diff --git a/core/src/stark/folder.rs b/core/src/stark/folder.rs
index 47d4217e3..28aa49e65 100644
--- a/core/src/stark/folder.rs
+++ b/core/src/stark/folder.rs
@@ -113,7 +113,7 @@ pub struct GenericVerifierConstraintFolder<'a, F, EF, Var, Expr> {
     pub is_first_row: Var,
     pub is_last_row: Var,
     pub is_transition: Var,
-    pub alpha: EF,
+    pub alpha: Var,
     pub accumulator: Expr,
     pub _marker: PhantomData<F>,
 }
@@ -170,7 +170,7 @@ where
 
     fn assert_zero<I: Into<Self::Expr>>(&mut self, x: I) {
         let x: Expr = x.into();
-        self.accumulator *= self.alpha;
+        self.accumulator *= self.alpha.into();
         self.accumulator += x;
     }
 }
diff --git a/recursion/compiler/Cargo.toml b/recursion/compiler/Cargo.toml
index 2fbff1a25..9c1a82e5e 100644
--- a/recursion/compiler/Cargo.toml
+++ b/recursion/compiler/Cargo.toml
@@ -6,11 +6,11 @@ edition = "2021"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+p3-air = { workspace = true }
 p3-field = { workspace = true }
 sp1-recursion-core = { path = "../core" }
+sp1-core = { path = "../../core" }
 
 [dev-dependencies]
 p3-baby-bear = { workspace = true }
-p3-air = { workspace = true }
-sp1-core = { path = "../../core" }
 rand = "0.8.4"
diff --git a/recursion/compiler/examples/verifier.rs b/recursion/compiler/examples/verifier.rs
index 36d340ae3..feb15fde1 100644
--- a/recursion/compiler/examples/verifier.rs
+++ b/recursion/compiler/examples/verifier.rs
@@ -1,33 +1,63 @@
-use p3_air::Air;
+use std::fs::File;
+use std::marker::PhantomData;
 
+use p3_field::AbstractField;
 use sp1_core::air::MachineAir;
-use sp1_core::stark::{GenericVerifierConstraintFolder, MachineChip, StarkGenericConfig};
-use sp1_recursion_compiler::ir::{Ext, SymbolicExt};
-
-#[allow(clippy::type_complexity)]
-#[allow(dead_code)]
-fn verify_constraints<SC: StarkGenericConfig, A: MachineAir<SC::Val>>(
-    chip: MachineChip<SC, A>,
-    folder: &mut GenericVerifierConstraintFolder<
-        SC::Val,
-        SC::Challenge,
-        Ext<SC::Val, SC::Challenge>,
-        SymbolicExt<SC::Val, SC::Challenge>,
-    >,
-) where
-    A: for<'a> Air<
-        GenericVerifierConstraintFolder<
-            'a,
-            SC::Val,
-            SC::Challenge,
-            Ext<SC::Val, SC::Challenge>,
-            SymbolicExt<SC::Val, SC::Challenge>,
-        >,
-    >,
-{
-    chip.eval(folder);
-}
+use sp1_core::stark::RiscvAir;
+use sp1_core::stark::StarkGenericConfig;
+use sp1_core::utils;
+use sp1_core::utils::BabyBearPoseidon2;
+use sp1_core::SP1Prover;
+use sp1_core::SP1Stdin;
+use sp1_recursion_compiler::gnark::GnarkBackend;
+use sp1_recursion_compiler::ir::Builder;
+use sp1_recursion_compiler::ir::{Ext, Felt};
+use sp1_recursion_compiler::verifier::verify_constraints;
+use sp1_recursion_compiler::verifier::StarkGenericBuilderConfig;
+use std::collections::HashMap;
+use std::io::Write;
 
 fn main() {
-    println!("Hello, world!");
+    type SC = BabyBearPoseidon2;
+    type F = <SC as StarkGenericConfig>::Val;
+    type EF = <SC as StarkGenericConfig>::Challenge;
+
+    // Generate a dummy proof.
+    utils::setup_logger();
+    let elf =
+        include_bytes!("../../../examples/cycle-tracking/program/elf/riscv32im-succinct-zkvm-elf");
+    let proofs = SP1Prover::prove(elf, SP1Stdin::new())
+        .unwrap()
+        .proof
+        .shard_proofs;
+    let proof = &proofs[0];
+
+    // Extract verification metadata.
+    let machine = RiscvAir::machine(SC::new());
+    let chips = machine
+        .chips()
+        .iter()
+        .filter(|chip| proof.chip_ids.contains(&chip.name()))
+        .collect::<Vec<_>>();
+    let chip = chips[0];
+    let opened_values = &proof.opened_values.chips[0];
+
+    // Run the verify inside the DSL.
+    let mut builder = Builder::<StarkGenericBuilderConfig<F, SC>>::default();
+    let g: Felt<F> = builder.eval(F::one());
+    let zeta: Ext<F, EF> = builder.eval(F::one());
+    let alpha: Ext<F, EF> = builder.eval(F::one());
+    verify_constraints::<F, SC, _>(&mut builder, chip, opened_values, g, zeta, alpha);
+
+    // Emit the constraints using the Gnark backend.
+    let mut backend = GnarkBackend::<StarkGenericBuilderConfig<F, BabyBearPoseidon2>> {
+        nb_backend_vars: 0,
+        used: HashMap::new(),
+        phantom: PhantomData,
+    };
+    let result = backend.compile(builder.operations);
+    let manifest_dir = env!("CARGO_MANIFEST_DIR");
+    let path = format!("{}/src/gnark/lib/main.go", manifest_dir);
+    let mut file = File::create(path).unwrap();
+    file.write_all(result.as_bytes()).unwrap();
 }
diff --git a/recursion/compiler/src/gnark/lib/main.go b/recursion/compiler/src/gnark/lib/main.go
index 60831197b..b39e4c2e1 100644
--- a/recursion/compiler/src/gnark/lib/main.go
+++ b/recursion/compiler/src/gnark/lib/main.go
@@ -13,15 +13,15 @@ type Circuit struct {
 
 func (circuit *Circuit) Define(api frontend.API) error {
 	fieldChip := babybear.NewChip(api)
-	
+
 	// Variables.
-	var felt2 *babybear.Variable
-	var backend1 frontend.Variable
 	var var0 frontend.Variable
-	var backend0 frontend.Variable
-	var felt1 *babybear.Variable
 	var felt0 *babybear.Variable
-	
+	var felt1 *babybear.Variable
+	var backend0 frontend.Variable
+	var felt2 *babybear.Variable
+	var backend1 frontend.Variable
+
 	// Operations.
 	var0 = frontend.Variable(0)
 	felt0 = babybear.NewVariable(0)
@@ -33,10 +33,10 @@ func (circuit *Circuit) Define(api frontend.API) error {
 	}
 	fieldChip.AssertEq(felt0, babybear.NewVariable(144))
 	backend0 = api.IsZero(api.Sub(var0, var0))
-	felt0 = fieldChip.Select(backend0,  fieldChip.Add(felt1, babybear.NewVariable(0)), felt0)
-	felt0 = fieldChip.Select(backend0,  fieldChip.Add(felt0, felt1), felt0)
+	felt0 = fieldChip.Select(backend0, fieldChip.Add(felt1, babybear.NewVariable(0)), felt0)
+	felt0 = fieldChip.Select(backend0, fieldChip.Add(felt0, felt1), felt0)
 	backend1 = api.Sub(frontend.Variable(1), api.IsZero(api.Sub(var0, var0)))
-	felt0 = fieldChip.Select(backend1,  fieldChip.Add(felt1, babybear.NewVariable(0)), felt0)
-	felt0 = fieldChip.Select(backend1,  fieldChip.Add(felt0, felt1), felt0)
+	felt0 = fieldChip.Select(backend1, fieldChip.Add(felt1, babybear.NewVariable(0)), felt0)
+	felt0 = fieldChip.Select(backend1, fieldChip.Add(felt0, felt1), felt0)
 	return nil
 }
diff --git a/recursion/compiler/src/ir/builder.rs b/recursion/compiler/src/ir/builder.rs
index c2d587c33..dcad47353 100644
--- a/recursion/compiler/src/ir/builder.rs
+++ b/recursion/compiler/src/ir/builder.rs
@@ -8,7 +8,7 @@ pub struct Builder<C: Config> {
     pub(crate) felt_count: u32,
     pub(crate) ext_count: u32,
     pub(crate) var_count: u32,
-    pub(crate) operations: Vec<DslIR<C>>,
+    pub operations: Vec<DslIR<C>>,
 }
 
 impl<C: Config> Default for Builder<C> {
diff --git a/recursion/compiler/src/ir/mod.rs b/recursion/compiler/src/ir/mod.rs
index cc7378c44..79677f7fd 100644
--- a/recursion/compiler/src/ir/mod.rs
+++ b/recursion/compiler/src/ir/mod.rs
@@ -6,6 +6,7 @@ mod instructions;
 mod ptr;
 mod symbolic;
 mod types;
+mod utils;
 mod var;
 
 pub use builder::*;
diff --git a/recursion/compiler/src/ir/symbolic.rs b/recursion/compiler/src/ir/symbolic.rs
index 5a13b2e92..53fd76c57 100644
--- a/recursion/compiler/src/ir/symbolic.rs
+++ b/recursion/compiler/src/ir/symbolic.rs
@@ -1002,7 +1002,21 @@ impl<F: Field, EF: ExtensionField<F>, E: Any> ExtensionOperand<F, EF> for E {
                 let value = value_ref.clone();
                 ExtOperand::<F, EF>::Sym(value)
             }
-            _ => unimplemented!("Unsupported type"),
+            ty if ty == TypeId::of::<ExtOperand<F, EF>>() => {
+                let value_ref = unsafe { mem::transmute::<&E, &ExtOperand<F, EF>>(&self) };
+                value_ref.clone()
+            }
+            _ => unimplemented!("unsupported type"),
         }
     }
 }
+
+impl<F: Field> Div<F> for Felt<F> {
+    type Output = SymbolicFelt<F>;
+
+    fn div(self, rhs: F) -> Self::Output {
+        let lhs = SymbolicFelt::Val(self);
+        let rhs = SymbolicFelt::Const(rhs);
+        SymbolicFelt::Div(lhs.into(), rhs.into())
+    }
+}
diff --git a/recursion/compiler/src/ir/utils.rs b/recursion/compiler/src/ir/utils.rs
new file mode 100644
index 000000000..a993bdaf2
--- /dev/null
+++ b/recursion/compiler/src/ir/utils.rs
@@ -0,0 +1,20 @@
+use std::ops::MulAssign;
+
+use super::{Builder, Config, Variable};
+
+impl<C: Config> Builder<C> {
+    pub fn exp_power_of_2<V: Variable<C>, E: Into<V::Expression>>(
+        &mut self,
+        e: E,
+        power_log: usize,
+    ) -> V
+    where
+        V::Expression: MulAssign<V::Expression> + Clone,
+    {
+        let mut e = e.into();
+        for _ in 0..power_log {
+            e *= e.clone();
+        }
+        self.eval(e)
+    }
+}
diff --git a/recursion/compiler/src/lib.rs b/recursion/compiler/src/lib.rs
index 752c91323..ae52d5d1a 100644
--- a/recursion/compiler/src/lib.rs
+++ b/recursion/compiler/src/lib.rs
@@ -5,6 +5,7 @@ pub mod builder;
 pub mod gnark;
 pub mod ir;
 pub mod util;
+pub mod verifier;
 
 pub mod prelude {
     pub use crate::asm::AsmCompiler;
diff --git a/recursion/compiler/src/verifier/constraints.rs b/recursion/compiler/src/verifier/constraints.rs
new file mode 100644
index 000000000..b98a74697
--- /dev/null
+++ b/recursion/compiler/src/verifier/constraints.rs
@@ -0,0 +1,116 @@
+use std::marker::PhantomData;
+
+use p3_air::Air;
+use p3_field::AbstractExtensionField;
+use p3_field::AbstractField;
+use p3_field::Field;
+use sp1_core::air::MachineAir;
+use sp1_core::stark::ChipOpenedValues;
+use sp1_core::stark::{
+    AirOpenedValues, GenericVerifierConstraintFolder, MachineChip, StarkGenericConfig,
+};
+
+use crate::prelude::{Builder, Config, Ext, Felt, SymbolicExt};
+use crate::verifier::StarkGenericBuilderConfig;
+
+impl<C: Config> Builder<C> {
+    pub fn const_opened_values(
+        &mut self,
+        opened_values: &AirOpenedValues<C::EF>,
+    ) -> AirOpenedValues<Ext<C::F, C::EF>> {
+        AirOpenedValues::<Ext<C::F, C::EF>> {
+            local: opened_values
+                .local
+                .iter()
+                .map(|s| self.eval(SymbolicExt::Const(*s)))
+                .collect(),
+            next: opened_values
+                .next
+                .iter()
+                .map(|s| self.eval(SymbolicExt::Const(*s)))
+                .collect(),
+        }
+    }
+}
+
+pub fn verify_constraints<N: Field, SC: StarkGenericConfig + Clone, A: MachineAir<SC::Val>>(
+    builder: &mut Builder<StarkGenericBuilderConfig<N, SC>>,
+    chip: &MachineChip<SC, A>,
+    opening: &ChipOpenedValues<SC::Challenge>,
+    g: Felt<SC::Val>,
+    zeta: Ext<SC::Val, SC::Challenge>,
+    alpha: Ext<SC::Val, SC::Challenge>,
+) where
+    A: for<'a> Air<
+        GenericVerifierConstraintFolder<
+            'a,
+            SC::Val,
+            SC::Challenge,
+            Ext<SC::Val, SC::Challenge>,
+            SymbolicExt<SC::Val, SC::Challenge>,
+        >,
+    >,
+{
+    let g_inv: Felt<SC::Val> = builder.eval(g / SC::Val::one());
+    let z_h: Ext<SC::Val, SC::Challenge> = builder.exp_power_of_2(zeta, opening.log_degree);
+    let one: Ext<SC::Val, SC::Challenge> = builder.eval(SC::Val::one());
+    let is_first_row = builder.eval(z_h / (zeta - one));
+    let is_last_row = builder.eval(z_h / (zeta - g_inv));
+    let is_transition = builder.eval(zeta - g_inv);
+
+    let preprocessed = builder.const_opened_values(&opening.preprocessed);
+    let main = builder.const_opened_values(&opening.main);
+    let perm = builder.const_opened_values(&opening.permutation);
+
+    let zero: Ext<SC::Val, SC::Challenge> = builder.eval(SC::Val::zero());
+    let zero_expr: SymbolicExt<SC::Val, SC::Challenge> = zero.into();
+    let mut folder = GenericVerifierConstraintFolder::<
+        SC::Val,
+        SC::Challenge,
+        Ext<SC::Val, SC::Challenge>,
+        SymbolicExt<SC::Val, SC::Challenge>,
+    > {
+        preprocessed: preprocessed.view(),
+        main: main.view(),
+        perm: perm.view(),
+        perm_challenges: &[SC::Challenge::zero(), SC::Challenge::zero()],
+        cumulative_sum: builder.eval(SC::Val::zero()),
+        is_first_row,
+        is_last_row,
+        is_transition,
+        alpha,
+        accumulator: zero_expr,
+        _marker: PhantomData,
+    };
+
+    let monomials = (0..SC::Challenge::D)
+        .map(SC::Challenge::monomial)
+        .collect::<Vec<_>>();
+
+    let quotient_parts = opening
+        .quotient
+        .chunks_exact(SC::Challenge::D)
+        .map(|chunk| {
+            chunk
+                .iter()
+                .zip(monomials.iter())
+                .map(|(x, m)| *x * *m)
+                .sum()
+        })
+        .collect::<Vec<SC::Challenge>>();
+
+    let mut zeta_powers = zeta;
+    let quotient: Ext<SC::Val, SC::Challenge> = builder.eval(SC::Val::zero());
+    let quotient_expr: SymbolicExt<SC::Val, SC::Challenge> = quotient.into();
+    for quotient_part in quotient_parts {
+        zeta_powers = builder.eval(zeta_powers * zeta);
+        builder.assign(quotient, zeta_powers * quotient_part);
+    }
+    let quotient: Ext<SC::Val, SC::Challenge> = builder.eval(quotient_expr);
+    folder.alpha = alpha;
+
+    chip.eval(&mut folder);
+    let folded_constraints = folder.accumulator;
+    let expected_folded_constraints = z_h * quotient;
+    builder.assert_ext_eq(folded_constraints, expected_folded_constraints);
+}
diff --git a/recursion/compiler/src/verifier/mod.rs b/recursion/compiler/src/verifier/mod.rs
new file mode 100644
index 000000000..a43e7638b
--- /dev/null
+++ b/recursion/compiler/src/verifier/mod.rs
@@ -0,0 +1,21 @@
+mod constraints;
+
+use std::marker::PhantomData;
+
+#[allow(unused_imports)]
+pub use constraints::*;
+use p3_field::Field;
+use sp1_core::stark::StarkGenericConfig;
+
+use crate::prelude::Config;
+
+#[derive(Clone)]
+pub struct StarkGenericBuilderConfig<N, SC> {
+    marker: PhantomData<(N, SC)>,
+}
+
+impl<N: Field, SC: StarkGenericConfig + Clone> Config for StarkGenericBuilderConfig<N, SC> {
+    type N = N;
+    type F = SC::Val;
+    type EF = SC::Challenge;
+}