diff --git a/halo2_proofs/src/plonk/assigned.rs b/halo2_proofs/src/plonk/assigned.rs
index 637d2a58..fcf6b2a3 100644
--- a/halo2_proofs/src/plonk/assigned.rs
+++ b/halo2_proofs/src/plonk/assigned.rs
@@ -389,26 +389,108 @@ mod tests {
 #[cfg(test)]
 mod proptests {
     use std::{
+        cmp,
         convert::TryFrom,
-        ops::{Add, Mul, Sub},
+        ops::{Add, Mul, Neg, Sub},
     };
 
+    use group::ff::Field;
     use pasta_curves::{arithmetic::FieldExt, Fp};
     use proptest::{collection::vec, prelude::*, sample::select};
 
     use super::Assigned;
 
+    trait UnaryOperand: Neg<Output = Self> {
+        fn double(&self) -> Self;
+        fn square(&self) -> Self;
+        fn cube(&self) -> Self;
+        fn inv0(&self) -> Self;
+    }
+
+    impl<F: Field> UnaryOperand for F {
+        fn double(&self) -> Self {
+            self.double()
+        }
+
+        fn square(&self) -> Self {
+            self.square()
+        }
+
+        fn cube(&self) -> Self {
+            self.cube()
+        }
+
+        fn inv0(&self) -> Self {
+            self.invert().unwrap_or(F::zero())
+        }
+    }
+
+    impl<F: Field> UnaryOperand for Assigned<F> {
+        fn double(&self) -> Self {
+            self.double()
+        }
+
+        fn square(&self) -> Self {
+            self.square()
+        }
+
+        fn cube(&self) -> Self {
+            self.cube()
+        }
+
+        fn inv0(&self) -> Self {
+            self.invert()
+        }
+    }
+
     #[derive(Clone, Debug)]
-    enum Operation {
+    enum UnaryOperator {
+        Neg,
+        Double,
+        Square,
+        Cube,
+        Inv0,
+    }
+
+    const UNARY_OPERATORS: &[UnaryOperator] = &[
+        UnaryOperator::Neg,
+        UnaryOperator::Double,
+        UnaryOperator::Square,
+        UnaryOperator::Cube,
+        UnaryOperator::Inv0,
+    ];
+
+    impl UnaryOperator {
+        fn apply<F: UnaryOperand>(&self, a: F) -> F {
+            match self {
+                Self::Neg => -a,
+                Self::Double => a.double(),
+                Self::Square => a.square(),
+                Self::Cube => a.cube(),
+                Self::Inv0 => a.inv0(),
+            }
+        }
+    }
+
+    trait BinaryOperand: Sized + Add<Output = Self> + Sub<Output = Self> + Mul<Output = Self> {}
+    impl<F: Field> BinaryOperand for F {}
+    impl<F: Field> BinaryOperand for Assigned<F> {}
+
+    #[derive(Clone, Debug)]
+    enum BinaryOperator {
         Add,
         Sub,
         Mul,
     }
 
-    const OPERATIONS: &[Operation] = &[Operation::Add, Operation::Sub, Operation::Mul];
+    const BINARY_OPERATORS: &[BinaryOperator] = &[
+        BinaryOperator::Add,
+        BinaryOperator::Sub,
+        BinaryOperator::Mul,
+    ];
 
-    impl Operation {
-        fn apply<F: Add<Output = F> + Sub<Output = F> + Mul<Output = F>>(&self, a: F, b: F) -> F {
+    impl BinaryOperator {
+        fn apply<F: BinaryOperand>(&self, a: F, b: F) -> F {
             match self {
                 Self::Add => a + b,
                 Self::Sub => a - b,
@@ -417,6 +499,12 @@ mod proptests {
         }
     }
 
+    #[derive(Clone, Debug)]
+    enum Operator {
+        Unary(UnaryOperator),
+        Binary(BinaryOperator),
+    }
+
     prop_compose! {
         /// Use narrow that can be easily reduced.
         fn arb_element()(val in any::<u64>()) -> Fp {
@@ -440,15 +528,31 @@ mod proptests {
         }
     }
 
+    prop_compose! {
+        fn arb_operators(num_unary: usize, num_binary: usize)(
+            unary in vec(select(UNARY_OPERATORS), num_unary),
+            binary in vec(select(BINARY_OPERATORS), num_binary),
+        ) -> Vec<Operator> {
+            unary.into_iter()
+                .map(Operator::Unary)
+                .chain(binary.into_iter().map(Operator::Binary))
+                .collect()
+        }
+    }
+
     prop_compose! {
         fn arb_testcase()(
-            num_operations in 1usize..5,
+            num_unary in 0usize..5,
+            num_binary in 0usize..5,
         )(
             values in vec(
                 prop_oneof![Just(Assigned::Zero), arb_trivial(), arb_rational()],
-                num_operations + 1),
-            operations in vec(select(OPERATIONS), num_operations),
-        ) -> (Vec<Assigned<Fp>>, Vec<Operation>) {
+                // Ensure that:
+                // - we have at least one value to apply unary operators to.
+                // - we can apply every binary operator pairwise sequentially.
+                cmp::max(if num_unary > 0 { 1 } else { 0 }, num_binary + 1)),
+            operations in arb_operators(num_unary, num_binary).prop_shuffle(),
+        ) -> (Vec<Assigned<Fp>>, Vec<Operator>) {
             (values, operations)
         }
     }
@@ -460,14 +564,36 @@ mod proptests {
             let elements: Vec<_> = values.iter().cloned().map(|v| v.evaluate()).collect();
 
             // Apply the operations to both the deferred and evaluated values.
-            let deferred_result = {
-                let mut ops = operations.iter();
-                values.into_iter().reduce(|a, b| ops.next().unwrap().apply(a, b)).unwrap()
-            };
-            let evaluated_result = {
-                let mut ops = operations.iter();
-                elements.into_iter().reduce(|a, b| ops.next().unwrap().apply(a, b)).unwrap()
-            };
+            fn evaluate<F: UnaryOperand + BinaryOperand>(
+                items: Vec<F>,
+                operators: &[Operator],
+            ) -> F {
+                let mut ops = operators.iter();
+
+                // Process all binary operators. We are guaranteed to have exactly as many
+                // binary operators as we need calls to the reduction closure.
+                let mut res = items.into_iter().reduce(|mut a, b| loop {
+                    match ops.next() {
+                        Some(Operator::Unary(op)) => a = op.apply(a),
+                        Some(Operator::Binary(op)) => break op.apply(a, b),
+                        None => unreachable!(),
+                    }
+                }).unwrap();
+
+                // Process any unary operators that weren't handled in the reduce() call
+                // above (either if we only had one item, or there were unary operators
+                // after the last binary operator). We are guaranteed to have no binary
+                // operators remaining at this point.
+                loop {
+                    match ops.next() {
+                        Some(Operator::Unary(op)) => res = op.apply(res),
+                        Some(Operator::Binary(_)) => unreachable!(),
+                        None => break res,
+                    }
+                }
+            }
+            let deferred_result = evaluate(values, &operations);
+            let evaluated_result = evaluate(elements, &operations);
 
             // The two should be equal, i.e. deferred inversion should commute with the
             // list of operations.