diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -2,7 +2,7 @@
 #
 #   runghc make_travis_yml_2.hs '-o' '.travis.yml' '--ghc-head' '--irc-channel=irc.freenode.org#haskell-lens' '--no-no-tests-no-bench' '--no-unconstrained' 'cabal.project'
 #
-# For more information, see https://github.com/hvr/multi-ghc-travis
+# For more information, see https://github.com/haskell-CI/haskell-ci
 #
 language: c
 sudo: false
@@ -36,37 +36,36 @@
 
 matrix:
   include:
-    - compiler: "ghc-8.6.1"
-      env: GHCHEAD=true
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-8.6.1], sources: [hvr-ghc]}}
-    - compiler: "ghc-8.4.3"
+    - compiler: "ghc-8.6.3"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-8.4.3], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-8.6.3], sources: [hvr-ghc]}}
+    - compiler: "ghc-8.4.4"
+    # env: TEST=--disable-tests BENCH=--disable-benchmarks
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-8.4.4], sources: [hvr-ghc]}}
     - compiler: "ghc-8.2.2"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-8.2.2], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-8.2.2], sources: [hvr-ghc]}}
     - compiler: "ghc-8.0.2"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-8.0.2], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-8.0.2], sources: [hvr-ghc]}}
     - compiler: "ghc-7.10.3"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.10.3], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-7.10.3], sources: [hvr-ghc]}}
     - compiler: "ghc-7.8.4"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.8.4], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-7.8.4], sources: [hvr-ghc]}}
     - compiler: "ghc-7.6.3"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.6.3], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-7.6.3], sources: [hvr-ghc]}}
     - compiler: "ghc-7.4.2"
     # env: TEST=--disable-tests BENCH=--disable-benchmarks
-      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.2,ghc-7.4.2], sources: [hvr-ghc]}}
+      addons: {apt: {packages: [ghc-ppa-tools,cabal-install-2.4,ghc-7.4.2], sources: [hvr-ghc]}}
     - compiler: "ghc-head"
       env: GHCHEAD=true
       addons: {apt: {packages: [ghc-ppa-tools,cabal-install-head,ghc-head], sources: [hvr-ghc]}}
 
   allow_failures:
     - compiler: "ghc-head"
-    - compiler: "ghc-8.6.1"
 
 before_install:
   - HC=${CC}
@@ -110,8 +109,9 @@
     fi
   - grep -Ev -- '^\s*--' ${HOME}/.cabal/config | grep -Ev '^\s*$'
   - "printf 'packages: \".\"\\n' > cabal.project"
+  - "printf 'write-ghc-environment-files: always\\n' >> cabal.project"
   - touch cabal.project.local
-  - "if ! $NOINSTALLEDCONSTRAINTS; then for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/^/constraints: /' | sed 's/-[^-]*$/ installed/' >> cabal.project.local; done; fi"
+  - "if ! $NOINSTALLEDCONSTRAINTS; then for pkg in $($HCPKG list --simple-output); do echo $pkg  | grep -vw -- recursion-schemes | sed 's/^/constraints: /' | sed 's/-[^-]*$/ installed/' >> cabal.project.local; done; fi"
   - cat cabal.project || true
   - cat cabal.project.local || true
   - if [ -f "./configure.ac" ]; then
@@ -126,13 +126,14 @@
 # any command which exits with a non-zero exit code causes the build to fail.
 script:
   # test that source-distributions can be generated
-  - (cd "." && cabal sdist)
-  - mv "."/dist/recursion-schemes-*.tar.gz ${DISTDIR}/
+  - cabal new-sdist all
+  - mv dist-newstyle/sdist/*.tar.gz ${DISTDIR}/
   - cd ${DISTDIR} || false
   - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
   - "printf 'packages: recursion-schemes-*/*.cabal\\n' > cabal.project"
+  - "printf 'write-ghc-environment-files: always\\n' >> cabal.project"
   - touch cabal.project.local
-  - "if ! $NOINSTALLEDCONSTRAINTS; then for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/^/constraints: /' | sed 's/-[^-]*$/ installed/' >> cabal.project.local; done; fi"
+  - "if ! $NOINSTALLEDCONSTRAINTS; then for pkg in $($HCPKG list --simple-output); do echo $pkg  | grep -vw -- recursion-schemes | sed 's/^/constraints: /' | sed 's/-[^-]*$/ installed/' >> cabal.project.local; done; fi"
   - cat cabal.project || true
   - cat cabal.project.local || true
 
@@ -144,7 +145,6 @@
   - (cd recursion-schemes-* && 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","--ghc-head","--irc-channel=irc.freenode.org#haskell-lens","--no-no-tests-no-bench","--no-unconstrained","cabal.project"]
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,10 @@
+## 5.1
+* Export gfutu
+* `distGHisto`, `ghisto`, and `gchrono` now use `Cofree (Base t)`
+* `distGFutu`, `gfutu`, and `gchrono` now use `Free (Base t)`
+* Add `hoist`, `hoistMu` and `hoistNu`
+* Add `transverse` and `cataA`
+
 ## 5.0.3 [2018.07.01]
 * Make the Template Haskell machinery look through type synonyms.
 * Avoid incurring some dependencies when using recent GHCs.
diff --git a/Data/Functor/Base.hs b/Data/Functor/Base.hs
--- a/Data/Functor/Base.hs
+++ b/Data/Functor/Base.hs
@@ -1,14 +1,5 @@
 {-# LANGUAGE CPP #-}
-
--- See Data.Functor.Foldable for explanation
-#ifndef MIN_VERSION_transformers_compat
-#define MIN_VERSION_transformers_compat(x,y,z) 0
-#endif
-
-#define EXPLICIT_DICT_FUNCTOR_CLASSES (MIN_VERSION_base(4,9,0) || MIN_VERSION_transformers(0,5,0) || (MIN_VERSION_transformers_compat(0,5,0) && !MIN_VERSION_transformers(0,4,0)))
-
-#define HAS_GENERIC (__GLASGOW_HASKELL__ >= 702)
-#define HAS_GENERIC1 (__GLASGOW_HASKELL__ >= 706)
+#include "recursion-schemes-common.h"
 
 #ifdef __GLASGOW_HASKELL__
 {-# LANGUAGE DeriveDataTypeable #-}
@@ -37,7 +28,7 @@
 
 import Data.Functor.Classes
   ( Eq1(..), Ord1(..), Show1(..), Read1(..)
-#if EXPLICIT_DICT_FUNCTOR_CLASSES
+#ifdef LIFTED_FUNCTOR_CLASSES
   , Eq2(..), Ord2(..), Show2(..), Read2(..)
 #endif
   )
@@ -62,7 +53,7 @@
 #endif
           )
 
-#if EXPLICIT_DICT_FUNCTOR_CLASSES
+#ifdef LIFTED_FUNCTOR_CLASSES
 instance Eq2 NonEmptyF where
   liftEq2 f g (NonEmptyF a mb) (NonEmptyF a' mb') = f a a' && liftEq g mb mb'
 
diff --git a/Data/Functor/Foldable.hs b/Data/Functor/Foldable.hs
--- a/Data/Functor/Foldable.hs
+++ b/Data/Functor/Foldable.hs
@@ -1,22 +1,5 @@
 {-# LANGUAGE CPP, TypeFamilies, Rank2Types, FlexibleContexts, FlexibleInstances, GADTs, StandaloneDeriving, UndecidableInstances #-}
-
--- explicit dictionary higher-kind instances are defined in
--- - base-4.9
--- - transformers >= 0.5
--- - transformes-compat >= 0.5 when transformers aren't 0.4
---
--- We don't always depend on transformers-compat, so we need a shim for its version check.
-#ifndef MIN_VERSION_transformers_compat
-#define MIN_VERSION_transformers_compat(x,y,z) 0
-#endif
-
-#define EXPLICIT_DICT_FUNCTOR_CLASSES (MIN_VERSION_base(4,9,0) || MIN_VERSION_transformers(0,5,0) || (MIN_VERSION_transformers_compat(0,5,0) && !MIN_VERSION_transformers(0,4,0)))
-
-#define HAS_GENERIC (__GLASGOW_HASKELL__ >= 702)
-#define HAS_GENERIC1 (__GLASGOW_HASKELL__ >= 706)
-
--- Polymorphic typeable
-#define HAS_POLY_TYPEABLE MIN_VERSION_base(4,7,0)
+#include "recursion-schemes-common.h"
 
 #ifdef __GLASGOW_HASKELL__
 {-# LANGUAGE DeriveDataTypeable #-}
@@ -28,8 +11,6 @@
 #endif
 #endif
 
-
-
 -----------------------------------------------------------------------------
 -- |
 -- Copyright   :  (C) 2008-2015 Edward Kmett
@@ -47,8 +28,8 @@
   , ListF(..)
   -- * Fixed points
   , Fix(..), unfix
-  , Mu(..)
-  , Nu(..)
+  , Mu(..), hoistMu
+  , Nu(..), hoistNu
   -- * Folding
   , Recursive(..)
   -- ** Combinators
@@ -59,6 +40,7 @@
   , histo
   , ghisto
   , futu
+  , gfutu
   , chrono
   , gchrono
   -- ** Distributive laws
@@ -84,6 +66,7 @@
   , hylo
   , ghylo
   -- ** Changing representation
+  , hoist
   , refix
   -- * Common names
   , fold, gfold
@@ -97,6 +80,9 @@
   , coelgot
   -- * Zygohistomorphic prepromorphisms
   , zygoHistoPrepro
+  -- * Effectful combinators
+  , cataA
+  , transverse
   ) where
 
 import Control.Applicative
@@ -171,7 +157,7 @@
     -> (Base t a -> a)
     -> t
     -> a
-  prepro e f = c where c = f . fmap (c . cata (embed . e)) . project
+  prepro e f = c where c = f . fmap (c . hoist e) . project
 
   --- | A generalized prepromorphism
   gprepro
@@ -181,7 +167,7 @@
     -> (Base t (w a) -> a)
     -> t
     -> a
-  gprepro k e f = extract . c where c = fmap f . k . fmap (duplicate . c . cata (embed . e)) . project
+  gprepro k e f = extract . c where c = fmap f . k . fmap (duplicate . c . hoist e) . project
 
 distPara :: Corecursive t => Base t (t, a) -> (t, Base t a)
 distPara = distZygo embed
@@ -207,7 +193,7 @@
     -> (a -> Base t a)                  -- a (Base t)-coalgebra
     -> a                                -- seed
     -> t
-  postpro e g = a where a = embed . fmap (ana (e . project) . a) . g
+  postpro e g = a where a = embed . fmap (hoist e . a) . g
 
   -- | A generalized postpromorphism
   gpostpro
@@ -217,7 +203,7 @@
     -> (a -> Base t (m a))                      -- a (Base t)-m-coalgebra
     -> a                                        -- seed
     -> t
-  gpostpro k e g = a . return where a = embed . fmap (ana (e . project) . a . join) . k . liftM g
+  gpostpro k e g = a . return where a = embed . fmap (hoist e . a . join) . k . liftM g
 
 hylo :: Functor f => (f b -> b) -> (a -> f a) -> a -> b
 hylo f g = h where h = f . fmap h . g
@@ -242,7 +228,7 @@
 #endif
           )
 
-#if EXPLICIT_DICT_FUNCTOR_CLASSES
+#ifdef LIFTED_FUNCTOR_CLASSES
 instance Eq2 ListF where
   liftEq2 _ _ Nil        Nil          = True
   liftEq2 f g (Cons a b) (Cons a' b') = f a a' && g b b'
@@ -448,12 +434,18 @@
 futu :: Corecursive t => (a -> Base t (Free (Base t) a)) -> a -> t
 futu = gana distFutu
 
+gfutu :: (Corecursive t, Functor m, Monad m) => (forall b. m (Base t b) -> Base t (m b)) -> (a -> Base t (FreeT (Base t) m a)) -> a -> t
+gfutu g = gana (distGFutu g)
+
 distFutu :: Functor f => Free f (f a) -> f (Free f a)
-distFutu = distGFutu id
+distFutu (Pure fx) = Pure <$> fx
+distFutu (Free ff) = Free . distFutu <$> ff
 
-distGFutu :: (Functor f, Functor h) => (forall b. h (f b) -> f (h b)) -> Free h (f a) -> f (Free h a)
-distGFutu _ (Pure fa) = Pure <$> fa
-distGFutu k (Free as) = Free <$> k (distGFutu k <$> as)
+distGFutu :: (Functor f, Functor h) => (forall b. h (f b) -> f (h b)) -> FreeT f h (f a) -> f (FreeT f h a)
+distGFutu k = d where
+  d = fmap FreeT . k . fmap d' . runFreeT
+  d' (CMTF.Pure ff) = CMTF.Pure <$> ff
+  d' (CMTF.Free ff) = CMTF.Free . d <$> ff
 
 -------------------------------------------------------------------------------
 -- Fix
@@ -521,6 +513,10 @@
 instance Functor f => Corecursive (Fix f) where
   embed = Fix
 
+hoist :: (Recursive s, Corecursive t)
+      => (forall a. Base s a -> Base t a) -> s -> t
+hoist n = cata (embed . n)
+
 refix :: (Recursive s, Corecursive t, Base s ~ Base t) => s -> t
 refix = cata embed
 
@@ -530,6 +526,7 @@
 fromFix :: Corecursive t => Fix (Base t) -> t
 fromFix = refix
 
+
 -------------------------------------------------------------------------------
 -- Lambek
 -------------------------------------------------------------------------------
@@ -567,6 +564,11 @@
     fromFix <$> step readPrec
 #endif
 
+-- | A specialized, faster version of 'hoist' for 'Mu'.
+hoistMu :: (forall a. f a -> g a) -> Mu f -> Mu g
+hoistMu n (Mu mk) = Mu $ \roll -> mk (roll . n)
+
+
 -- | Church encoded free monads are Recursive/Corecursive, in the same way that
 -- 'Mu' is.
 type instance Base (CMFC.F f a) = FreeF f a
@@ -579,6 +581,7 @@
   embed (CMTF.Pure a)  = CMFC.F $ \p _ -> p a
   embed (CMTF.Free fr) = CMFC.F $ \p f -> f $ fmap (cmfcCata p f) fr
 
+
 data Nu f where Nu :: (a -> f a) -> a -> Nu f
 type instance Base (Nu f) = f
 instance Functor f => Corecursive (Nu f) where
@@ -604,6 +607,11 @@
     fromFix <$> step readPrec
 #endif
 
+-- | A specialized, faster version of 'hoist' for 'Nu'.
+hoistNu :: (forall a. f a -> g a) -> Nu f -> Nu g
+hoistNu n (Nu next seed) = Nu (n . next) seed
+
+
 zygo :: Recursive t => (Base t b -> b) -> (Base t (b, a) -> a) -> t -> a
 zygo f = gfold (distZygo f)
 
@@ -651,22 +659,22 @@
 histo :: Recursive t => (Base t (Cofree (Base t) a) -> a) -> t -> a
 histo = gcata distHisto
 
-ghisto :: (Recursive t, Functor h) => (forall b. Base t (h b) -> h (Base t b)) -> (Base t (Cofree h a) -> a) -> t -> a
+ghisto :: (Recursive t, Comonad w) => (forall b. Base t (w b) -> w (Base t b)) -> (Base t (CofreeT (Base t) w a) -> a) -> t -> a
 ghisto g = gcata (distGHisto g)
 
 distHisto :: Functor f => f (Cofree f a) -> Cofree f (f a)
-distHisto = distGHisto id
+distHisto fc = fmap extract fc :< fmap (distHisto . Cofree.unwrap) fc
 
-distGHisto :: (Functor f, Functor h) => (forall b. f (h b) -> h (f b)) -> f (Cofree h a) -> Cofree h (f a)
-distGHisto k = Cofree.unfold (\as -> (extract <$> as, k (Cofree.unwrap <$> as)))
+distGHisto :: (Functor f, Functor h) => (forall b. f (h b) -> h (f b)) -> f (CofreeT f h a) -> CofreeT f h (f a)
+distGHisto k = d where d = CofreeT . fmap (\fc -> fmap CCTC.headF fc CCTC.:< fmap (d . CCTC.tailF) fc) . k . fmap runCofreeT
 
 chrono :: Functor f => (f (Cofree f b) -> b) -> (a -> f (Free f a)) -> (a -> b)
 chrono = ghylo distHisto distFutu
 
-gchrono :: (Functor f, Functor w, Functor m) =>
+gchrono :: (Functor f, Functor w, Functor m, Comonad w, Monad m) =>
            (forall c. f (w c) -> w (f c)) ->
            (forall c. m (f c) -> f (m c)) ->
-           (f (Cofree w b) -> b) -> (a -> f (Free m a)) ->
+           (f (CofreeT f w b) -> b) -> (a -> f (FreeT f m a)) ->
            (a -> b)
 gchrono w m = ghylo (distGHisto w) (distGFutu m)
 
@@ -697,6 +705,53 @@
   -> t
   -> a
 zygoHistoPrepro f g t = gprepro (distZygoT f distHisto) g t
+
+-------------------------------------------------------------------------------
+-- Effectful combinators
+-------------------------------------------------------------------------------
+
+-- | Effectful |fold|.
+--
+-- This is a type specialisation of 'cata'.
+--
+-- An example terminating a recursion immediately:
+--
+-- >>> cataA (\alg -> case alg of { Nil -> pure (); Cons a _ -> Const [a] })  "hello"
+-- Const "h"
+--
+cataA :: (Recursive t) => (Base t (f a) -> f a) -> t -> f a
+cataA = cata
+
+-- | An effectful version of 'hoist'.
+--
+-- Properties:
+--
+-- @
+-- 'transverse' 'sequenceA' = 'pure'
+-- @
+--
+-- Examples:
+--
+-- The weird type of first argument allows user to decide
+-- an order of sequencing:
+--
+-- >>> transverse (\x -> print (void x) *> sequence x) "foo" :: IO String
+-- Cons 'f' ()
+-- Cons 'o' ()
+-- Cons 'o' ()
+-- Nil
+-- "foo"
+--
+-- >>> transverse (\x -> sequence x <* print (void x)) "foo" :: IO String
+-- Nil
+-- Cons 'o' ()
+-- Cons 'o' ()
+-- Cons 'f' ()
+-- "foo"
+--
+transverse :: (Recursive s, Corecursive t, Functor f)
+           => (forall a. Base s (f a) -> f (Base t a)) -> s -> f t
+transverse n = cata (fmap embed . n)
 
 -------------------------------------------------------------------------------
 -- Not exposed anywhere
diff --git a/include/recursion-schemes-common.h b/include/recursion-schemes-common.h
new file mode 100644
--- /dev/null
+++ b/include/recursion-schemes-common.h
@@ -0,0 +1,28 @@
+#ifndef MIN_VERSION_base
+#define MIN_VERSION_base(x,y,z) 1
+#endif
+
+#ifndef MIN_VERSION_transformers
+#define MIN_VERSION_tarnsformers(x,y,z) 1
+#endif
+
+#ifndef MIN_VERSION_transformers_compat
+#define MIN_VERSION_transformers_compat(x,y,z) 0
+#endif
+
+
+#if MIN_VERSION_base(4,9,0)
+#define LIFTED_FUNCTOR_CLASSES 1
+
+#elif MIN_VERSION_transformers(0,5,0)
+#define LIFTED_FUNCTOR_CLASSES 1
+
+#elif MIN_VERSION_transformers_compat(0,5,0) && !MIN_VERSION_transformers(0,4,0)
+#define LIFTED_FUNCTOR_CLASSES 1
+#endif
+
+
+#define HAS_GENERIC (__GLASGOW_HASKELL__ >= 702)
+#define HAS_GENERIC1 (__GLASGOW_HASKELL__ >= 706)
+
+#define HAS_POLY_TYPEABLE MIN_VERSION_base(4,7,0)
diff --git a/recursion-schemes.cabal b/recursion-schemes.cabal
--- a/recursion-schemes.cabal
+++ b/recursion-schemes.cabal
@@ -1,6 +1,6 @@
 name:          recursion-schemes
 category:      Control, Recursion
-version:       5.0.3
+version:       5.1
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
@@ -16,10 +16,10 @@
   "Generalized bananas, lenses and barbed wire"
   by Erik Meijer, Maarten Fokkinga and Ross Paterson.
 
-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==8.4.3, GHC==8.6.1
+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==8.4.4, GHC==8.6.3
 
 build-type:    Simple
-extra-source-files: .travis.yml CHANGELOG.markdown .gitignore README.markdown
+extra-source-files: .travis.yml CHANGELOG.markdown .gitignore README.markdown include/recursion-schemes-common.h
 
 source-repository head
   type: git
@@ -41,6 +41,9 @@
     StandaloneDeriving
     UndecidableInstances
 
+  include-dirs: include
+  -- includes: recursion-schemes-common.h
+
   build-depends:
     base                 >= 4.5     && < 5,
     comonad              >= 4       && < 6,
@@ -76,9 +79,9 @@
 
   if flag(template-haskell)
     build-depends:
-      template-haskell >= 2.5.0.0 && < 2.14,
-      base-orphans     >= 0.5.4   && < 0.8,
-      th-abstraction   >= 0.2.4   && < 1
+      template-haskell >= 2.5.0.0 && < 2.15,
+      base-orphans     >= 0.5.4   && < 0.9,
+      th-abstraction   >= 0.2.4   && < 0.3
     exposed-modules:
       Data.Functor.Foldable.TH
 
@@ -96,5 +99,5 @@
     base,
     HUnit <1.7,
     recursion-schemes,
-    template-haskell >= 2.5.0.0 && < 2.14,
+    template-haskell,
     transformers     >= 0.2     && < 1