diff --git a/.gitignore b/.gitignore
--- a/.gitignore
+++ b/.gitignore
@@ -1,4 +1,5 @@
 dist
+dist-newstyle
 docs
 wiki
 TAGS
@@ -15,3 +16,21 @@
 *#
 *.prof
 *.hp
+.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
@@ -1,95 +1,138 @@
-# 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:
+      - "\x0313ersatz\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
+      - minisat
+      - alex-3.1.7
+      - happy-1.19.5
+
 matrix:
   include:
-    - env: CABALVER=1.24 GHCVER=7.10.3 GHCOPTS="" JOPTS="-j2"
-      compiler: ": #GHC 7.10.3"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-7.10.3,minisat],sources: [hvr-ghc]}}
-    - env: CABALVER=1.24 GHCVER=8.0.2 GHCOPTS="" JOPTS="-j2"
-      compiler: ": #GHC 8.0.2"
-      addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.2,minisat],sources: [hvr-ghc]}}
-    - env: CABALVER=2.0 GHCVER=8.2.1 GHCOPTS="" JOPTS="-j2"
-      compiler: ": #GHC 8.2.1"
-      addons: {apt: {packages: [cabal-install-2.0,ghc-8.2.1,minisat],sources: [hvr-ghc]}}
-    - env: CABALVER=head GHCVER=head GHCOPTS="" JOPTS="-j2"
-      compiler: ": #GHC head"
-      addons: {apt: {packages: [cabal-install-head,ghc-head,minisat],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=head GHCVER=head GHCOPTS="" JOPTS="-j2"
+    - compiler: "ghc-8.4.1"
+    - compiler: "ghc-head"
 
 before_install:
- - unset CC
- - export HAPPYVER=1.19.5
- - export ALEXVER=3.1.7
- - 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;
-   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 --enable-benchmarks -v2  # -v2 provides useful information for debugging
- - cabal build $JOPTS --ghc-options=$GHCOPTS # this builds all libraries and executables (including tests)
- - cabal test
- - cabal sdist   # tests that a source-distribution can be generated
+  # test that source-distributions can be generated
+  - (cd "." && cabal sdist)
+  - mv "."/dist/ersatz-*.tar.gz ${DISTDIR}/
+  - cd ${DISTDIR} || false
+  - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - "printf 'packages: ersatz-*/*.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 $JOPTS --ghc-options=$GHCOPTS --force-reinstalls "$SRC_TGZ")
 
-notifications:
-  irc:
-    channels:
-      - "irc.freenode.org#haskell-lens"
-    skip_join: true
-    template:
-      - "\x0313ersatz\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 ersatz-* && 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.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,14 @@
+0.4.2
+-----
+* Add `Semigroup` instances for `Clause` and `Formula`.
+* Generalize `regular`, `regular_in_degree`, `regular_out_degree`,
+  `max_in_degree`, `min_in_degree`, `max_out_degree`, and `min_out_degree` to
+  work over heterogeneous relations.
+* Add `buildFrom` to `Ersatz.Relation.Data`.
+* Add `difference`, `reflexive_closure`, and `symmetric_closure` to
+  `Ersatz.Relation.Op`.
+* Add `anti_symmetric` and `total` to `Ersatz.Relation.Prop`.
+
 0.4.1
 -----
 * Add a library dependency on the `doctests` test suite
diff --git a/ersatz.cabal b/ersatz.cabal
--- a/ersatz.cabal
+++ b/ersatz.cabal
@@ -1,5 +1,5 @@
 name:           ersatz
-version:        0.4.1
+version:        0.4.2
 license:        BSD3
 license-file:   LICENSE
 author:         Edward A. Kmett, Eric Mertens, Johan Kiviniemi
@@ -75,7 +75,7 @@
 
 build-type:     Custom
 cabal-version:  >= 1.10
-tested-with:    GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.1
+tested-with:    GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.1
 extra-source-files:
   .ghci
   .gitignore
@@ -183,6 +183,7 @@
     lens                 >= 3.8      && < 5,
     mtl                  >= 1.1      && < 2.3,
     process              >= 1.1      && < 1.7,
+    semigroups           >= 0.16     && < 1,
     temporary            >= 1.1      && < 1.3,
     transformers         >= 0.3      && < 0.6,
     unordered-containers == 0.2.*,
@@ -227,7 +228,8 @@
       ersatz,
       lens,
       mtl,
-      parsec >= 3.1 && < 3.2
+      parsec >= 3.1 && < 3.2,
+      semigroups
     if impl(ghc >= 7.4 && < 7.6)
       build-depends: ghc-prim
   else
diff --git a/examples/regexp-grid/RegexpGrid/Problem.hs b/examples/regexp-grid/RegexpGrid/Problem.hs
--- a/examples/regexp-grid/RegexpGrid/Problem.hs
+++ b/examples/regexp-grid/RegexpGrid/Problem.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE CPP #-}
 {-# LANGUAGE TupleSections #-}
 {-# LANGUAGE TemplateHaskell #-}
 
@@ -9,11 +10,14 @@
 
 import Control.Applicative
 import Control.Monad.Reader
-import Control.Monad.RWS.Strict
+import Control.Monad.RWS.Strict hiding ((<>))
 import Control.Lens
 import Data.Foldable (asum)
 import Data.Map (Map)
 import qualified Data.Map as Map
+#if !(MIN_VERSION_base(4,11,0))
+import Data.Semigroup (Semigroup(..))
+#endif
 import Data.Sequence (Seq)
 import qualified Data.Sequence as Seq
 import Ersatz
@@ -41,12 +45,18 @@
 makeLenses ''ReBitState
 makeLenses ''ReBitResult
 
+instance Semigroup ReBitResult where
+  ReBitResult fieldsA bitA <> ReBitResult fieldsB bitB =
+    ReBitResult (fieldsA <> fieldsB) (bitA && bitB)
+  {-# INLINE (<>) #-}
+
 instance Monoid ReBitResult where
   mempty = ReBitResult mempty true
   {-# INLINE mempty #-}
-  ReBitResult fieldsA bitA `mappend` ReBitResult fieldsB bitB =
-    ReBitResult (fieldsA <> fieldsB) (bitA && bitB)
+#if !(MIN_VERSION_base(4,11,0))
+  mappend = (<>)
   {-# INLINE mappend #-}
+#endif
 
 problem :: (Applicative m, MonadState s m, HasSAT s) => m (Map Pos Field)
 problem = do
diff --git a/src/Ersatz/Internal/Formula.hs b/src/Ersatz/Internal/Formula.hs
--- a/src/Ersatz/Internal/Formula.hs
+++ b/src/Ersatz/Internal/Formula.hs
@@ -28,15 +28,9 @@
   , formulaFAS, formulaFAC
   ) where
 
-#if __GLASGOW_HASKELL__ < 710
-import Control.Applicative
-#endif
 import Data.IntSet (IntSet)
 import qualified Data.IntSet as IntSet
 import qualified Data.List as List (intersperse)
-#if __GLASGOW_HASKELL__ < 710
-import Data.Monoid
-#endif
 import Data.Typeable
 import Ersatz.Internal.Literal
 
@@ -44,6 +38,15 @@
 import qualified Data.Sequence as Seq
 import Data.Foldable (toList)
 
+#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
+
 ------------------------------------------------------------------------------
 -- Clauses
 ------------------------------------------------------------------------------
@@ -57,9 +60,14 @@
 clauseLiterals :: Clause -> [Literal]
 clauseLiterals (Clause is) = Literal <$> IntSet.toList is
 
+instance Semigroup Clause where
+  Clause x <> Clause y = Clause (x <> y)
+
 instance Monoid Clause where
   mempty = Clause mempty
-  mappend (Clause x) (Clause y) = Clause (mappend x y)
+#if !(MIN_VERSION_base(4,11,0))
+  mappend = (<>)
+#endif
 
 fromLiteral :: Literal -> Clause
 fromLiteral l = Clause { clauseSet = IntSet.singleton $ literalId l }
@@ -72,9 +80,14 @@
 newtype Formula = Formula { formulaSet :: Seq Clause }
   deriving (Eq, Ord, Typeable)
 
+instance Semigroup Formula where
+  Formula x <> Formula y = Formula (x <> y)
+
 instance Monoid Formula where
   mempty = Formula mempty
-  mappend (Formula x) (Formula y) = Formula (mappend x y)
+#if !(MIN_VERSION_base(4,11,0))
+  mappend = (<>)
+#endif
 
 instance Show Formula where
   showsPrec p = showParen (p > 2) . foldr (.) id
diff --git a/src/Ersatz/Problem.hs b/src/Ersatz/Problem.hs
--- a/src/Ersatz/Problem.hs
+++ b/src/Ersatz/Problem.hs
@@ -45,28 +45,18 @@
   ) where
 
 import Data.ByteString.Builder
-#if __GLASGOW_HASKELL__ < 710
-import Control.Applicative
-#endif
 import Control.Lens
 import Control.Monad
-#if !(MIN_VERSION_lens(4,0,0))
-import Control.Monad.Identity
-#endif
 import Control.Monad.State
 import Data.ByteString (ByteString)
 import qualified Data.ByteString.Lazy as Lazy
 import Data.Default
-#if __GLASGOW_HASKELL__ < 710
-import Data.Foldable (foldMap)
-#endif
 import Data.HashMap.Lazy (HashMap)
 import qualified Data.HashMap.Lazy as HashMap
 import Data.Int
 import Data.IntSet (IntSet)
 import qualified Data.IntSet as IntSet
 import qualified Data.List as List
-import Data.Monoid
 import Data.Typeable
 import Ersatz.Internal.Formula
 import Ersatz.Internal.Literal
@@ -74,6 +64,20 @@
 import System.IO.Unsafe
 import Data.Sequence (Seq)
 import qualified Data.Sequence as Seq
+
+#if !(MIN_VERSION_base(4,8,0))
+import Control.Applicative
+import Data.Foldable (foldMap)
+import Data.Monoid (Monoid(..))
+#endif
+
+#if !(MIN_VERSION_base(4,11,0))
+import Data.Semigroup (Semigroup(..))
+#endif
+
+#if !(MIN_VERSION_lens(4,0,0))
+import Control.Monad.Identity
+#endif
 
 ------------------------------------------------------------------------------
 -- SAT Problems
diff --git a/src/Ersatz/Relation/Data.hs b/src/Ersatz/Relation/Data.hs
--- a/src/Ersatz/Relation/Data.hs
+++ b/src/Ersatz/Relation/Data.hs
@@ -3,6 +3,7 @@
 module Ersatz.Relation.Data ( Relation
 , relation, symmetric_relation
 , build
+, buildFrom
 , identity
 , bounds, (!), indices, assocs, elems
 , table
@@ -47,16 +48,20 @@
                    ++ [ ((q,p), x) | p /= q ]
     return $ build bnd $ concat pairs
 
-identity :: ( Ix a )
-         => ((a,a),(a,a)) ->  Relation a a
-identity bnd = build bnd $ flip map (A.range bnd) $ \ (i,j) ->
-        ((i,j), if i == j then true else false )
-
 build :: ( Ix a, Ix b )
       => ((a,b),(a,b))
       -> [ ((a,b), Bit ) ]
       -> Relation a b
 build bnd pairs = Relation $ A.array bnd pairs
+
+buildFrom :: (Ix a, Ix b)
+          => (a -> b -> Bit) -> ((a,b),(a,b)) -> Relation a b
+buildFrom p bnd = build bnd $ flip map (A.range bnd) $ \ (i,j) ->
+    ((i,j), p i j)
+
+identity :: (Ix a)
+         => ((a,a),(a,a)) -> Relation a a
+identity = buildFrom (\ i j -> bool $ i == j)
 
 
 bounds :: (Ix a, Ix b) => Relation a b -> ((a,b),(a,b))
diff --git a/src/Ersatz/Relation/Op.hs b/src/Ersatz/Relation/Op.hs
--- a/src/Ersatz/Relation/Op.hs
+++ b/src/Ersatz/Relation/Op.hs
@@ -5,8 +5,11 @@
 ( mirror
 , union
 , complement
+, difference
 , product, power
 , intersection
+, reflexive_closure
+, symmetric_closure
 )
 
 where
@@ -27,6 +30,10 @@
 complement r =
     build (bounds r) $ do i <- indices r ; return ( i, not $ r!i )
 
+difference :: ( Ix a , Ix b )
+        => Relation a b -> Relation a b ->  Relation a b
+difference r s =
+    intersection r $ complement s
 
 union :: ( Ix a , Ix b )
         => Relation a b -> Relation a b ->  Relation a b
@@ -66,3 +73,10 @@
         i <- indices r
         return (i, and [ r!i, s!i ] )
 
+reflexive_closure :: Ix a => Relation a a -> Relation a a
+reflexive_closure t =
+    union t $ identity $ bounds t
+
+symmetric_closure :: Ix a => Relation a a -> Relation a a
+symmetric_closure r =
+    union r $ mirror r
diff --git a/src/Ersatz/Relation/Prop.hs b/src/Ersatz/Relation/Prop.hs
--- a/src/Ersatz/Relation/Prop.hs
+++ b/src/Ersatz/Relation/Prop.hs
@@ -3,6 +3,7 @@
 
 ( implies
 , symmetric
+, anti_symmetric
 , transitive
 , irreflexive
 , reflexive
@@ -15,6 +16,7 @@
 , min_out_degree
 , empty
 , complete
+, total
 , disjoint
 , equals
 )
@@ -44,6 +46,9 @@
 complete :: (Ix a, Ix b) => Relation a b -> Bit
 complete r = empty $ complement r
 
+total :: ( Ix a) => Relation a a -> Bit
+total r = complete $ symmetric_closure r
+
 disjoint :: (Ix a, Ix b) => Relation a b -> Relation a b -> Bit
 disjoint r s = empty $ intersection r s
 
@@ -53,6 +58,9 @@
 symmetric :: ( Ix a) => Relation a a -> Bit
 symmetric r = implies r ( mirror r )
 
+anti_symmetric :: ( Ix a) => Relation a a -> Bit
+anti_symmetric r = implies (intersection r (mirror r)) (identity (bounds r))
+
 irreflexive :: ( Ix a ) => Relation a a -> Bit
 irreflexive r = and $ do
     let ((a,_),(c,_)) = bounds r
@@ -65,7 +73,7 @@
     x <- range (a,c)
     return $ r ! (x,x)
 
-regular, regular_in_degree, regular_out_degree, max_in_degree, min_in_degree, max_out_degree, min_out_degree :: ( Ix a ) => Int -> Relation a a -> Bit
+regular, regular_in_degree, regular_out_degree, max_in_degree, min_in_degree, max_out_degree, min_out_degree :: (Ix a, Ix b) => Int -> Relation a b -> Bit
 
 regular deg r = and [ regular_in_degree deg r, regular_out_degree deg r ]