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diff --git a/apt-pkg/solver3.h b/apt-pkg/solver3.h
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+/*
+ * solver3.h - The APT 3.0 solver
+ *
+ * Copyright (c) 2023 Julian Andres Klode
+ * Copyright (c) 2023 Canonical Ltd
+ *
+ * SPDX-License-Identifier: GPL-2.0+
+ */
+
+#include <vector>
+
+#include <apt-pkg/configuration.h>
+#include <apt-pkg/depcache.h>
+#include <apt-pkg/pkgcache.h>
+#include <apt-pkg/policy.h>
+
+namespace APT
+{
+
+/*
+ * \brief APT 3.0 solver
+ *
+ * This is a simple solver focused on understandability and sensible results, it
+ * will not generally find all solutions to the problem but will try to find the best
+ * ones.
+ *
+ * It is a brute force solver with heuristics, conflicts learning, and 2**32 levels
+ * of backtracking.
+ */
+class Solver
+{
+   enum class Decision : uint16_t;
+   enum class Hint : uint16_t;
+   struct Reason;
+   template <typename T>
+   struct State;
+   struct Work;
+
+   // \brief Type to record depth at. This may very well be a 16-bit
+   // unsigned integer, then change Solver::State::Decision to be a
+   // uint16_t class enum as well to get a more compact space.
+   using depth_type = unsigned int;
+
+   // Documentation
+   template <typename T>
+   using heap = std::vector<T>;
+
+   static_assert(sizeof(depth_type) >= sizeof(map_id_t));
+
+   // Cache is needed to construct Iterators from Version objects we see
+   pkgCache &cache;
+   // Policy is needed for determining candidate version.
+   pkgDepCache::Policy &policy;
+   // States for packages
+   std::vector<State<pkgCache::Package>> pkgStates{};
+   // States for versions
+   std::vector<State<pkgCache::Version>> verStates{};
+
+   // \brief Helper function for safe access to package state.
+   inline State<pkgCache::Package> &operator[](pkgCache::Package *P)
+   {
+      return pkgStates[P->ID];
+   }
+
+   // \brief Helper function for safe access to version state.
+   inline State<pkgCache::Version> &operator[](pkgCache::Version *V)
+   {
+      return verStates[V->ID];
+   }
+
+   // \brief Heap of the remaining work.
+   //
+   // We are using an std::vector with std::make_heap(), std::push_heap(),
+   // and std::pop_heap() rather than a priority_queue because we need to
+   // be able to iterate over the queued work and see if a choice would
+   // invalidate any work.
+   heap<Work> work{};
+   // \brief Whether RescoreWork() actually needs to rescore the work.
+   bool needsRescore{false};
+
+   // \brief Current decision level.
+   //
+   // Each time a decision needs to be made we can push the item under
+   // consideration to our backlog of choices made and then later we can
+   // restore it easily.
+   std::vector<Work> choices{};
+   // \brief Backlog of solved work.
+   //
+   // Solved work may become invalidated when backtracking, so store it
+   // here to revisit it later.
+   std::vector<Work> solved{};
+
+   /// Various configuration options
+   // \brief Debug level
+   int debug{_config->FindI("Debug::APT::Solver")};
+   // \brief If set, we try to keep automatically installed packages installed.
+   bool KeepAuto{not _config->FindB("APT::Get::AutomaticRemove")};
+   // \brief If set, removals are allowed.
+   bool AllowRemove{_config->FindB("APT::Solver::Remove", true)};
+   // \brief If set, installs are allowed.
+   bool AllowInstall{_config->FindB("APT::Solver::Install", true)};
+   // \brief If set, we use strict pinning.
+   bool StrictPinning{_config->FindB("APT::Solver::Strict-Pinning", true)};
+
+   // \brief Enqueue dependencies shared by all versions of the package.
+   bool EnqueueCommonDependencies(pkgCache::PkgIterator Pkg);
+   // \brief Reject reverse dependencies. Must call std::make_heap() after.
+   bool RejectReverseDependencies(pkgCache::VerIterator Ver);
+   // \brief Enqueue a single or group
+   bool EnqueueOrGroup(pkgCache::DepIterator start, pkgCache::DepIterator end, Reason reason);
+   // \brief Check if a version is allowed by policy.
+   bool IsAllowedVersion(pkgCache::Version *V);
+
+   // \brief Return the current depth (choices.size() with casting)
+   depth_type depth()
+   {
+      return static_cast<depth_type>(choices.size());
+   }
+
+   public:
+   // \brief Create a new decision level.
+   bool Pop();
+   // \brief Revert to the previous decision level.
+   void Push(Work work);
+   // \brief Add work to our work queue.
+   void AddWork(Work &&work);
+   // \brief Rescore the work after a reject or a pop
+   void RescoreWorkIfNeeded();
+
+   // \brief Basic solver initializer. This cannot fail.
+   Solver(pkgCache &Cache, pkgDepCache::Policy &Policy);
+
+   // \brief Mark the package for install. This is annoying as it incurs a decision
+   bool Install(pkgCache::PkgIterator Pkg, Reason reason);
+   // \brief Install a version.
+   bool Install(pkgCache::VerIterator Ver, Reason reason);
+   // \brief Do not install this package
+   bool Reject(pkgCache::PkgIterator Pkg, Reason reason);
+   // \brief Do not install this version.
+   bool Reject(pkgCache::VerIterator Ver, Reason reason);
+
+   // \brief Apply the selections from the dep cache to the solver
+   bool FromDepCache(pkgDepCache &depcache);
+   // \brief Apply the solver result to the depCache
+   bool ToDepCache(pkgDepCache &depcache);
+
+   // \brief Solve the dependencies
+   bool Solve();
+
+   // Print dependency chain
+   std::string WhyStr(Reason reason);
+};
+
+}; // namespace APT
+
+/**
+ * \brief Tagged union holding either a package, version, or nothing; representing the reason for installing something.
+ *
+ * We want to keep track of the reason why things are being installed such that
+ * we can have sensible debugging abilities.
+ *
+ * If the reason is empty, this means the package is automatically installed.
+ */
+struct APT::Solver::Reason
+{
+   uint32_t IsVersion : 1;
+   uint32_t MapPtr : 31;
+
+   Reason() : IsVersion(0), MapPtr(0) {}
+   explicit Reason(pkgCache::PkgIterator const &Pkg) : IsVersion(0), MapPtr(Pkg.MapPointer()) {}
+   explicit Reason(pkgCache::VerIterator const &Ver) : IsVersion(1), MapPtr(Ver.MapPointer()) {}
+
+   // \brief Return the package, if any, otherwise 0.
+   map_pointer<pkgCache::Package> Pkg() const
+   {
+      return IsVersion ? 0 : map_pointer<pkgCache::Package>{(uint32_t)MapPtr};
+   }
+   // \brief Return the version, if any, otherwise 0.
+   map_pointer<pkgCache::Version> Ver() const
+   {
+      return IsVersion ? map_pointer<pkgCache::Version>{(uint32_t)MapPtr} : 0;
+   }
+   // \brief Check if there is no reason.
+   bool empty() const
+   {
+      return IsVersion == 0 && MapPtr == 0;
+   }
+};
+
+/**
+ * \brief A single work item
+ *
+ * A work item is a positive dependency that still needs to be resolved. Work
+ * is ordered, by depth, length of solutions, and optionality.
+ *
+ * The work can always be recalculated from the state by iterating over dependencies
+ * of all packages in there, finding solutions to them, and then adding all dependencies
+ * not yet resolved to the work queue.
+ */
+struct APT::Solver::Work
+{
+   // \brief Reason for the work
+   Reason reason;
+   // \brief The depth at which the item has been added
+   depth_type depth;
+
+   // \brief Possible solutions to this task, ordered in order of preference.
+   std::vector<pkgCache::Version *> solutions{};
+
+   // This is a union because we only need to store the choice we made when adding
+   // to the choice vector, and we don't need the size of valid choices in there.
+   union
+   {
+      // The choice we took
+      pkgCache::Version *choice;
+      // Number of valid choices
+      size_t size;
+   };
+
+   // \brief Whether this is an optional work item, they will be processed last
+   bool optional;
+   // \brief Whether this is an ugprade
+   bool upgrade;
+   // \brief This item should be removed from the queue.
+   bool dirty;
+
+   bool operator<(APT::Solver::Work const &b) const;
+   // \brief Dump the work item to std::cerr
+   void Dump(pkgCache &cache);
+
+   inline Work(Reason reason, depth_type depth, bool optional = false, bool upgrade = false) : reason(reason), depth(depth), size(0), optional(optional), upgrade(upgrade), dirty(false) {}
+};
+
+// \brief This essentially describes the install state in RFC2119 terms.
+enum class APT::Solver::Decision : uint16_t
+{
+   // \brief We have not made a choice about the package yet
+   NONE,
+   // \brief We need to install this package
+   MUST,
+   // \brief We cannot install this package (need conflicts with it)
+   MUSTNOT,
+};
+
+// \brief Hints for the solver about the item.
+enum class APT::Solver::Hint : uint16_t
+{
+   // \brief We have not made a choice about the package yet
+   NONE,
+   // \brief This package was listed as a Recommends of a must package,
+   SHOULD,
+   // \brief This package was listed as a Suggests of a must-not package
+   MAY,
+};
+
+/**
+ * \brief The solver state
+ *
+ * For each version, the solver records a decision at a certain level. It
+ * maintains an array mapping from version ID to state.
+ */
+template <typename T>
+struct APT::Solver::State
+{
+   // \brief The reason for causing this state (invalid for NONE).
+   //
+   // Rejects may have been caused by a later state. Consider we select
+   // between x1 and x2 in depth = N. If we now find dependencies of x1
+   // leading to a conflict with a package in K < N, we will record all
+   // of them as REJECT in depth = K.
+   //
+   // You can follow the reason chain upwards as long as the depth
+   // doesn't increase to unwind.
+   //
+   // Reasons < 0 are package ID, reasons > 0 are version IDs.
+   Reason reason{};
+
+   // \brief The depth at which the decision has been taken
+   depth_type depth{0};
+
+   // \brief This essentially describes the install state in RFC2119 terms.
+   Decision decision{Decision::NONE};
+
+   // \brief Any hint.
+   Hint hint{Hint::NONE};
+};