diff --git a/what4/CHANGES.md b/what4/CHANGES.md
index 938335de..7dd6ef46 100644
--- a/what4/CHANGES.md
+++ b/what4/CHANGES.md
@@ -1,3 +1,10 @@
+# next
+
+* The `BoolMap` parameter of `ConjPred` is now a `ConjMap`. This is a `newtype`
+  wrapper around `BoolMap` that makes clear that the `BoolMap` in question
+  represents a conjunction (as `BoolMap`s may also represent disjunctions).
+  See the Haddocks on `ConjMap` for more details.
+
 # 1.6.2 (Sep 2024)
 
 * Allow building with GHC 9.10.
diff --git a/what4/src/What4/Expr/App.hs b/what4/src/What4/Expr/App.hs
index f4943f33..511de035 100644
--- a/what4/src/What4/Expr/App.hs
+++ b/what4/src/What4/Expr/App.hs
@@ -80,7 +80,7 @@ import           What4.ProgramLoc
 import qualified What4.SemiRing as SR
 import qualified What4.SpecialFunctions as SFn
 import qualified What4.Expr.ArrayUpdateMap as AUM
-import           What4.Expr.BoolMap (BoolMap, Polarity(..), BoolMapView(..), Wrap(..))
+import           What4.Expr.BoolMap (BoolMap, Polarity(..), Wrap(..))
 import qualified What4.Expr.BoolMap as BM
 import           What4.Expr.MATLAB
 import           What4.Expr.WeightedSum (WeightedSum, SemiRingProduct)
@@ -191,10 +191,10 @@ data App (e :: BaseType -> Type) (tp :: BaseType) where
   -- Invariant: The argument to a NotPred must not be another NotPred.
   NotPred :: !(e BaseBoolType) -> App e BaseBoolType
 
-  -- Invariant: The BoolMap must contain at least two elements. No
-  -- element may be a NotPred; negated elements must be represented
-  -- with Negative element polarity.
-  ConjPred :: !(BoolMap e) -> App e BaseBoolType
+  -- Invariant: The 'BM.ConjMap' must contain at least two elements. No element
+  -- may be a NotPred; negated elements must be represented with Negative
+  -- element polarity. See also 'isNormal' in @test/Bool.hs@.
+  ConjPred :: !(BM.ConjMap e) -> App e BaseBoolType
 
   ------------------------------------------------------------------------
   -- Semiring operations
@@ -814,6 +814,9 @@ traverseApp =
     , ( ConType [t|BoolMap|] `TypeApp` AnyType
       , [| BM.traverseVars |]
       )
+    , ( ConType [t|BM.ConjMap|] `TypeApp` AnyType
+      , [| \f cm -> BM.ConjMap <$> BM.traverseVars f (BM.getConjMap cm) |]
+      )
     , ( ConType [t|Ctx.Assignment|] `TypeApp` AnyType `TypeApp` AnyType
       , [| traverseFC |]
       )
@@ -1158,20 +1161,20 @@ asWeightedSum sr x
 asConjunction :: Expr t BaseBoolType -> [(Expr t BaseBoolType, Polarity)]
 asConjunction (BoolExpr True _) = []
 asConjunction (asApp -> Just (ConjPred xs)) =
- case BM.viewBoolMap xs of
-   BoolMapUnit     -> []
-   BoolMapDualUnit -> [(BoolExpr False initializationLoc, Positive)]
-   BoolMapTerms (tm:|tms) -> tm:tms
+ case BM.viewConjMap xs of
+   BM.ConjTrue -> []
+   BM.ConjFalse -> [(BoolExpr False initializationLoc, Positive)]
+   BM.Conjuncts (tm:|tms) -> tm:tms
 asConjunction x = [(x,Positive)]
 
 
 asDisjunction :: Expr t BaseBoolType -> [(Expr t BaseBoolType, Polarity)]
 asDisjunction (BoolExpr False _) = []
 asDisjunction (asApp -> Just (NotPred (asApp -> Just (ConjPred xs)))) =
- case BM.viewBoolMap xs of
-   BoolMapUnit     -> []
-   BoolMapDualUnit -> [(BoolExpr True initializationLoc, Positive)]
-   BoolMapTerms (tm:|tms) -> map (over _2 BM.negatePolarity) (tm:tms)
+ case BM.viewConjMap xs of
+   BM.ConjTrue -> []
+   BM.ConjFalse -> [(BoolExpr True initializationLoc, Positive)]
+   BM.Conjuncts (tm:|tms) -> map (over _2 BM.negatePolarity) (tm:tms)
 asDisjunction x = [(x,Positive)]
 
 asPosAtom :: Expr t BaseBoolType -> (Expr t BaseBoolType, Polarity)
@@ -2086,11 +2089,11 @@ reduceApp sym unary a0 = do
     BaseEq _ x y -> isEq sym x y
 
     NotPred x -> notPred sym x
-    ConjPred bm ->
-      case BM.viewBoolMap bm of
-        BoolMapDualUnit -> return $ falsePred sym
-        BoolMapUnit     -> return $ truePred sym
-        BoolMapTerms tms ->
+    ConjPred cm ->
+      case BM.viewConjMap cm of
+        BM.ConjFalse -> return $ falsePred sym
+        BM.ConjTrue -> return $ truePred sym
+        BM.Conjuncts tms ->
           do let pol (p, Positive) = return p
                  pol (p, Negative) = notPred sym p
              x:|xs <- mapM pol tms
@@ -2337,14 +2340,14 @@ ppApp' a0 = do
 
     NotPred x -> ppSExpr "not" [x]
 
-    ConjPred xs ->
+    ConjPred cm ->
       let pol (x,Positive) = exprPrettyArg x
           pol (x,Negative) = PrettyFunc "not" [ exprPrettyArg x ]
        in
-       case BM.viewBoolMap xs of
-         BoolMapUnit      -> prettyApp "true" []
-         BoolMapDualUnit  -> prettyApp "false" []
-         BoolMapTerms tms -> prettyApp "and" (map pol (toList tms))
+       case BM.viewConjMap cm of
+         BM.ConjTrue -> prettyApp "true" []
+         BM.ConjFalse-> prettyApp "false" []
+         BM.Conjuncts tms -> prettyApp "and" (map pol (toList tms))
 
     RealIsInteger x -> ppSExpr "isInteger" [x]
     BVTestBit i x   -> prettyApp "testBit"  [exprPrettyArg x, showPrettyArg i]
diff --git a/what4/src/What4/Expr/BoolMap.hs b/what4/src/What4/Expr/BoolMap.hs
index d5ff7e4f..8e8f9767 100644
--- a/what4/src/What4/Expr/BoolMap.hs
+++ b/what4/src/What4/Expr/BoolMap.hs
@@ -11,8 +11,12 @@ laws like commutativity, associativity and resolution.
 -}
 
 {-# LANGUAGE DataKinds #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+{-# LANGUAGE PatternSynonyms #-}
 {-# LANGUAGE PolyKinds #-}
-{-# LANGUAGE ViewPatterns #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications #-}
+
 module What4.Expr.BoolMap
   ( BoolMap
   , var
@@ -26,18 +30,30 @@ module What4.Expr.BoolMap
   , isNull
   , BoolMapView(..)
   , viewBoolMap
+  , foldMapVars
   , traverseVars
   , reversePolarities
   , removeVar
   , Wrap(..)
+    -- * 'ConjMap'
+  , ConjMap(..)
+  , ConjMapView
+  , pattern ConjTrue
+  , pattern ConjFalse
+  , pattern Conjuncts
+  , viewConjMap
+  , addConjunct
+  , evalConj
   ) where
 
 import           Control.Lens (_1, over)
+import           Data.Coerce (coerce)
 import           Data.Hashable
 import qualified Data.List as List (foldl')
 import           Data.List.NonEmpty (NonEmpty(..))
 import           Data.Kind (Type)
 import           Data.Parameterized.Classes
+import           Data.Parameterized.TraversableF
 
 import           What4.BaseTypes
 import qualified What4.Utils.AnnotatedMap as AM
@@ -66,18 +82,20 @@ instance OrdF f => Ord (Wrap f x) where
 instance (HashableF f, TestEquality f) => Hashable (Wrap f x) where
   hashWithSalt s (Wrap a) = hashWithSaltF s a
 
--- | This data structure keeps track of a collection of expressions
---   together with their polarities. Such a collection might represent
---   either a conjunction or a disjunction of expressions.  The
---   implementation uses a map from expression values to their
---   polarities, and thus automatically implements the associative,
---   commutative and idempotency laws common to both conjunctions and
---   disjunctions.  Moreover, if the same expression occurs in the
---   collection with opposite polarities, the entire collection
---   collapses via a resolution step to an \"inconsistent\" map.  For
---   conjunctions this corresponds to a contradiction and
---   represents false; for disjunction, this corresponds to the law of
---   the excluded middle and represents true.
+-- | A representation of a conjunction or a disjunction.
+--
+--   This data structure keeps track of a collection of expressions together
+--   with their polarities.  The implementation uses a map from expression
+--   values to their polarities, and thus automatically implements the
+--   associative, commutative and idempotency laws common to both conjunctions
+--   and disjunctions.  Moreover, if the same expression occurs in the
+--   collection with opposite polarities, the entire collection collapses
+--   via a resolution step to an \"inconsistent\" map.  For conjunctions this
+--   corresponds to a contradiction and represents false; for disjunction, this
+--   corresponds to the law of the excluded middle and represents true.
+--
+--   The annotation on the 'AM.AnnotatedMap' is an incremental hash ('IncrHash')
+--   of the map, used to support a fast 'Hashable' instance.
 
 data BoolMap (f :: BaseType -> Type)
   = InconsistentMap
@@ -88,6 +106,16 @@ instance OrdF f => Eq (BoolMap f) where
   BoolMap m1 == BoolMap m2 = AM.eqBy (==) m1 m2
   _ == _ = False
 
+instance OrdF f => Semigroup (BoolMap f) where
+  (<>) = combine
+
+-- | Specialized version of 'foldMapVars'
+instance FoldableF BoolMap where
+  foldMapF f = foldMapVars f
+
+foldMapVars :: Monoid m => (f BaseBoolType -> m) -> BoolMap f -> m
+foldMapVars _ InconsistentMap = mempty
+foldMapVars f (BoolMap am) = foldMap (f . unWrap . fst) (AM.toList am)
 
 -- | Traverse the expressions in a bool map, and rebuild the map.
 traverseVars :: (Applicative m, HashableF g, OrdF g) =>
@@ -107,7 +135,10 @@ instance (OrdF f, HashableF f) => Hashable (BoolMap f) where
       Nothing -> hashWithSalt s (1::Int)
       Just h  -> hashWithSalt (hashWithSalt s (1::Int)) h
 
--- | Represents the state of a bool map
+-- | Represents the state of a 'BoolMap' (either a conjunction or disjunction).
+--
+-- If you know you are dealing with a 'BoolMap' that represents a conjunction,
+-- consider using 'ConjMap' and 'viewConjMap' for the sake of clarity.
 data BoolMapView f
   = BoolMapUnit
        -- ^ A bool map with no expressions, represents the unit of the corresponding operation
@@ -179,3 +210,66 @@ reversePolarities (BoolMap m) = BoolMap $! fmap negatePolarity m
 removeVar :: OrdF f => BoolMap f -> f BaseBoolType -> BoolMap f
 removeVar InconsistentMap _ = InconsistentMap
 removeVar (BoolMap m) x = BoolMap (AM.delete (Wrap x) m)
+
+--------------------------------------------------------------------------------
+-- ConjMap
+
+-- | A 'BoolMap' representing a conjunction.
+newtype ConjMap f = ConjMap { getConjMap :: BoolMap f }
+  deriving (Eq, FoldableF, Hashable, Semigroup)
+
+-- | Represents the state of a 'ConjMap'. See 'viewConjMap'.
+--
+-- Like 'BoolMapView', but with more specific patterns for readability.
+newtype ConjMapView f = ConjMapView (BoolMapView f)
+
+pattern ConjTrue :: ConjMapView f
+pattern ConjTrue = ConjMapView BoolMapUnit
+
+pattern ConjFalse :: ConjMapView f
+pattern ConjFalse = ConjMapView BoolMapDualUnit
+
+pattern Conjuncts :: NonEmpty (f BaseBoolType, Polarity) -> ConjMapView f
+pattern Conjuncts ts = ConjMapView (BoolMapTerms ts)
+
+{-# COMPLETE ConjTrue, ConjFalse, Conjuncts #-}
+
+-- | Deconstruct the given 'ConjMap' for later processing
+viewConjMap :: forall f. ConjMap f -> ConjMapView f
+viewConjMap =
+  -- The explicit type annotations on `coerce` are likely necessary because of
+  -- https://gitlab.haskell.org/ghc/ghc/-/issues/21003
+  coerce @(BoolMap f -> BoolMapView f) @(ConjMap f -> ConjMapView f) viewBoolMap
+{-# INLINE viewConjMap #-}
+
+-- | Add a conjunct to a 'ConjMap'.
+--
+-- Wrapper around 'addVar'.
+addConjunct ::
+  forall f.
+  (HashableF f, OrdF f) =>
+  f BaseBoolType ->
+  Polarity ->
+  ConjMap f ->
+  ConjMap f
+addConjunct =
+  -- The explicit type annotations on `coerce` are likely necessary because of
+  -- https://gitlab.haskell.org/ghc/ghc/-/issues/21003
+  coerce
+    @(f BaseBoolType -> Polarity -> BoolMap f -> BoolMap f)
+    @(f BaseBoolType -> Polarity -> ConjMap f -> ConjMap f)
+    addVar
+{-# INLINE addConjunct #-}
+
+-- | Given the means to evaluate the conjuncts of a 'ConjMap' to a concrete
+-- 'Bool', evaluate the whole conjunction to a 'Bool'.
+evalConj :: Applicative m => (f BaseBoolType -> m Bool) -> ConjMap f -> m Bool
+evalConj f cm =
+  let pol (x, Positive) = f x
+      pol (x, Negative) = not <$> f x
+  in
+  case viewConjMap cm of
+    ConjTrue -> pure True
+    ConjFalse -> pure False
+    Conjuncts (t:|ts) ->
+      List.foldl' (&&) <$> pol t <*> traverse pol ts
diff --git a/what4/src/What4/Expr/Builder.hs b/what4/src/What4/Expr/Builder.hs
index dc39a467..d27a2829 100644
--- a/what4/src/What4/Expr/Builder.hs
+++ b/what4/src/What4/Expr/Builder.hs
@@ -19,6 +19,20 @@ threads may still clobber state others have set (e.g., the current
 program location) so the potential for truly multithreaded use is
 somewhat limited.  Consider the @exprBuilderFreshConfig@ or
 @exprBuilderSplitConfig@ operations if this is a concern.
+
+-- * Boolean expressions
+
+'ExprBuilder' tries to rewrite expressions in order to keep them as simple
+and concrete as possible. In particular, here are a few considerations for
+boolean-typed expressions:
+
+* Disjunctions are implicitly represented as negated conjunctions
+* Conjunctions are represented via 'BM.ConjMap' (see docs on that type)
+* @xor@ is represented as the negation of equality
+
+Boolean expressions are expected to be somewhat normalized at all times.
+For example, there should never be a double negation (nested 'NotPred').
+See @isNormal@ in @test/Bool.hs@ for the exact expectations.
 -}
 {-# LANGUAGE CPP #-}
 {-# LANGUAGE BangPatterns #-}
@@ -233,7 +247,7 @@ import           What4.Symbol
 import           What4.Expr.Allocator
 import           What4.Expr.App
 import qualified What4.Expr.ArrayUpdateMap as AUM
-import           What4.Expr.BoolMap (BoolMap, Polarity(..), BoolMapView(..))
+import           What4.Expr.BoolMap (BoolMap, Polarity(..))
 import qualified What4.Expr.BoolMap as BM
 import           What4.Expr.MATLAB
 import           What4.Expr.WeightedSum (WeightedSum, SemiRingProduct)
@@ -1548,16 +1562,16 @@ realSum sym s = semiRingSum sym s
 bvSum :: ExprBuilder t st fs -> WeightedSum (Expr t) (SR.SemiRingBV flv w) -> IO (BVExpr t w)
 bvSum sym s = semiRingSum sym s
 
-conjPred :: ExprBuilder t st fs -> BoolMap (Expr t) -> IO (BoolExpr t)
-conjPred sym bm =
-  case BM.viewBoolMap bm of
-    BoolMapUnit     -> return $ truePred sym
-    BoolMapDualUnit -> return $ falsePred sym
-    BoolMapTerms ((x,p):|[]) ->
+conjPred :: ExprBuilder t st fs -> BM.ConjMap (Expr t) -> IO (BoolExpr t)
+conjPred sym cm =
+  case BM.viewConjMap cm of
+    BM.ConjTrue -> return $ truePred sym
+    BM.ConjFalse -> return $ falsePred sym
+    BM.Conjuncts ((x,p):|[]) ->
       case p of
         Positive -> return x
         Negative -> notPred sym x
-    _ -> sbMakeExpr sym $ ConjPred bm
+    _ -> sbMakeExpr sym $ ConjPred cm
 
 bvUnary :: (1 <= w) => ExprBuilder t st fs -> UnaryBV (BoolExpr t) w -> IO (BVExpr t w)
 bvUnary sym u
@@ -1985,7 +1999,7 @@ tryAndAbsorption ::
   BoolExpr t ->
   Bool
 tryAndAbsorption (asApp -> Just (NotPred (asApp -> Just (ConjPred as)))) (asConjunction -> bs)
-  = checkAbsorption (BM.reversePolarities as) bs
+  = checkAbsorption (BM.reversePolarities (BM.getConjMap as)) bs
 tryAndAbsorption _ _ = False
 
 
@@ -1997,7 +2011,7 @@ tryOrAbsorption ::
   BoolExpr t ->
   Bool
 tryOrAbsorption (asApp -> Just (ConjPred as)) (asDisjunction -> bs)
-  = checkAbsorption as bs
+  = checkAbsorption (BM.getConjMap as) bs
 tryOrAbsorption _ _ = False
 
 
@@ -2048,6 +2062,8 @@ instance IsExprBuilder (ExprBuilder t st fs) where
 
   ----------------------------------------------------------------------
   -- Bool operations.
+  --
+  -- See Boolean expressions in the module-level docs for some discussion.
 
   truePred  = sbTrue
   falsePred = sbFalse
@@ -2095,7 +2111,7 @@ instance IsExprBuilder (ExprBuilder t st fs) where
    go a b
      | Just (ConjPred as) <- asApp a
      , Just (ConjPred bs) <- asApp b
-     = conjPred sym $ BM.combine as bs
+     = conjPred sym $ as <> bs
 
      | tryAndAbsorption a b
      = return b
@@ -2104,13 +2120,13 @@ instance IsExprBuilder (ExprBuilder t st fs) where
      = return a
 
      | Just (ConjPred as) <- asApp a
-     = conjPred sym $ uncurry BM.addVar (asPosAtom b) as
+     = conjPred sym $ uncurry BM.addConjunct (asPosAtom b) as
 
      | Just (ConjPred bs) <- asApp b
-     = conjPred sym $ uncurry BM.addVar (asPosAtom a) bs
+     = conjPred sym $ uncurry BM.addConjunct (asPosAtom a) bs
 
      | otherwise
-     = conjPred sym $ BM.fromVars [asPosAtom a, asPosAtom b]
+     = conjPred sym $ BM.ConjMap (BM.fromVars [asPosAtom a, asPosAtom b])
 
   orPred sym x y =
     case (asConstantPred x, asConstantPred y) of
@@ -2125,7 +2141,7 @@ instance IsExprBuilder (ExprBuilder t st fs) where
    go a b
      | Just (NotPred (asApp -> Just (ConjPred as))) <- asApp a
      , Just (NotPred (asApp -> Just (ConjPred bs))) <- asApp b
-     = notPred sym =<< conjPred sym (BM.combine as bs)
+     = notPred sym =<< conjPred sym (as <> bs)
 
      | tryOrAbsorption a b
      = return b
@@ -2134,13 +2150,13 @@ instance IsExprBuilder (ExprBuilder t st fs) where
      = return a
 
      | Just (NotPred (asApp -> Just (ConjPred as))) <- asApp a
-     = notPred sym =<< conjPred sym (uncurry BM.addVar (asNegAtom b) as)
+     = notPred sym =<< conjPred sym (uncurry BM.addConjunct (asNegAtom b) as)
 
      | Just (NotPred (asApp -> Just (ConjPred bs))) <- asApp b
-     = notPred sym =<< conjPred sym (uncurry BM.addVar (asNegAtom a) bs)
+     = notPred sym =<< conjPred sym (uncurry BM.addConjunct (asNegAtom a) bs)
 
      | otherwise
-     = notPred sym =<< conjPred sym (BM.fromVars [asNegAtom a, asNegAtom b])
+     = notPred sym =<< conjPred sym (BM.ConjMap (BM.fromVars [asNegAtom a, asNegAtom b]))
 
   itePred sb c x y
       -- ite c c y = c || y
diff --git a/what4/src/What4/Expr/GroundEval.hs b/what4/src/What4/Expr/GroundEval.hs
index 4179cd77..827f9248 100644
--- a/what4/src/What4/Expr/GroundEval.hs
+++ b/what4/src/What4/Expr/GroundEval.hs
@@ -44,7 +44,6 @@ import           Control.Monad
 import           Control.Monad.Trans.Class
 import           Control.Monad.Trans.Maybe
 import qualified Data.BitVector.Sized as BV
-import           Data.List.NonEmpty (NonEmpty(..))
 import           Data.Foldable
 import qualified Data.Map.Strict as Map
 import           Data.Maybe ( fromMaybe )
@@ -320,15 +319,7 @@ evalGroundApp f a0 = do
       if xv then f y else f z
 
     NotPred x -> not <$> f x
-    ConjPred xs ->
-      let pol (x,Positive) = f x
-          pol (x,Negative) = not <$> f x
-      in
-      case BM.viewBoolMap xs of
-        BM.BoolMapUnit -> return True
-        BM.BoolMapDualUnit -> return False
-        BM.BoolMapTerms (t:|ts) ->
-          foldl' (&&) <$> pol t <*> mapM pol ts
+    ConjPred cm -> BM.evalConj f cm
 
     RealIsInteger x -> (\xv -> denominator xv == 1) <$> f x
     BVTestBit i x ->
diff --git a/what4/src/What4/Expr/VarIdentification.hs b/what4/src/What4/Expr/VarIdentification.hs
index 279ac13e..b42c8870 100644
--- a/what4/src/What4/Expr/VarIdentification.hs
+++ b/what4/src/What4/Expr/VarIdentification.hs
@@ -306,14 +306,14 @@ recurseAssertedAppExprVars scope p e = go e
  go (asApp -> Just (NotPred x)) =
         recordAssertionVars scope (BM.negatePolarity p) x
 
- go (asApp -> Just (ConjPred xs)) =
+ go (asApp -> Just (ConjPred cm)) =
    let pol (x,BM.Positive) = recordAssertionVars scope p x
        pol (x,BM.Negative) = recordAssertionVars scope (BM.negatePolarity p) x
    in
-   case BM.viewBoolMap xs of
-     BM.BoolMapUnit -> return ()
-     BM.BoolMapDualUnit -> return ()
-     BM.BoolMapTerms (t:|ts) -> mapM_ pol (t:ts)
+   case BM.viewConjMap cm of
+     BM.ConjTrue -> return ()
+     BM.ConjFalse -> return ()
+     BM.Conjuncts (t:|ts) -> mapM_ pol (t:ts)
 
  go (asApp -> Just (BaseIte BaseBoolRepr _ c x y)) =
    do recordExprVars scope c
diff --git a/what4/src/What4/Protocol/SMTWriter.hs b/what4/src/What4/Protocol/SMTWriter.hs
index a97e9344..4dfc7213 100644
--- a/what4/src/What4/Protocol/SMTWriter.hs
+++ b/what4/src/What4/Protocol/SMTWriter.hs
@@ -2134,14 +2134,14 @@ appSMTExpr ae = do
       let pol (x,Positive) = mkBaseExpr x
           pol (x,Negative) = notExpr <$> mkBaseExpr x
       in
-      case BM.viewBoolMap xs of
-        BM.BoolMapUnit ->
+      case BM.viewConjMap xs of
+        BM.ConjTrue ->
           return $ SMTExpr BoolTypeMap $ boolExpr True
-        BM.BoolMapDualUnit ->
+        BM.ConjFalse ->
           return $ SMTExpr BoolTypeMap $ boolExpr False
-        BM.BoolMapTerms (t:|[]) ->
+        BM.Conjuncts (t:|[]) ->
           SMTExpr BoolTypeMap <$> pol t
-        BM.BoolMapTerms (t:|ts) ->
+        BM.Conjuncts (t:|ts) ->
           do cnj <- andAll <$> mapM pol (t:ts)
              freshBoundTerm BoolTypeMap cnj
 
diff --git a/what4/src/What4/Protocol/VerilogWriter/Backend.hs b/what4/src/What4/Protocol/VerilogWriter/Backend.hs
index c10b6ed9..da85cc11 100644
--- a/what4/src/What4/Protocol/VerilogWriter/Backend.hs
+++ b/what4/src/What4/Protocol/VerilogWriter/Backend.hs
@@ -156,7 +156,7 @@ appVerilogExpr app =
       e' <- exprToVerilogExpr e
       unop Not e'
     --DisjPred es -> boolMapToExpr False True Or es
-    ConjPred es -> boolMapToExpr True False And es
+    ConjPred es -> boolMapToExpr True False And (BMap.getConjMap es)
 
     -- Semiring operations
     -- We only support bitvector semiring operations
diff --git a/what4/src/What4/Serialize/Printer.hs b/what4/src/What4/Serialize/Printer.hs
index 26fa5707..1d34f5ee 100644
--- a/what4/src/What4/Serialize/Printer.hs
+++ b/what4/src/What4/Serialize/Printer.hs
@@ -479,7 +479,7 @@ convertAppExpr' = go . W4.appExprApp
         go (W4.NotPred e) = do
           s <- goE e
           return $ S.L [ident "notp", s]
-        go (W4.ConjPred bm) = convertBoolMap "andp" True bm
+        go (W4.ConjPred cm) = convertBoolMap "andp" True (BooM.getConjMap cm)
         go (W4.BVSlt e1 e2) = do
           s1 <- goE e1
           s2 <- goE e2
diff --git a/what4/test/Bool.hs b/what4/test/Bool.hs
new file mode 100644
index 00000000..0a9f181f
--- /dev/null
+++ b/what4/test/Bool.hs
@@ -0,0 +1,295 @@
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE ViewPatterns #-}
+
+module Bool where
+
+import Control.Monad (unless, when)
+import Control.Monad.IO.Class (MonadIO, liftIO)
+import qualified Control.Monad.State.Strict as State
+import Control.Monad.Trans (lift)
+import Data.Coerce (coerce)
+import Data.Either (isRight)
+import Data.Foldable (traverse_)
+import qualified Data.Map as Map
+import qualified Data.Parameterized.Map as MapF
+import Data.Parameterized.Nonce (newIONonceGenerator)
+import Data.Parameterized.Some (Some(Some))
+import Hedgehog (GenT)
+import qualified Hedgehog.Gen as Gen
+import qualified Hedgehog.Internal.Gen as HG
+import qualified Hedgehog.Internal.Property as HG
+import qualified Test.Tasty.Hedgehog as THG
+import qualified Test.Tasty as T
+import qualified What4.Expr.BoolMap as BM
+import What4.Expr.Builder
+import What4.Expr (EmptyExprBuilderState(EmptyExprBuilderState))
+import What4.Interface
+
+-- | A tree of API calls to 'IsExprBuilder' methods.
+--
+-- Instances may be \"interpreted\" into 'IsExprBuilder' calls via 'toSymExpr'.
+-- Data flows from children to parents.
+--
+-- Given a means to evaluate variables to 'Bool's, these expressions can
+-- also be evaluated directly (via 'eval'), in order to compare the result to
+-- 'asConstantPred'.
+data BExpr var
+  = -- 0-ary
+    -- | 'falsePred', 'truePred'
+    Lit !Bool
+    -- | 'freshConstant'
+  | Var !var
+    -- unary
+    -- | 'notPred'
+  | Not !(BExpr var)
+    -- binary
+    -- | 'andPred'
+  | And !(BExpr var) !(BExpr var)
+    -- | 'eqPred'
+  | Eq !(BExpr var) !(BExpr var)
+    -- | 'orPred'
+  | Or !(BExpr var) !(BExpr var)
+    -- | 'xorPred'
+  | Xor !(BExpr var) !(BExpr var)
+    -- tertiary
+    -- | 'itePred'
+  | Ite !(BExpr var) !(BExpr var) !(BExpr var)
+  deriving Show
+
+genBExpr :: HG.MonadGen m => m var -> m (BExpr var)
+genBExpr var =
+  Gen.recursive
+    Gen.choice
+    [ -- 0-ary
+      Lit <$> Gen.bool
+    , Var <$> var
+    ]
+    [ -- unary
+      Not <$> genBExpr var
+      -- binary
+    , And <$> genBExpr var <*> genBExpr var
+    -- TODO: Generate Eq, Xor.
+    --
+    -- This would require updating 'isNormal' to take these into account.
+    --
+    -- , Eq <$> genBExpr var <*> genBExpr var
+    , Or <$> genBExpr var <*> genBExpr var
+    -- , Xor <$> genBExpr var <*> genBExpr var
+    , Ite <$> genBExpr var <*> genBExpr var <*> genBExpr var
+    ]
+
+newtype Valuation t
+  = Valuation { getValuation :: Map.Map (ExprBoundVar t BaseBoolType) Bool }
+  deriving Show
+
+getValue :: ExprBoundVar t BaseBoolType -> Valuation t -> Bool
+getValue v vs =
+  case Map.lookup v (getValuation vs) of
+    Nothing -> error "getValue: bad variable"
+    Just b -> b
+
+genFreshVar ::
+  (HG.MonadGen m, MonadIO m) =>
+  ExprBuilder t st fs ->
+  State.StateT (Valuation t) m (ExprBoundVar t BaseBoolType)
+genFreshVar sym = do
+  v <- lift (liftIO (freshConstant sym (safeSymbol "b") BaseBoolRepr))
+  case v of
+    BoundVarExpr v' -> do
+      b <- Gen.bool
+      State.modify (coerce (Map.insert v' b))
+      pure v'
+    _ -> error "Not a bound variable?"
+
+-- | Generate a new variable ('genFreshVar') or reuse an existing one
+genVar ::
+  (HG.MonadGen m, MonadIO m) =>
+  ExprBuilder t st fs ->
+  State.StateT (Valuation t) m (ExprBoundVar t BaseBoolType)
+genVar sym = do
+  b <- Gen.bool
+  if b
+    then genFreshVar sym
+    else do
+      vs <- State.gets (Map.toList . getValuation)
+      case vs of
+        [] -> genFreshVar sym
+        _ -> Gen.choice (map (pure . fst) vs)
+
+doGenExpr ::
+  ExprBuilder t st fs ->
+  GenT IO (BExpr (ExprBoundVar t BaseBoolType), Valuation t)
+doGenExpr sym =
+  let vars0 = Valuation Map.empty in
+  State.runStateT (genBExpr @(State.StateT _ (GenT IO)) (genVar @(GenT IO) sym)) vars0
+
+toSymExpr ::
+  IsExprBuilder sym =>
+  sym ->
+  -- | How to handle variables
+  (var -> IO (SymExpr sym BaseBoolType)) ->
+  BExpr var ->
+  IO (SymExpr sym BaseBoolType)
+toSymExpr sym var = go
+  where
+  go =
+    \case
+      Lit True -> pure (truePred sym)
+      Lit False -> pure (falsePred sym)
+      Var v -> var v
+      Not e -> notPred sym =<< go e
+      And l r -> do
+        l' <- go l
+        r' <- go r
+        andPred sym l' r'
+      Eq l r -> do
+        l' <- go l
+        r' <- go r
+        eqPred sym l' r'
+      Or l r -> do
+        l' <- go l
+        r' <- go r
+        orPred sym l' r'
+      Xor l r -> do
+        l' <- go l
+        r' <- go r
+        xorPred sym l' r'
+      Ite c l r -> do
+        c' <- go c
+        l' <- go l
+        r' <- go r
+        itePred sym c' l' r'
+
+-- | For use with 'toSymExpr', to leave variables uninterpreted
+uninterpVar :: ExprBoundVar t BaseBoolType -> Expr t BaseBoolType
+uninterpVar = BoundVarExpr
+
+eval :: Applicative f => (var -> f Bool) -> BExpr var -> f Bool
+eval var = go
+  where
+  ite c l r = if c then l else r
+  go =
+    \case
+      Lit True -> pure True
+      Lit False -> pure False
+      Var v -> var v
+      Not e -> not <$> go e
+      And l r -> (&&) <$> go l <*> go r
+      Eq l r -> (==) <$> go l <*> go r
+      Or l r -> (||) <$> go l <*> go r
+      Xor l r -> (/=) <$> go l <*> go r
+      Ite c l r -> ite <$> go c <*> go l <*> go r
+
+-- | For use with 'eval', to interpret variables
+getVar :: ExprBoundVar t BaseBoolType -> State.State (Valuation t) Bool
+getVar v = State.gets (getValue v)
+
+isNot :: Expr t BaseBoolType -> Bool
+isNot e =
+  case e of
+    AppExpr ae ->
+      case appExprApp ae of
+        NotPred {} -> True
+        _ -> False
+    _ -> False
+
+isNormalIte ::
+  ExprBuilder t st fs ->
+  Expr t BaseBoolType -> 
+  Expr t BaseBoolType -> 
+  Expr t BaseBoolType -> 
+  Either String ()
+isNormalIte sym c l r = do
+  isNormal sym c
+  isNormal sym l
+  isNormal sym r
+  when (isNot c) (Left "negated ite condition")
+  when (c == l) (Left "ite cond == LHS")
+  when (c == r) (Left "ite cond == RHS")
+  when (c == truePred sym) (Left "ite cond == true")
+  when (c == falsePred sym) (Left "ite cond == false")
+
+isNormalConjunct ::
+  ExprBuilder t st fs ->
+  Expr t BaseBoolType ->
+  BM.Polarity ->
+  Either String ()
+isNormalConjunct sym expr pol =
+  case expr of
+    BoolExpr {} -> Left "boolean literal inside conjunction"
+    BoundVarExpr {} -> Right ()
+    AppExpr ae ->
+      case appExprApp ae of
+        NotPred {} -> Left "not should be expressed via polarity"
+        -- This must be an OR, if it is an AND it should be combined with
+        -- its parent
+        ConjPred cm' -> do
+          when (pol == BM.Positive) (Left "and inside and")
+          -- Note that it is possible to have ORs inside ORs, e.g., if the outer
+          -- OR used to be an AND but was negated.
+          isNormalMap sym cm'
+        BaseIte BaseBoolRepr _sz c l r -> isNormalIte sym c l r
+        _ -> Left "non-normal app in conjunct"
+    _ -> Left "non-normal expr in conjunct"
+
+isNormalMap :: ExprBuilder t st fs -> BM.ConjMap (Expr t) -> Either String ()
+isNormalMap sym cm =
+  case BM.viewConjMap cm of
+    BM.ConjTrue -> Left "empty conjunction map"
+    BM.ConjFalse -> Left "inconsistent conjunction map"
+    BM.Conjuncts conjs -> traverse_ (uncurry (isNormalConjunct sym)) conjs
+
+-- | Is this boolean expression sufficiently normalized?
+isNormal :: ExprBuilder t st fs -> Expr t BaseBoolType -> Either String ()
+isNormal sym =
+  \case
+    BoolExpr {} -> Right ()
+    BoundVarExpr {} -> Right ()
+    AppExpr ae ->
+      case appExprApp ae of
+        NotPred (asApp -> Just NotPred {}) -> Left "double negation"
+        NotPred e -> isNormal sym e
+        ConjPred cm -> isNormalMap sym cm
+        BaseIte BaseBoolRepr _sz c l r -> isNormalIte sym c l r
+        _ -> Left "non-normal app"
+    _ -> Left "non-normal expr"
+
+boolTests :: T.TestTree
+boolTests =
+  T.testGroup
+    "boolean normalization tests"
+    [ -- Test that the rewrite rules rewrite expressions into a sufficiently
+      -- normal form (defined by 'isNormal').
+      THG.testProperty "boolean rewrites normalize" $
+        HG.property $ do
+          Some ng <- liftIO newIONonceGenerator
+          sym <- liftIO (newExprBuilder FloatIEEERepr EmptyExprBuilderState ng)
+          (e, _vars) <- HG.forAllT (doGenExpr sym)
+          e' <- liftIO (toSymExpr sym (pure . uninterpVar) e)
+          let ok = isNormal sym e'
+          unless (isRight ok) $
+            liftIO (putStrLn ("Not normalized:\n" ++ show (printSymExpr e')))
+          ok HG.=== Right ()
+    , THG.testProperty "boolean rewrites preserve semantics" $
+        HG.property $ do
+          Some ng <- liftIO newIONonceGenerator
+          sym <- liftIO (newExprBuilder FloatIEEERepr EmptyExprBuilderState ng)
+          (e, vars) <- HG.forAllT (doGenExpr sym)
+          -- Concretely evaluate the `BExpr` to get the expected semantics.
+          let expected = State.evalState (eval getVar e) vars
+          -- Generate a `Expr` with uninterpreted variables. It is important to
+          -- not interpret the variables into `truePred` and `falsePred` here,
+          -- to avoid only hitting the `asConstantPred` cases in the rewrites.
+          e' <- liftIO (toSymExpr sym (pure . uninterpVar) e)
+          -- Finally, substitute values in for the variables, simplifying the
+          -- `Expr` along the way until we get a concrete boolean.
+          let vs = Map.toList (getValuation vars)
+          let substs = foldr (\(v, b) -> MapF.insert v (if b then truePred sym else falsePred sym)) MapF.empty vs
+          e'' <- liftIO (substituteBoundVars sym substs e')
+          -- Check that the `BExpr` and `Expr` agreed on the semantics.
+          case asConstantPred e'' of
+            Just actual -> actual HG.=== expected
+            Nothing -> HG.failure
+    ]
diff --git a/what4/test/BoolNormalization.hs b/what4/test/BoolNormalization.hs
new file mode 100644
index 00000000..76d29699
--- /dev/null
+++ b/what4/test/BoolNormalization.hs
@@ -0,0 +1,62 @@
+-- See what percentage of randomly-generated boolean expressions can be
+-- completely simplified away. Higher is better. This is one mechanism for
+-- evaluating rewrite rules.
+
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE LambdaCase #-}
+
+module Main (main) where
+
+import Control.Monad (foldM)
+import qualified Control.Monad.State.Strict as State
+import Data.Parameterized.Nonce (newIONonceGenerator)
+import Data.Parameterized.Some (Some(Some))
+import Data.Parameterized.TraversableFC (traverseFC_)
+import qualified Hedgehog.Internal.Gen as HG
+import qualified Hedgehog.Internal.Tree as HG
+import qualified Hedgehog as HG
+import What4.Expr.Builder
+import What4.Expr (EmptyExprBuilderState(EmptyExprBuilderState))
+import What4.Interface
+
+import Bool
+
+-- | Get the size of an expression. Lower is better.
+sz :: Expr t tp -> Int
+sz =
+  \case
+    SemiRingLiteral {} -> 1
+    BoolExpr {} -> 1
+    FloatExpr {} -> 1
+    StringExpr {} -> 1
+    AppExpr ae ->
+      State.execState (traverseFC_ (\e -> State.modify (+ sz e)) (appExprApp ae)) 1
+    NonceAppExpr nae ->
+      State.execState (traverseFC_ (\e -> State.modify (+ sz e)) (nonceExprApp nae)) 1
+    BoundVarExpr {} -> 1
+
+main :: IO ()
+main = do
+  Some ng <- newIONonceGenerator
+  sym <- newExprBuilder FloatIEEERepr EmptyExprBuilderState ng
+  let eliminated i = do
+        x <- HG.runTreeT (HG.evalGenT (HG.Size 100) (HG.Seed i 1) (doGenExpr sym))
+        case HG.nodeValue x of
+          Nothing -> error "whoops"
+          Just (bExpr, _vars) -> do
+            e <- toSymExpr sym (pure . uninterpVar) bExpr
+            -- Audit the quality of the generated expressions:
+            -- putStrLn "--------------------------------------"
+            -- putStrLn (show bExpr)
+            -- putStrLn "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
+            -- putStrLn (show (printSymExpr e))
+            -- putStrLn "______________________________________"
+            -- putStrLn (show (sz e))
+            case asConstantPred e of
+              Just {} -> pure (1, sz e)
+              Nothing -> pure (0, sz e)
+  let total = 20000
+  let count (accFull, accSize) (full, size) = (accFull + full, accSize + size)
+  (full, size) <- foldM (\acc seed -> count acc <$> eliminated seed) (0 :: Int, 0 :: Int) [0..total]
+  putStrLn ("Fully eliminated " ++ show full ++ "/" ++ show total)
+  putStrLn ("Total size: " ++ show size)
diff --git a/what4/test/ExprsTest.hs b/what4/test/ExprsTest.hs
index d4b4d81f..3f2258f7 100644
--- a/what4/test/ExprsTest.hs
+++ b/what4/test/ExprsTest.hs
@@ -33,6 +33,8 @@ import           What4.Concrete
 import           What4.Expr
 import           What4.Interface
 
+import Bool (boolTests)
+
 type IteExprBuilder t fs = ExprBuilder t EmptyExprBuilderState fs
 
 withTestSolver :: (forall t. IteExprBuilder t (Flags FloatIEEE) -> IO a) -> IO a
@@ -385,4 +387,5 @@ main = defaultMain $ testGroup "What4 Expressions"
       return (asConcrete s)
     (fromConcreteString <$> s) === Just ""
   , testInjectiveConversions
+  , boolTests
   ]
diff --git a/what4/what4.cabal b/what4/what4.cabal
index 84a62292..e4c6ceb3 100644
--- a/what4/what4.cabal
+++ b/what4/what4.cabal
@@ -363,9 +363,20 @@ test-suite exprs_tests
   main-is: ExprsTest.hs
 
   other-modules:
+    Bool
     GenWhat4Expr
 
   build-depends: bv-sized
+               , containers
+               , mtl
+
+executable bool-normalization
+  import: bldflags, testdefs-hedgehog, testdefs-hunit
+  main-is: BoolNormalization.hs
+  other-modules: Bool
+  build-depends: containers
+               , mtl
+               , transformers
 
 
 test-suite iteexprs_tests