diff --git a/examples/factorial.py b/examples/factorial.py
new file mode 100644
index 00000000..7a5bc510
--- /dev/null
+++ b/examples/factorial.py
@@ -0,0 +1,121 @@
+from chiquito.dsl import Circuit, StepType
+from chiquito.cb import eq
+from chiquito.util import F
+from chiquito.chiquito_ast import Last
+
+MAX_FACTORIAL = 10
+
+"""
+|    step_type      |  i  |  x   |
+----------------------------------
+|  first_step       |  0  |  1   |
+|  operation_step   |  1  |  1   |
+|  operation_step   |  2  |  2   |
+|  operation_step   |  3  |  6   |
+|  result_step      |  4  |  24  |
+|  result_step      |  4  |  24  |
+|  result_step      |  4  |  24  |
+        ...
+"""
+
+
+class FirstStep(StepType):
+    def setup(self):
+        # constrain `i` to zero
+        self.constr(eq(self.circuit.i, 0))
+        # constrain `x` to one
+        self.constr(eq(self.circuit.x, 1))
+        # constrain the next `x` to be equal to the current `x`
+        self.transition(eq(self.circuit.x, self.circuit.x.next()))
+
+    def wg(self):
+        self.assign(self.circuit.i, F(0))
+        self.assign(self.circuit.x, F(1))
+
+
+class OperationStep(StepType):
+    def setup(self):
+        # constrain i.prev() + 1 == i
+        self.transition(eq(self.circuit.i.rot(-1) + 1, self.circuit.i))
+        # constrain i + 1 == i.next()
+        self.transition(eq(self.circuit.i + 1, self.circuit.i.next()))
+        # constrain the next `x` to be the product of the current `x` and the next `i`
+        self.transition(eq(self.circuit.x * (self.circuit.i + 1), self.circuit.x.next()))
+
+    def wg(self, i_value, x_value):
+        self.assign(self.circuit.i, F(i_value))
+        self.assign(self.circuit.x, F(x_value))
+
+
+class ResultStep(StepType):
+    def setup(self):
+        # constrain `x` to not change
+        self.transition(eq(self.circuit.x, self.circuit.x.next()))
+        # constrain `i` to not change
+        self.transition(eq(self.circuit.i, self.circuit.i.next()))
+
+    def wg(self, i_value, x_value):
+        self.assign(self.circuit.i, F(i_value))
+        self.assign(self.circuit.x, F(x_value))
+
+
+class Factorial(Circuit):
+    def setup(self):
+        # `i` holds the current iteration number
+        self.i = self.shared("i")
+        # `x` holds the current total result
+        self.x = self.forward("x")
+
+        self.first_step = self.step_type(FirstStep(self, "first_step"))
+        self.operation_step = self.step_type(OperationStep(self, "operation_step"))
+        self.result_step = self.step_type(ResultStep(self, "result_step"))
+
+        self.pragma_num_steps(MAX_FACTORIAL + 1)
+        self.pragma_first_step(self.first_step)
+        self.pragma_last_step(self.result_step)
+
+        self.expose(self.x, Last())
+        self.expose(self.i, Last())
+
+    def trace(self, n):
+        self.add(self.first_step)
+        current_result = 1
+
+        for i in range(1, n + 1):
+            current_result *= i
+            if i == n:
+                # we found the result
+                self.add(self.result_step, i, current_result)
+            else:
+                # more operations need to be done
+                self.add(self.operation_step, i, current_result)
+
+        while self.needs_padding():
+            # if padding is needed, we propagate final values
+            self.add(self.result_step, n, current_result)
+
+
+class Examples:
+    def test_zero(self):
+        factorial = Factorial()
+        factorial_witness = factorial.gen_witness(0)
+        last_assignments = list(factorial_witness.step_instances[10].assignments.values())
+        assert last_assignments[0] == 0  # i
+        assert last_assignments[1] == 1  # x
+        factorial.halo2_mock_prover(factorial_witness)
+
+    def test_basic(self):
+        factorial = Factorial()
+        factorial_witness = factorial.gen_witness(7)
+        last_assignments = list(factorial_witness.step_instances[10].assignments.values())
+        assert last_assignments[0] == 7  # i
+        assert last_assignments[1] == 5040  # x
+        factorial.halo2_mock_prover(factorial_witness)
+
+
+if __name__ == "__main__":
+    x = Examples()
+    for method in [
+        method for method in dir(x) if callable(getattr(x, method)) if not method.startswith('_')
+    ]:
+        getattr(x, method)()
diff --git a/examples/factorial.rs b/examples/factorial.rs
new file mode 100644
index 00000000..5da8391b
--- /dev/null
+++ b/examples/factorial.rs
@@ -0,0 +1,180 @@
+use std::hash::Hash;
+
+use chiquito::{
+    field::Field,
+    frontend::dsl::circuit, // main function for constructing an AST circuit
+    plonkish::backend::halo2::{chiquito2Halo2, ChiquitoHalo2Circuit}, /* compiles to
+                             * Chiquito Halo2
+                             * backend,
+                             * which can be
+                             * integrated into
+                             * Halo2
+                             * circuit */
+    plonkish::compiler::{
+        cell_manager::SingleRowCellManager, // input for constructing the compiler
+        compile,                            // input for constructing the compiler
+        config,
+        step_selector::SimpleStepSelectorBuilder,
+    },
+    plonkish::ir::{assignments::AssignmentGenerator, Circuit}, // compiled circuit type
+    poly::ToField,
+};
+use halo2_proofs::{dev::MockProver, halo2curves::bn256::Fr};
+
+const MAX_FACTORIAL: usize = 10;
+
+fn generate<F: Field + From<u64> + Hash>() -> (Circuit<F>, Option<AssignmentGenerator<F, u32>>) {
+    //
+    // table for the circuit:
+    // |    step_type      |  i  |  x   |
+    // ----------------------------------
+    // |  first_step       |  0  |  1   |
+    // |  operation_step   |  1  |  1   |
+    // |  operation_step   |  2  |  2   |
+    // |  operation_step   |  3  |  6   |
+    // |  result_step      |  4  |  24  |
+    // |  result_step      |  4  |  24  |
+    // |  result_step      |  4  |  24  |
+    // ...
+
+    use chiquito::frontend::dsl::cb::*; // functions for constraint building
+
+    let factorial_circuit = circuit::<F, u32, _>("factorial", |ctx| {
+        let i = ctx.shared("i");
+        let x = ctx.forward("x");
+
+        // first step will make sure the circuit is initialized correctly
+        let first_step = ctx.step_type_def("first_step", |ctx| {
+            // define the setup
+            ctx.setup(move |ctx| {
+                // constrain `i` to zero
+                ctx.constr(eq(i, 0));
+                // constrain `x` to one
+                ctx.constr(eq(x, 1));
+                // constrain the next `x` to be equal to the current `x`
+                ctx.transition(eq(x, x.next()));
+            });
+            // witness assignment
+            ctx.wg(move |ctx, ()| {
+                ctx.assign(i, 0.into());
+                ctx.assign(x, 1.into());
+            })
+        });
+
+        // operation step will make sure every state transition is correct
+        let operation_step = ctx.step_type_def("operation_step", |ctx| {
+            // define the setup
+            ctx.setup(move |ctx| {
+                // constrain i.prev() + 1 == i
+                ctx.transition(eq(i.rot(-1) + 1, i));
+                // constrain i + 1 == i.next()
+                ctx.transition(eq(i + 1, i.next()));
+                // constrain the next `x` to be the product of the current `x` and the next `i`
+                ctx.transition(eq(x * i.next(), x.next()));
+            });
+            // witness assignment
+            ctx.wg(move |ctx, (i_value, x_value): (u32, u32)| {
+                ctx.assign(i, i_value.field());
+                ctx.assign(x, x_value.field());
+            })
+        });
+
+        // result step will hold and propagate the value
+        let result_step = ctx.step_type_def("result_step", |ctx| {
+            // define the setup
+            ctx.setup(move |ctx| {
+                // constrain `i` to not change
+                ctx.transition(eq(i, i.next()));
+                // constrain `x` to not change
+                ctx.transition(eq(x, x.next()));
+            });
+            // witness assignment
+            ctx.wg(move |ctx, (i_value, x_value): (u32, u32)| {
+                ctx.assign(i, i_value.field());
+                ctx.assign(x, x_value.field());
+            })
+        });
+
+        ctx.pragma_first_step(&first_step);
+        ctx.pragma_last_step(&result_step);
+        ctx.pragma_num_steps(MAX_FACTORIAL + 1);
+
+        ctx.trace(move |ctx, n| {
+            ctx.add(&first_step, ());
+
+            let mut current_result = 1;
+
+            for i in 1..n + 1 {
+                current_result *= i;
+                if i == n {
+                    // we found the result
+                    ctx.add(&result_step, (i, current_result));
+                } else {
+                    // more operations need to be done
+                    ctx.add(&operation_step, (i, current_result));
+                }
+            }
+
+            // if padding is needed, propagate final values
+            ctx.padding(&result_step, || (n, current_result));
+        })
+    });
+
+    compile(
+        config(SingleRowCellManager {}, SimpleStepSelectorBuilder {}),
+        &factorial_circuit,
+    )
+}
+
+// After compiling Chiquito AST to an IR, it is further parsed by a Chiquito Halo2 backend and
+// integrated into a Halo2 circuit, which is done by the boilerplate code below.
+
+// standard main function for a Halo2 circuit
+fn main() {
+    let (chiquito, wit_gen) = generate::<Fr>();
+    let compiled = chiquito2Halo2(chiquito);
+    let circuit = ChiquitoHalo2Circuit::new(compiled, wit_gen.map(|g| g.generate(0)));
+
+    let prover = MockProver::<Fr>::run(10, &circuit, circuit.instance()).unwrap();
+
+    let result = prover.verify_par();
+
+    println!("result = {:#?}", result);
+
+    if let Err(failures) = &result {
+        for failure in failures.iter() {
+            println!("{}", failure);
+        }
+    }
+
+    // plaf boilerplate
+    use chiquito::plonkish::backend::plaf::chiquito2Plaf;
+    use polyexen::plaf::{backends::halo2::PlafH2Circuit};
+
+    // get Chiquito ir
+    let (circuit, wit_gen) = generate::<Fr>();
+    // get Plaf
+    let (plaf, plaf_wit_gen) = chiquito2Plaf(circuit, 8, false);
+    let wit = plaf_wit_gen.generate(wit_gen.map(|v| v.generate(7)));
+
+    // debug only: print witness
+    // println!("{}", polyexen::plaf::WitnessDisplayCSV(&wit));
+
+    // get Plaf halo2 circuit from Plaf's halo2 backend
+    // this is just a proof of concept, because Plaf only has backend for halo2
+    // this is unnecessary because Chiquito has a halo2 backend already
+    let plaf_circuit = PlafH2Circuit { plaf, wit };
+
+    // same as halo2 boilerplate above
+    let prover_plaf = MockProver::<Fr>::run(8, &plaf_circuit, Vec::new()).unwrap();
+
+    let result_plaf = prover_plaf.verify_par();
+
+    println!("result = {:#?}", result_plaf);
+
+    if let Err(failures) = &result_plaf {
+        for failure in failures.iter() {
+            println!("{}", failure);
+        }
+    }
+}