- droppingWhile :: (a -> Bool) -> Process a a
 -- droppingWhile p = before echo loop where
@@ -282,6 +289,7 @@
 -- Avoids returning empty lists and deals with the truncation of the final group.
 --
 -- An approximation of this can be constructed from a plan with
+--
 -- @
 -- buffered :: Int -> Process a [a]
 -- buffered = repeatedly . go [] where
@@ -401,12 +409,14 @@
 -- Like 'fold', but yielding intermediate values.
 --
 -- It may be useful to consider this alternative signature
+--
 -- @
 -- 'scan' :: (a -> b -> a) -> a -> Process b a
 -- @
 --
 -- For stateful 'scan' use 'auto' with "Data.Machine.Mealy" machine.
 -- This can be constructed from a plan with
+--
 -- @
 -- scan :: Category k => (a -> b -> a) -> a -> Machine (k b) a
 -- scan func seed = construct $ go seed where
@@ -439,6 +449,7 @@
 -- 'scan1' is a variant of 'scan' that has no starting value argument
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- scan1 :: Category k => (a -> a -> a) -> Machine (k a) a
 -- scan1 func = construct $ await >>= go where
@@ -483,11 +494,13 @@
 -- Like 'scan', but only yielding the final value.
 --
 -- It may be useful to consider this alternative signature
+--
 -- @
 -- 'fold' :: (a -> b -> a) -> a -> Process b a
 -- @
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- fold :: Category k => (a -> b -> a) -> a -> Machine (k b) a
 -- fold func seed = construct $ go seed where
@@ -505,18 +518,19 @@
 -- [5]
 --
 fold :: Category k => (a -> b -> a) -> a -> Machine (k b) a
-fold func =
+fold func x =
   let step t = t `seq` encased
              $ Await (step . func t)
                      id
                      (encased $ Yield t stopped)
-  in  step
+  in  step x
 {-# INLINABLE fold #-}
 
 -- |
 -- 'fold1' is a variant of 'fold' that has no starting value argument
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- fold1 :: Category k => (a -> a -> a) -> Machine (k a) a
 -- fold1 func = construct $ await >>= go where
@@ -543,6 +557,7 @@
 -- individually.
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- asParts :: Foldable f => Process (f a) a
 -- asParts = repeatedly $ await >>= traverse_ yield
@@ -590,6 +605,7 @@
 -- | Apply a monadic function to each element of a 'ProcessT'.
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- autoM :: Monad m => (a -> m b) -> ProcessT m a b
 -- autoM :: (Category k, Monad m) => (a -> m b) -> MachineT m (k a) b
@@ -615,6 +631,7 @@
 -- Skip all but the final element of the input
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- 'final' :: 'Process' a a
 -- final :: Category k => Machine (k a) a
@@ -643,6 +660,7 @@
 -- If the input is empty, the default value is emitted
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- 'finalOr' :: a -> 'Process' a a
 -- finalOr :: Category k => a -> Machine (k a) a
@@ -660,10 +678,10 @@
 -- [-1]
 --
 finalOr :: Category k => a -> Machine (k a) a
-finalOr =
+finalOr y =
   let step x = encased (Await step id (emit x))
       emit x = encased (Yield x stopped)
-  in step
+  in step y
 {-# INLINABLE finalOr #-}
 
 -- |
@@ -696,6 +714,7 @@
 -- Convert a stream of actions to a stream of values
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- sequencing :: Monad m => (a -> m b) -> ProcessT m a b
 -- sequencing :: (Category k, Monad m) => MachineT m (k (m a)) a
@@ -721,6 +740,7 @@
 -- Apply a function to all values coming from the input
 --
 -- This can be constructed from a plan with
+--
 -- @
 -- mapping :: Category k => (a -> b) -> Machine (k a) b
 -- mapping f = repeatedly $ await >>= yield . f
diff --git a/src/Data/Machine/Source.hs b/src/Data/Machine/Source.hs
--- a/src/Data/Machine/Source.hs
+++ b/src/Data/Machine/Source.hs
@@ -95,7 +95,7 @@
 -- [1,2]
 --
 source :: Foldable f => f b -> Source b
-source = foldr go stopped
+source f = foldr go stopped f
   where
     go x m = encased $ Yield x m
 
diff --git a/src/Data/Machine/Type.hs b/src/Data/Machine/Type.hs
--- a/src/Data/Machine/Type.hs
+++ b/src/Data/Machine/Type.hs
@@ -109,7 +109,7 @@
     f' Stop            = Stop
 
 instance Monad m => Pointed (MachineT m k) where
-  point = repeatedly . yield
+  point x = repeatedly $ yield x
 
 instance Monad m => Semigroup (MachineT m k o) where
   a <> b = stepMachine a $ \step -> case step of
diff --git a/src/Data/Machine/Wye.hs b/src/Data/Machine/Wye.hs
--- a/src/Data/Machine/Wye.hs
+++ b/src/Data/Machine/Wye.hs
@@ -102,7 +102,7 @@
 
 -- | Tie off both inputs of a wye by connecting them to known sources.
 capWye :: Monad m => SourceT m a -> SourceT m b -> WyeT m a b c -> SourceT m c
-capWye a b = plug . wye a b
+capWye a b w = plug $ wye a b w
 {-# INLINE capWye #-}
 
 -- | Natural transformation used by 'capX' and 'capY'