feat(avm-main): pil -> permutations (#3650)

Replacing the toy_avm with a pil version that defines a permutation in
pil.

```
    pol commit q_tuple_set;

    // Set 1
    pol commit set_1_column_1;
    pol commit set_1_column_2;
    // Set 2
    pol commit set_2_column_1;
    pol commit set_2_column_2;

    // This is a column based tuple permutation
    
    #[two_column_perm] // the name of the inverse polynomial
    q_tuple_set { set_1_column_1, set_1_column_2 } is { set_2_column_1, set_2_column_2 };
```

Syntax is as shown.

barretenberg/.gitignore

@@ -5,4 +5,5 @@ node_modules
 ts/dest
 .tsbuildinfo
 .idea
-cmake-build-debug
+cmake-build-debug
+*_opt.pil

barretenberg/cpp/pil/avm/toy_avm.pil

@@ -0,0 +1,20 @@
+namespace toy(256);
+    pol commit q_tuple_set;
+
+    // Set 1
+    pol commit set_1_column_1;
+    pol commit set_1_column_2;
+    // Set 2
+    pol commit set_2_column_1;
+    pol commit set_2_column_2;
+
+    // This is a column based tuple lookup
+    #[two_column_perm] // the name of the inverse
+    q_tuple_set { set_1_column_1, set_1_column_2 } is { set_2_column_1, set_2_column_2 };
+
+    // Relation not used -> we currently require a single relation for codegen
+    pol commit x;
+    x' - x = 0;
+
+    // Also needs a fixed relation 
+    pol fixed first = [1] + [0]*;

barretenberg/cpp/src/barretenberg/flavor/generated/AvmMini_flavor.hpp

@@ -7,6 +7,8 @@
 #include "barretenberg/polynomials/barycentric.hpp"
 #include "barretenberg/polynomials/univariate.hpp"
 
+#include "barretenberg/relations/generic_permutation/generic_permutation_relation.hpp"
+
 #include "barretenberg/flavor/flavor.hpp"
 #include "barretenberg/flavor/flavor_macros.hpp"
 #include "barretenberg/polynomials/evaluation_domain.hpp"
@@ -40,7 +42,7 @@ class AvmMiniFlavor {
     // the unshifted and one for the shifted
     static constexpr size_t NUM_ALL_ENTITIES = 30;
 
-    using Relations = std::tuple<AvmMini_vm::avm_mini<FF>, AvmMini_vm::mem_trace<FF>>;
+    using Relations = std::tuple<AvmMini_vm::mem_trace<FF>, AvmMini_vm::avm_mini<FF>>;
 
     static constexpr size_t MAX_PARTIAL_RELATION_LENGTH = compute_max_partial_relation_length<Relations>();
 
@@ -144,8 +146,8 @@ class AvmMiniFlavor {
                               avmMini_mem_idx_c,
                               avmMini_last,
                               memTrace_m_rw_shift,
-                              memTrace_m_val_shift,
-                              memTrace_m_addr_shift)
+                              memTrace_m_addr_shift,
+                              memTrace_m_val_shift)
 
         RefVector<DataType> get_wires()
         {
@@ -177,8 +179,8 @@ class AvmMiniFlavor {
                      avmMini_mem_idx_c,
                      avmMini_last,
                      memTrace_m_rw_shift,
-                     memTrace_m_val_shift,
-                     memTrace_m_addr_shift };
+                     memTrace_m_addr_shift,
+                     memTrace_m_val_shift };
         };
         RefVector<DataType> get_unshifted()
         {
@@ -210,10 +212,10 @@ class AvmMiniFlavor {
                      avmMini_mem_idx_c,
                      avmMini_last };
         };
-        RefVector<DataType> get_to_be_shifted() { return { memTrace_m_rw, memTrace_m_val, memTrace_m_addr }; };
+        RefVector<DataType> get_to_be_shifted() { return { memTrace_m_rw, memTrace_m_addr, memTrace_m_val }; };
         RefVector<DataType> get_shifted()
         {
-            return { memTrace_m_rw_shift, memTrace_m_val_shift, memTrace_m_addr_shift };
+            return { memTrace_m_rw_shift, memTrace_m_addr_shift, memTrace_m_val_shift };
         };
     };
 
@@ -467,4 +469,6 @@ class AvmMiniFlavor {
 };
 
 } // namespace flavor
+
+namespace sumcheck {}
 } // namespace proof_system::honk

barretenberg/cpp/src/barretenberg/flavor/generated/Toy_flavor.hpp

@@ -0,0 +1,304 @@
+
+
+#pragma once
+#include "../relation_definitions_fwd.hpp"
+#include "barretenberg/commitment_schemes/kzg/kzg.hpp"
+#include "barretenberg/ecc/curves/bn254/g1.hpp"
+#include "barretenberg/polynomials/barycentric.hpp"
+#include "barretenberg/polynomials/univariate.hpp"
+
+#include "barretenberg/relations/generic_permutation/generic_permutation_relation.hpp"
+
+#include "barretenberg/flavor/flavor.hpp"
+#include "barretenberg/flavor/flavor_macros.hpp"
+#include "barretenberg/polynomials/evaluation_domain.hpp"
+#include "barretenberg/polynomials/polynomial.hpp"
+#include "barretenberg/relations/generated/Toy/toy_avm.hpp"
+#include "barretenberg/relations/generated/Toy/two_column_perm.hpp"
+#include "barretenberg/transcript/transcript.hpp"
+
+namespace proof_system::honk {
+namespace flavor {
+
+class ToyFlavor {
+  public:
+    using Curve = curve::BN254;
+    using G1 = Curve::Group;
+    using PCS = pcs::kzg::KZG<Curve>;
+
+    using FF = G1::subgroup_field;
+    using Polynomial = barretenberg::Polynomial<FF>;
+    using PolynomialHandle = std::span<FF>;
+    using GroupElement = G1::element;
+    using Commitment = G1::affine_element;
+    using CommitmentHandle = G1::affine_element;
+    using CommitmentKey = pcs::CommitmentKey<Curve>;
+    using VerifierCommitmentKey = pcs::VerifierCommitmentKey<Curve>;
+
+    static constexpr size_t NUM_PRECOMPUTED_ENTITIES = 1;
+    static constexpr size_t NUM_WITNESS_ENTITIES = 7;
+    static constexpr size_t NUM_WIRES = NUM_WITNESS_ENTITIES + NUM_PRECOMPUTED_ENTITIES;
+    // We have two copies of the witness entities, so we subtract the number of fixed ones (they have no shift), one for
+    // the unshifted and one for the shifted
+    static constexpr size_t NUM_ALL_ENTITIES = 9;
+
+    using Relations = std::tuple<Toy_vm::toy_avm<FF>, sumcheck::two_column_perm_relation<FF>>;
+
+    static constexpr size_t MAX_PARTIAL_RELATION_LENGTH = compute_max_partial_relation_length<Relations>();
+
+    // BATCHED_RELATION_PARTIAL_LENGTH = algebraic degree of sumcheck relation *after* multiplying by the `pow_zeta`
+    // random polynomial e.g. For \sum(x) [A(x) * B(x) + C(x)] * PowZeta(X), relation length = 2 and random relation
+    // length = 3
+    static constexpr size_t BATCHED_RELATION_PARTIAL_LENGTH = MAX_PARTIAL_RELATION_LENGTH + 1;
+    static constexpr size_t NUM_RELATIONS = std::tuple_size<Relations>::value;
+
+    template <size_t NUM_INSTANCES>
+    using ProtogalaxyTupleOfTuplesOfUnivariates =
+        decltype(create_protogalaxy_tuple_of_tuples_of_univariates<Relations, NUM_INSTANCES>());
+    using SumcheckTupleOfTuplesOfUnivariates = decltype(create_sumcheck_tuple_of_tuples_of_univariates<Relations>());
+    using TupleOfArraysOfValues = decltype(create_tuple_of_arrays_of_values<Relations>());
+
+    static constexpr bool has_zero_row = true;
+
+  private:
+    template <typename DataType_> class PrecomputedEntities : public PrecomputedEntitiesBase {
+      public:
+        using DataType = DataType_;
+
+        DEFINE_FLAVOR_MEMBERS(DataType, toy_first)
+
+        RefVector<DataType> get_selectors() { return { toy_first }; };
+        RefVector<DataType> get_sigma_polynomials() { return {}; };
+        RefVector<DataType> get_id_polynomials() { return {}; };
+        RefVector<DataType> get_table_polynomials() { return {}; };
+    };
+
+    template <typename DataType> class WitnessEntities {
+      public:
+        DEFINE_FLAVOR_MEMBERS(DataType,
+                              toy_q_tuple_set,
+                              toy_set_1_column_1,
+                              toy_set_1_column_2,
+                              toy_set_2_column_1,
+                              toy_set_2_column_2,
+                              toy_x,
+                              two_column_perm)
+
+        RefVector<DataType> get_wires()
+        {
+            return { toy_q_tuple_set, toy_set_1_column_1, toy_set_1_column_2, toy_set_2_column_1, toy_set_2_column_2,
+                     toy_x,           two_column_perm };
+        };
+        RefVector<DataType> get_sorted_polynomials() { return {}; };
+    };
+
+    template <typename DataType> class AllEntities {
+      public:
+        DEFINE_FLAVOR_MEMBERS(DataType,
+                              toy_first,
+                              toy_q_tuple_set,
+                              toy_set_1_column_1,
+                              toy_set_1_column_2,
+                              toy_set_2_column_1,
+                              toy_set_2_column_2,
+                              toy_x,
+                              two_column_perm,
+                              toy_x_shift)
+
+        RefVector<DataType> get_wires()
+        {
+            return { toy_first,          toy_q_tuple_set, toy_set_1_column_1, toy_set_1_column_2, toy_set_2_column_1,
+                     toy_set_2_column_2, toy_x,           two_column_perm,    toy_x_shift };
+        };
+        RefVector<DataType> get_unshifted()
+        {
+            return { toy_first,          toy_q_tuple_set, toy_set_1_column_1, toy_set_1_column_2, toy_set_2_column_1,
+                     toy_set_2_column_2, toy_x,           two_column_perm };
+        };
+        RefVector<DataType> get_to_be_shifted() { return { toy_x }; };
+        RefVector<DataType> get_shifted() { return { toy_x_shift }; };
+    };
+
+  public:
+    class ProvingKey : public ProvingKey_<PrecomputedEntities<Polynomial>, WitnessEntities<Polynomial>> {
+      public:
+        // Expose constructors on the base class
+        using Base = ProvingKey_<PrecomputedEntities<Polynomial>, WitnessEntities<Polynomial>>;
+        using Base::Base;
+
+        // The plookup wires that store plookup read data.
+        std::array<PolynomialHandle, 0> get_table_column_wires() { return {}; };
+    };
+
+    using VerificationKey = VerificationKey_<PrecomputedEntities<Commitment>>;
+
+    using ProverPolynomials = AllEntities<PolynomialHandle>;
+
+    using FoldedPolynomials = AllEntities<std::vector<FF>>;
+
+    class AllValues : public AllEntities<FF> {
+      public:
+        using Base = AllEntities<FF>;
+        using Base::Base;
+    };
+
+    class AllPolynomials : public AllEntities<Polynomial> {
+      public:
+        [[nodiscard]] size_t get_polynomial_size() const { return this->toy_q_tuple_set.size(); }
+        [[nodiscard]] AllValues get_row(const size_t row_idx) const
+        {
+            AllValues result;
+            for (auto [result_field, polynomial] : zip_view(result.get_all(), get_all())) {
+                result_field = polynomial[row_idx];
+            }
+            return result;
+        }
+    };
+
+    using RowPolynomials = AllEntities<FF>;
+
+    class PartiallyEvaluatedMultivariates : public AllEntities<Polynomial> {
+      public:
+        PartiallyEvaluatedMultivariates() = default;
+        PartiallyEvaluatedMultivariates(const size_t circuit_size)
+        {
+            // Storage is only needed after the first partial evaluation, hence polynomials of size (n / 2)
+            for (auto& poly : get_all()) {
+                poly = Polynomial(circuit_size / 2);
+            }
+        }
+    };
+
+    /**
+     * @brief A container for univariates used during Protogalaxy folding and sumcheck.
+     * @details During folding and sumcheck, the prover evaluates the relations on these univariates.
+     */
+    template <size_t LENGTH> using ProverUnivariates = AllEntities<barretenberg::Univariate<FF, LENGTH>>;
+
+    /**
+     * @brief A container for univariates produced during the hot loop in sumcheck.
+     */
+    using ExtendedEdges = ProverUnivariates<MAX_PARTIAL_RELATION_LENGTH>;
+
+    class CommitmentLabels : public AllEntities<std::string> {
+      private:
+        using Base = AllEntities<std::string>;
+
+      public:
+        CommitmentLabels()
+            : AllEntities<std::string>()
+        {
+            Base::toy_first = "TOY_FIRST";
+            Base::toy_q_tuple_set = "TOY_Q_TUPLE_SET";
+            Base::toy_set_1_column_1 = "TOY_SET_1_COLUMN_1";
+            Base::toy_set_1_column_2 = "TOY_SET_1_COLUMN_2";
+            Base::toy_set_2_column_1 = "TOY_SET_2_COLUMN_1";
+            Base::toy_set_2_column_2 = "TOY_SET_2_COLUMN_2";
+            Base::toy_x = "TOY_X";
+            Base::two_column_perm = "TWO_COLUMN_PERM";
+        };
+    };
+
+    class VerifierCommitments : public AllEntities<Commitment> {
+      private:
+        using Base = AllEntities<Commitment>;
+
+      public:
+        VerifierCommitments(const std::shared_ptr<VerificationKey>& verification_key)
+        {
+            toy_first = verification_key->toy_first;
+        }
+    };
+
+    class Transcript : public BaseTranscript {
+      public:
+        uint32_t circuit_size;
+
+        Commitment toy_q_tuple_set;
+        Commitment toy_set_1_column_1;
+        Commitment toy_set_1_column_2;
+        Commitment toy_set_2_column_1;
+        Commitment toy_set_2_column_2;
+        Commitment toy_x;
+        Commitment two_column_perm;
+
+        std::vector<barretenberg::Univariate<FF, BATCHED_RELATION_PARTIAL_LENGTH>> sumcheck_univariates;
+        std::array<FF, NUM_ALL_ENTITIES> sumcheck_evaluations;
+        std::vector<Commitment> zm_cq_comms;
+        Commitment zm_cq_comm;
+        Commitment zm_pi_comm;
+
+        Transcript() = default;
+
+        Transcript(const std::vector<uint8_t>& proof)
+            : BaseTranscript(proof)
+        {}
+
+        void deserialize_full_transcript()
+        {
+            size_t num_bytes_read = 0;
+            circuit_size = deserialize_from_buffer<uint32_t>(proof_data, num_bytes_read);
+            size_t log_n = numeric::get_msb(circuit_size);
+
+            toy_q_tuple_set = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+            toy_set_1_column_1 = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+            toy_set_1_column_2 = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+            toy_set_2_column_1 = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+            toy_set_2_column_2 = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+            toy_x = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+            two_column_perm = deserialize_from_buffer<Commitment>(Transcript::proof_data, num_bytes_read);
+
+            for (size_t i = 0; i < log_n; ++i) {
+                sumcheck_univariates.emplace_back(
+                    deserialize_from_buffer<barretenberg::Univariate<FF, BATCHED_RELATION_PARTIAL_LENGTH>>(
+                        Transcript::proof_data, num_bytes_read));
+            }
+            sumcheck_evaluations =
+                deserialize_from_buffer<std::array<FF, NUM_ALL_ENTITIES>>(Transcript::proof_data, num_bytes_read);
+            for (size_t i = 0; i < log_n; ++i) {
+                zm_cq_comms.push_back(deserialize_from_buffer<Commitment>(proof_data, num_bytes_read));
+            }
+            zm_cq_comm = deserialize_from_buffer<Commitment>(proof_data, num_bytes_read);
+            zm_pi_comm = deserialize_from_buffer<Commitment>(proof_data, num_bytes_read);
+        }
+
+        void serialize_full_transcript()
+        {
+            size_t old_proof_length = proof_data.size();
+            Transcript::proof_data.clear();
+            size_t log_n = numeric::get_msb(circuit_size);
+
+            serialize_to_buffer(circuit_size, Transcript::proof_data);
+
+            serialize_to_buffer<Commitment>(toy_q_tuple_set, Transcript::proof_data);
+            serialize_to_buffer<Commitment>(toy_set_1_column_1, Transcript::proof_data);
+            serialize_to_buffer<Commitment>(toy_set_1_column_2, Transcript::proof_data);
+            serialize_to_buffer<Commitment>(toy_set_2_column_1, Transcript::proof_data);
+            serialize_to_buffer<Commitment>(toy_set_2_column_2, Transcript::proof_data);
+            serialize_to_buffer<Commitment>(toy_x, Transcript::proof_data);
+            serialize_to_buffer<Commitment>(two_column_perm, Transcript::proof_data);
+
+            for (size_t i = 0; i < log_n; ++i) {
+                serialize_to_buffer(sumcheck_univariates[i], Transcript::proof_data);
+            }
+            serialize_to_buffer(sumcheck_evaluations, Transcript::proof_data);
+            for (size_t i = 0; i < log_n; ++i) {
+                serialize_to_buffer(zm_cq_comms[i], proof_data);
+            }
+            serialize_to_buffer(zm_cq_comm, proof_data);
+            serialize_to_buffer(zm_pi_comm, proof_data);
+
+            // sanity check to make sure we generate the same length of proof as before.
+            ASSERT(proof_data.size() == old_proof_length);
+        }
+    };
+};
+
+} // namespace flavor
+
+namespace sumcheck {
+
+DECLARE_SUMCHECK_RELATION_CLASS(two_column_perm, flavor::ToyFlavor);
+
+}
+} // namespace proof_system::honk