diff --git a/DatapathVerification/BitHeap/BVComb.lean b/DatapathVerification/BitHeap/BVComb.lean
new file mode 100644
index 0000000..2354a4b
--- /dev/null
+++ b/DatapathVerification/BitHeap/BVComb.lean
@@ -0,0 +1,71 @@
+import DatapathVerification.BitHeap.BitHeap
+import DatapathVerification.BitHeap.Circuit
+import DatapathVerification.BitHeap.DaddaTree
+
+open BitHeap
+namespace Comb
+
+inductive ArithBinopKind
+| add
+| mul
+
+-- inductive ArithUnopKind
+-- | neg
+
+-- inductive BooleanBinopKind
+-- | and | or | xor
+
+inductive ArithCircuit
+  | var (width : Nat) (varIndex : Nat)
+  | arithbinop (kind : ArithBinopKind) (width : Nat) (l r : ArithCircuit)
+  -- | arithunop (kind : ArithUnopKind) (width : Nat) (arg : ArithCircuit)
+  -- | bvbinop (kind : BooleanBinopKind) (width : Nat) (l r : ArithCircuit)
+
+/--
+Convert a bitheap into a new bitheap that has a single row,
+by building a Dadda tree of adders to reduce the bitheap to a single row.
+-/
+def BitHeap.toSingleRow : BitHeap → CircuitVector
+  | bh =>
+    let (pp1, pp2) := DaddaTree.DaddaTree bh
+    -- add pp1 and pp2 to get the final row
+    sorry
+
+namespace ArithCircuit
+/--
+Given a bitvector (x : BV 3), but a bitheap
+```
+*   *  *
+x2 x1 x0
+```
+-/
+def bitheapOfVar (width : Nat) (varIndex : Nat) : BitHeap :=
+  --  I want to create a bitheap that has one bit-variable per bit in the bitvector variable.
+  -- | We need to know that this index is unique which is a gigantic pain.
+  List.range width |>.foldl (fun bh i => bh.addBit i (BitHeap.Circuit.bit (varIndex * width + i))) BitHeap.empty
+
+def toBitHeap (c : ArithCircuit) : BitHeap :=
+  match c with
+  | .var width varIndex => bitheapOfVar width varIndex
+  | .arithbinop kind width l r =>
+    match kind with
+    | .add => (toBitHeap l).addBitHeap (toBitHeap r)
+    | .mul => (toBitHeap l).mulBitHeap (toBitHeap r)
+  -- | .arithunop kind width arg =>
+  --   match kind with
+  --   | .neg => (toBitHeap arg).negBitHeap
+  -- | .bvbinop kind width l r =>
+  --   match kind with
+  --   | .and =>
+  --     let lRow := (l.toBitHeap).toSingleRow
+  --     let rRow := (r.toBitHeap).toSingleRow
+  --     let newRow := Array.zipWith (fun lBit rBit => Circuit.and lBit rBit) lRow rRow
+  --     BitHeap.fromRow newRow
+
+def toCircuitVector (c : ArithCircuit) : CircuitVector :=
+  let bh := c.toBitHeap
+  bh.toSingleRow
+
+end ArithCircuit
+
+end Comb
diff --git a/DatapathVerification/BitHeap/BitHeap.lean b/DatapathVerification/BitHeap/BitHeap.lean
index 251ba5f..ee9cb84 100644
--- a/DatapathVerification/BitHeap/BitHeap.lean
+++ b/DatapathVerification/BitHeap/BitHeap.lean
@@ -91,6 +91,30 @@ def addBit (column : Nat) (c : Circuit) (h : BitHeap w) : BitHeap w :=
       h.setColumn column (col.insert c) h1
       else addBit (column + 1) c (h.removeBit column c)
 
+-- TODO: make this variable size add
+def addBitHeap' (h1 h2 : BitHeap w) : BitHeap w:=
+  let h := BitHeap.empty w
+  let h := h1.columns.zipIdx.foldl (fun acc (column, index) =>
+             column.elems.toList.foldl (fun acc' c => acc'.addBit index c) acc) h
+  let h := h2.columns.zipIdx.foldl (fun acc (column, index) =>
+             column.elems.toList.foldl (fun acc' c => acc'.addBit index c) acc) h
+  h
+
+def addBitHeap (bhs : List (BitHeap w)) : BitHeap w:=
+  let h := BitHeap.empty w
+  let h := bhs.foldl (fun acc heap => heap.columns.zipIdx.foldl (fun acc' (column, index) =>
+             column.elems.toList.foldl (fun acc' c => acc'.addBit index c) acc') acc) h
+  h
+
+def mulBitHeap (h0 h1 : BitHeap w) : BitHeap (2 * w - 1) :=
+  let h := BitHeap.empty (2 * w - 1)
+  let h := h0.columns.zipIdx.foldl (fun acc (column0, i0) =>
+             h1.columns.zipIdx.foldl (fun acc' (column1, i2) =>
+               column0.elems.toList.foldl (fun acc'' c1 =>
+                 column1.elems.toList.foldl (fun acc''' c2 =>
+                   acc'''.addBit (i0 + i2) (Circuit.binop .and c1 c2)) acc'') acc') acc) h
+  h
+
 structure AdderResult (w : Nat) where
   heap : BitHeap w
   sum : Circuit
diff --git a/DatapathVerification/BitHeap/Circuit.lean b/DatapathVerification/BitHeap/Circuit.lean
index c34c06d..62cee0c 100644
--- a/DatapathVerification/BitHeap/Circuit.lean
+++ b/DatapathVerification/BitHeap/Circuit.lean
@@ -76,4 +76,16 @@ theorem eval_atLeastTwo (a b c : Circuit) (env : BitEnv) :
 
 end Circuit
 
+
+/-- A vector of circuits, used to represent symbolic BitVectors. -/
+def CircuitVector := Array Circuit
+
+namespace CircuitVector
+
+def eval (vec : CircuitVector) (env : Circuit.BitEnv) : Int :=
+  (vec.mapIdx (fun i c => 2^i * (if c.eval env then 1 else 0))).sum
+
+end CircuitVector
+
+
 end BitHeap
diff --git a/DatapathVerification/BitHeap/Examples/Examples.lean b/DatapathVerification/BitHeap/Examples/Examples.lean
index 4702bae..186a5b8 100644
--- a/DatapathVerification/BitHeap/Examples/Examples.lean
+++ b/DatapathVerification/BitHeap/Examples/Examples.lean
@@ -99,6 +99,43 @@ info: 6
 #eval (applyChain compressionChain fourBitsInCol1).eval
         (show BitEnv from fun n => n = 1 || n = 2 || n = 3)
 
+----------------------------
+
+def exampleHeap1 : BitHeap 4 :=
+  let h := BitHeap.empty 4
+  let h := h.addBit 0 (Circuit.bit 0)
+  let h := h.addBit 1 (Circuit.bit 1)
+  let h := h.addBit 2 (Circuit.bit 2)
+  let h := h.addBit 3 (Circuit.bit 3)
+  h
+
+def exampleHeap2 : BitHeap 4 :=
+  let h := BitHeap.empty 4
+  let h := h.addBit 0 (Circuit.bit 4)
+  let h := h.addBit 1 (Circuit.bit 5)
+  let h := h.addBit 2 (Circuit.bit 6)
+  let h := h.addBit 3 (Circuit.bit 7)
+  h
+
+def exampleHeap3 : BitHeap 4 :=
+  let h := BitHeap.empty 4
+  let h := h.addBit 0 (Circuit.bit 8)
+  let h := h.addBit 1 (Circuit.bit 9)
+  let h := h.addBit 2 (Circuit.bit 10)
+  let h := h.addBit 3 (Circuit.bit 11)
+  h
+/--
+info: {0 ↦ [b4, b8, b0], 1 ↦ [b1, b5, b9], 2 ↦ [b2, b10, b6], 3 ↦ [b3, b11, b7]}
+-/
+#guard_msgs in
+#eval addBitHeap [exampleHeap1, exampleHeap2, exampleHeap3]
+
+/--
+info: {0 ↦ [(b0 ∧ b4)], 1 ↦ [(b0 ∧ b5), (b1 ∧ b4)], 2 ↦ [(b1 ∧ b5), (b2 ∧ b4), (b0 ∧ b6)], 3 ↦ [(b3 ∧ b4), (b0 ∧ b7), (b2 ∧ b5), (b1 ∧ b6)], 4 ↦ [(b2 ∧ b6), (b3 ∧ b5), (b1 ∧ b7)], 5 ↦ [(b3 ∧ b6), (b2 ∧ b7)], 6 ↦ [(b3 ∧ b7)]}
+-/
+#guard_msgs in
+#eval mulBitHeap exampleHeap1 exampleHeap2
+
 end Examples
 
 end BitHeap