diff --git a/evm/src/cpu/kernel/assembler.rs b/evm/src/cpu/kernel/assembler.rs
index 334220fd..6d2b0ff2 100644
--- a/evm/src/cpu/kernel/assembler.rs
+++ b/evm/src/cpu/kernel/assembler.rs
@@ -29,6 +29,7 @@ pub struct Kernel {
 
     pub(crate) global_labels: HashMap<String, usize>,
 
+    /// Map from `PROVER_INPUT` offsets to their corresponding `ProverInputFn`.
     pub(crate) prover_inputs: HashMap<usize, ProverInputFn>,
 }
 
diff --git a/evm/src/cpu/kernel/evm_asm.pest b/evm/src/cpu/kernel/evm_asm.pest
index b0033391..0703798e 100644
--- a/evm/src/cpu/kernel/evm_asm.pest
+++ b/evm/src/cpu/kernel/evm_asm.pest
@@ -29,7 +29,7 @@ local_label = { identifier ~ ":" }
 bytes_item = { ^"BYTES " ~ literal ~ ("," ~ literal)* }
 push_instruction = { ^"PUSH " ~ push_target }
 push_target = { literal | identifier | variable | constant }
-prover_input_instruction = { ^"PROVER_INPUT" ~ "(" ~ prover_input_fn ~ ")" } // TODO: Could also support extra arguments.
+prover_input_instruction = { ^"PROVER_INPUT" ~ "(" ~ prover_input_fn ~ ")" }
 prover_input_fn = { identifier ~ ("::" ~ identifier)*}
 nullary_instruction = { identifier }
 
diff --git a/evm/src/cpu/kernel/prover_input.rs b/evm/src/cpu/kernel/prover_input.rs
index 5f3ecd42..733cbef7 100644
--- a/evm/src/cpu/kernel/prover_input.rs
+++ b/evm/src/cpu/kernel/prover_input.rs
@@ -7,6 +7,8 @@ use crate::cpu::kernel::prover_input::Field::{
 };
 use crate::cpu::kernel::prover_input::FieldOp::{Inverse, Sqrt};
 
+/// Prover input function represented as a scoped function name.
+/// Example: `PROVER_INPUT(ff::bn254_base::inverse)` is represented as `ProverInputFn([ff, bn254_base, inverse])`.
 #[derive(PartialEq, Eq, Debug, Clone)]
 pub struct ProverInputFn(Vec<String>);
 
@@ -17,20 +19,27 @@ impl From<Vec<String>> for ProverInputFn {
 }
 
 impl ProverInputFn {
+    /// Run the function on the stack.
     pub(crate) fn run(&self, stack: Vec<U256>) -> U256 {
         match self.0[0].as_str() {
             "ff" => self.run_ff(stack),
-            "storage" => todo!(),
+            "mpt" => todo!(),
             _ => panic!("Unrecognized prover input function."),
         }
     }
 
+    // Finite field operations.
     fn run_ff(&self, mut stack: Vec<U256>) -> U256 {
         let field = Field::from_str(self.0[1].as_str()).unwrap();
         let op = FieldOp::from_str(self.0[2].as_str()).unwrap();
         let x = stack.pop().expect("Empty stack");
         field.op(op, x)
     }
+
+    // MPT operations.
+    fn run_mpt(&self, mut stack: Vec<U256>) -> U256 {
+        todo!()
+    }
 }
 
 enum Field {
diff --git a/evm/src/cpu/kernel/tests/ecrecover.rs b/evm/src/cpu/kernel/tests/ecrecover.rs
index 790a4a2c..b105cf47 100644
--- a/evm/src/cpu/kernel/tests/ecrecover.rs
+++ b/evm/src/cpu/kernel/tests/ecrecover.rs
@@ -5,7 +5,7 @@ use ethereum_types::U256;
 
 use crate::cpu::kernel::aggregator::combined_kernel;
 use crate::cpu::kernel::assembler::Kernel;
-use crate::cpu::kernel::interpreter::run;
+use crate::cpu::kernel::interpreter::run_with_kernel;
 use crate::cpu::kernel::tests::u256ify;
 
 fn test_valid_ecrecover(
@@ -18,13 +18,7 @@ fn test_valid_ecrecover(
 ) -> Result<()> {
     let ecrecover = kernel.global_labels["ecrecover"];
     let initial_stack = u256ify(["0xdeadbeef", s, r, v, hash])?;
-    let stack = run(
-        &kernel.code,
-        ecrecover,
-        initial_stack,
-        &kernel.prover_inputs,
-    )?
-    .stack;
+    let stack = run_with_kernel(kernel, ecrecover, initial_stack)?.stack;
     assert_eq!(stack[0], U256::from_str(expected).unwrap());
 
     Ok(())
@@ -33,13 +27,7 @@ fn test_valid_ecrecover(
 fn test_invalid_ecrecover(hash: &str, v: &str, r: &str, s: &str, kernel: &Kernel) -> Result<()> {
     let ecrecover = kernel.global_labels["ecrecover"];
     let initial_stack = u256ify(["0xdeadbeef", s, r, v, hash])?;
-    let stack = run(
-        &kernel.code,
-        ecrecover,
-        initial_stack,
-        &kernel.prover_inputs,
-    )?
-    .stack;
+    let stack = run_with_kernel(kernel, ecrecover, initial_stack)?.stack;
     assert_eq!(stack, vec![U256::MAX]);
 
     Ok(())
diff --git a/evm/src/cpu/kernel/tests/exp.rs b/evm/src/cpu/kernel/tests/exp.rs
index 0858c37c..049fd23a 100644
--- a/evm/src/cpu/kernel/tests/exp.rs
+++ b/evm/src/cpu/kernel/tests/exp.rs
@@ -5,7 +5,7 @@ use ethereum_types::U256;
 use rand::{thread_rng, Rng};
 
 use crate::cpu::kernel::aggregator::combined_kernel;
-use crate::cpu::kernel::interpreter::run;
+use crate::cpu::kernel::interpreter::{run, run_with_kernel};
 
 #[test]
 fn test_exp() -> Result<()> {
@@ -18,7 +18,7 @@ fn test_exp() -> Result<()> {
 
     // Random input
     let initial_stack = vec![U256::from_str("0xdeadbeef")?, b, a];
-    let stack_with_kernel = run(&kernel.code, exp, initial_stack, &kernel.prover_inputs)?.stack;
+    let stack_with_kernel = run_with_kernel(&kernel, exp, initial_stack)?.stack;
     let initial_stack = vec![b, a];
     let code = [0xa, 0x63, 0xde, 0xad, 0xbe, 0xef, 0x56]; // EXP, PUSH4 deadbeef, JUMP
     let stack_with_opcode = run(&code, 0, initial_stack, &kernel.prover_inputs)?.stack;
@@ -26,7 +26,7 @@ fn test_exp() -> Result<()> {
 
     // 0 base
     let initial_stack = vec![U256::from_str("0xdeadbeef")?, b, U256::zero()];
-    let stack_with_kernel = run(&kernel.code, exp, initial_stack, &kernel.prover_inputs)?.stack;
+    let stack_with_kernel = run_with_kernel(&kernel, exp, initial_stack)?.stack;
     let initial_stack = vec![b, U256::zero()];
     let code = [0xa, 0x63, 0xde, 0xad, 0xbe, 0xef, 0x56]; // EXP, PUSH4 deadbeef, JUMP
     let stack_with_opcode = run(&code, 0, initial_stack, &kernel.prover_inputs)?.stack;
@@ -34,7 +34,7 @@ fn test_exp() -> Result<()> {
 
     // 0 exponent
     let initial_stack = vec![U256::from_str("0xdeadbeef")?, U256::zero(), a];
-    let stack_with_kernel = run(&kernel.code, exp, initial_stack, &kernel.prover_inputs)?.stack;
+    let stack_with_kernel = run_with_kernel(&kernel, exp, initial_stack)?.stack;
     let initial_stack = vec![U256::zero(), a];
     let code = [0xa, 0x63, 0xde, 0xad, 0xbe, 0xef, 0x56]; // EXP, PUSH4 deadbeef, JUMP
     let stack_with_opcode = run(&code, 0, initial_stack, &kernel.prover_inputs)?.stack;