scaffolding

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

src/nlsat/levelwise.cpp

@@ -1,290 +1,79 @@
-#include "levelwise.h"
+#include "nlsat/levelwise.h"
+#include "nlsat/nlsat_types.h"
 #include <vector>
-#include <string>
-#include <sstream>
-
 namespace nlsat {
 
-  // Context for property propagation (e.g., which case of rule 4.2 applies)
+// Local enums reused from previous scaffolding
-  enum class property_mapping_case : unsigned {
+enum class property_mapping_case : unsigned { case1 = 0, case2 = 1, case3 = 2 };
-    case1 = 0,
-    case2 = 1,
-    case3 = 2,
-  };
 
-  /**
+enum class polynom_property : unsigned {
-   * Properties for indexed roots, in the order specified by the levelwise paper.
+  ir_ord,
-   * The order is important for the algorithm and must match the paper exactly.
+  an_del,
-   */
+  non_null,
-  enum class polynom_property : unsigned {
+  sgn_inv_reducible,
-    ir_ord,              // ir_ord(≼, s) for all ≼ for roots of level i and s ∈ Ri−1
+  sgn_inv_irreducible,
-    an_del,              // an_del(p) for all p of level i
+  connected,
-    non_null,            // non_null(p) for all p of level i
+  an_sub,
-    ord_inv_reducible,   // ord_inv(p) for all reducible p of level i
+  sample,
-    ord_inv_irreducible, // ord_inv(p) for all irreducible p of level i
+  repr,
-    sgn_inv_reducible,   // sgn_inv(p) for all reducible p of level i
+  holds,
-    sgn_inv_irreducible, // sgn_inv(p) for all irreducible p of level i
+  _count
-    connected,           // connected(i)
+};
-    an_sub,              // an_sub(i)
+struct property_goal {
-    sample,              // sample(s) for all s ∈ Ri of level i
-    repr,                // repr(I, s) for all I of level i and s ∈ ...
-    holds,               // marker for "goal holds" (terminal)
-    _count               // always last: number of properties
-  };
-
-  // Utility: property to string (for debugging, logging, etc.)
-  inline const char* to_string(polynom_property prop) {
-    switch (prop) {
-    case polynom_property::ir_ord:              return "ir_ord";
-    case polynom_property::an_del:              return "an_del";
-    case polynom_property::non_null:            return "non_null";
-    case polynom_property::ord_inv_reducible:   return "ord_inv_reducible";
-    case polynom_property::ord_inv_irreducible: return "ord_inv_irreducible";
-    case polynom_property::sgn_inv_reducible:   return "sgn_inv_reducible";
-    case polynom_property::sgn_inv_irreducible: return "sgn_inv_irreducible";
-    case polynom_property::connected:           return "connected";
-    case polynom_property::an_sub:              return "an_sub";
-    case polynom_property::sample:              return "sample";
-    case polynom_property::repr:                return "repr";
-    case polynom_property::holds:               return "holds";
-    default:                                    return "?";
-    }
-  }
-
-  // A single property instance ("fact") subject.
-  // Note: Not all fields are used by every property; unused fields are left at defaults.
-  struct property_inst {
   polynom_property prop;
-    // Optional subject parameters
+  poly*            p = nullptr;
-    poly*            p      = nullptr;  // for properties about a polynomial p
+  unsigned         s_idx = 0; // index into current sample roots on level, if applicable
-    var              y      = -1;       // variable (e.g., indexed root variable)
+  unsigned         level = 0;
-    unsigned         i      = 0;        // level/index (paper's i)
+};
-    unsigned         s_idx  = 0;        // index for "s ∈ R_i" (sample/root index), if applicable
+struct levelwise::impl {
-    unsigned         I_idx  = 0;        // index for interval I (for repr), if applicable
+  polynomial_ref_vector const& m_ps;
-    unsigned         ord_id = 0;        // identifier for an indexed root ordering ≼, if applicable
+  var                          m_max_x;
+  assignment const&            m_sample;
+  std::vector<property_goal>   m_goals;
 
-    // Convenience builders
+  impl(polynomial_ref_vector const& ps, var max_x, assignment const& s)
-    static property_inst of(poly* p, polynom_property prop, unsigned level) {
+    : m_ps(ps), m_max_x(max_x), m_sample(s) {
-      property_inst r{prop}; r.p = p; r.i = level; return r;
+    seed_initial_goals();
   }
-    static property_inst at_level(polynom_property prop, unsigned level) {
+  void seed_initial_goals() {
-      property_inst r{prop}; r.i = level; return r;
+    // Algorithm 1: initial goals are sgn_inv(p, s) for p in ps at current level of max_x
-    }
+    for (unsigned i = 0; i < m_ps.size(); ++i) {
-    static property_inst sample_at(unsigned s_idx, unsigned level) {
+      poly* p = m_ps.get(i);
-      property_inst r{polynom_property::sample}; r.s_idx = s_idx; r.i = level; return r;
+      m_goals.push_back(property_goal{ polynom_property::sgn_inv_irreducible /*or reducible later*/, p, /*s_idx*/0, /*level*/0});
-    }
-    static property_inst repr_of(unsigned I_idx, unsigned s_idx, unsigned level) {
-      property_inst r{polynom_property::repr}; r.I_idx = I_idx; r.s_idx = s_idx; r.i = level; return r;
-    }
-
-    // Display
-    std::string str() const {
-      std::ostringstream out;
-      out << to_string(prop) << "(";
-      bool first = true;
-      auto add = [&](std::string const& k, uint64_t v) {
-        if (!first) out << ", ";
-        first = false;
-        out << k << "=" << v;
-      };
-      if (p) add("p", reinterpret_cast<uint64_t>(p));
-      if (y != -1) add("y", static_cast<uint64_t>(y));
-      add("i", i);
-      if (s_idx) add("s", s_idx);
-      if (I_idx) add("I", I_idx);
-      if (ord_id) add("ord", ord_id);
-      out << ")";
-      return out.str();
-    }
-
-    // Equality (coarse; pointer identity for p is intentional)
-    bool operator==(property_inst const& o) const {
-      return prop == o.prop &&
-             p == o.p &&
-             y == o.y &&
-             i == o.i &&
-             s_idx == o.s_idx &&
-             I_idx == o.I_idx &&
-             ord_id == o.ord_id;
-    }
-  };
-
-  // Proof rule identifiers (align roughly with paper sections; can be refined later).
-  enum class proof_rule : unsigned {
-    // Skeleton rules; refine/extend as we implement specific inferences
-    axiom,          // introduce a known/assumed property
-    derive,         // generic derivation step (placeholder)
-    r_ir_ord,       // rules for ir_ord propagation
-    r_an_del,
-    r_non_null,
-    r_ord_inv_red,
-    r_ord_inv_irred,
-    r_sgn_inv_red,
-    r_sgn_inv_irred,
-    r_connected,
-    r_an_sub,
-    r_sample,
-    r_repr,
-    r_close_holds   // closes to 'holds'
-  };
-
-  inline const char* to_string(proof_rule r) {
-    switch (r) {
-    case proof_rule::axiom:         return "axiom";
-    case proof_rule::derive:        return "derive";
-    case proof_rule::r_ir_ord:      return "r_ir_ord";
-    case proof_rule::r_an_del:      return "r_an_del";
-    case proof_rule::r_non_null:    return "r_non_null";
-    case proof_rule::r_ord_inv_red: return "r_ord_inv_red";
-    case proof_rule::r_ord_inv_irred:return "r_ord_inv_irred";
-    case proof_rule::r_sgn_inv_red: return "r_sgn_inv_red";
-    case proof_rule::r_sgn_inv_irred:return "r_sgn_inv_irred";
-    case proof_rule::r_connected:   return "r_connected";
-    case proof_rule::r_an_sub:      return "r_an_sub";
-    case proof_rule::r_sample:      return "r_sample";
-    case proof_rule::r_repr:        return "r_repr";
-    case proof_rule::r_close_holds: return "r_close_holds";
-    default:                        return "?";
     }
   }
+};
 
-  // A single proof step: premises -> conclusion, with metadata.
+levelwise::levelwise(polynomial_ref_vector const& ps, var max_x, assignment const& s)
-  struct proof_step {
+  : m_impl(new impl(ps, max_x, s)) {}
-    proof_rule                    rule;
-    property_mapping_case         ctx = property_mapping_case::case1; // for multi-case rules (e.g., 4.2)
-    std::vector<unsigned>         premises;   // indices into facts_
-    unsigned                      conclusion; // index into facts_
 
-    std::string str(std::vector<property_inst> const& facts) const {
+levelwise::~levelwise() { delete m_impl; }
-      std::ostringstream out;
+levelwise::levelwise(levelwise&& o) noexcept : m_impl(o.m_impl) { o.m_impl = nullptr; }
-      out << to_string(rule) << "[case=" << static_cast<unsigned>(ctx) << "]: ";
+
-      out << "{";
+levelwise& levelwise::operator=(levelwise&& o) noexcept { if (this != &o) { delete m_impl; m_impl = o.m_impl; o.m_impl = nullptr; } return *this; }
-      for (unsigned k = 0; k < premises.size(); ++k) {
+
-        if (k) out << ", ";
+// Free-function driver: create a local implementation and seed initial goals.
-        out << facts[premises[k]].str();
+void levelwise_project(polynomial_ref_vector const& ps, var max_x, assignment const& s) {
+  struct impl {
+    polynomial_ref_vector const& m_ps;
+    var                          m_max_x;
+    assignment const&            m_sample;
+    std::vector<property_goal>   m_goals;
+    impl(polynomial_ref_vector const& ps_, var mx, assignment const& sa)
+      : m_ps(ps_), m_max_x(mx), m_sample(sa) {
+      seed_initial_goals();
     }
-      out << "} => " << facts[conclusion].str();
+    void seed_initial_goals() {
-      return out.str();
+      for (unsigned i = 0; i < m_ps.size(); ++i) {
+        poly* p = m_ps.get(i);
+        m_goals.push_back(property_goal{ polynom_property::sgn_inv_irreducible, p, /*s_idx*/0, /*level*/0 });
       }
-  };
-
-  // A lightweight proof object to manage facts and steps.
-  class levelwise_proof {
-    std::vector<property_inst> m_facts;
-    std::vector<proof_step>    m_steps;
-
-    // Linear lookup to avoid hashing complexity here.
-    int find_fact(property_inst const& f) const {
-      for (unsigned i = 0; i < m_facts.size(); ++i)
-        if (m_facts[i] == f) return static_cast<int>(i);
-      return -1;
     }
-
+    void run() {
-  public:
+      // TODO: apply Levelwise rules to discharge goals and build a proof.
-    unsigned intern_fact(property_inst const& f) {
-      int idx = find_fact(f);
-      if (idx >= 0) return static_cast<unsigned>(idx);
-      m_facts.push_back(f);
-      return static_cast<unsigned>(m_facts.size() - 1);
-    }
-
-    unsigned add_axiom(property_inst const& concl) {
-      unsigned c = intern_fact(concl);
-      m_steps.push_back(proof_step{proof_rule::axiom, property_mapping_case::case1, {}, c});
-      return c;
-    }
-
-    unsigned add_step(proof_rule rule,
-                      property_mapping_case ctx,
-                      std::vector<unsigned> const& premises,
-                      property_inst const& conclusion) {
-      unsigned c = intern_fact(conclusion);
-      m_steps.push_back(proof_step{rule, ctx, premises, c});
-      return c;
-    }
-
-    std::string dump() const {
-      std::ostringstream out;
-      for (auto const& st : m_steps)
-        out << st.str(m_facts) << "\n";
-      return out.str();
-    }
-
-    std::vector<property_inst> const& facts() const { return m_facts; }
-    std::vector<proof_step>    const& steps() const { return m_steps; }
-  };
-
-  // Property propagation mapping: for each property, the set of properties it implies (see levelwise paper, e.g., rule 4.2)
-  // Overload: property_dependencies with context (for rules like 4.2 with multiple cases).
-  // Note: This is a scaffold. Fill per paper’s precise rules (TODO).
-  inline std::vector<polynom_property>
-  get_property_dependencies(polynom_property prop, property_mapping_case /*p_case*/, polynomial_ref& /*p*/, unsigned /*i*/) {
-    std::vector<polynom_property> ret;
-    switch (prop) {
-    case polynom_property::ir_ord:
-      // TODO: fill using Property 4.3 / Rule 4.2 cases; currently no direct property implications recorded here.
-      break;
-
-    case polynom_property::an_del:
-      // Example: an_del(p) might imply non_null(p) or be used in combination with others; leave empty until specified.
-      break;
-
-    case polynom_property::non_null:
-      // Usually terminal for p; no generic implications without context.
-      break;
-
-    case polynom_property::ord_inv_reducible:
-      // Often accompanies sign invariance for reducible polynomials; no generic implication recorded here.
-      break;
-
-    case polynom_property::ord_inv_irreducible:
-      // Likewise for irreducible.
-      break;
-
-    case polynom_property::sgn_inv_reducible:
-      // In many presentations, sign invariance implies order invariance on reducible components.
-      // If the paper states so, uncomment:
-      // ret.push_back(polynom_property::ord_inv_reducible);
-      break;
-
-    case polynom_property::sgn_inv_irreducible:
-      // If sign invariance implies order invariance for irreducible p, uncomment:
-      // ret.push_back(polynom_property::ord_inv_irreducible);
-      break;
-
-    case polynom_property::connected:
-      // connected(i) might enable sample or representation derivations; leave empty here.
-      break;
-
-    case polynom_property::an_sub:
-      // an_sub(i) may enable additional sampling; leave empty here.
-      break;
-
-    case polynom_property::sample:
-      // sample(s) is often a leaf for evaluating properties at s.
-      break;
-
-    case polynom_property::repr:
-      // repr(I, s) together with others may lead to holds; no generic implication alone.
-      break;
-
-    case polynom_property::holds:
-      // Terminal goal, no further implications.
-      break;
-
-    default:
-      break;
-    }
-    return ret;
-  }
-
-  // Example driver/stub that will eventually orchestrate Levelwise projection with proof logging.
-  void lewelwise_project(polynomial_ref_vector & /*ps*/, var /*max_x*/) {
-    //std::cout << "call\n";
-    //exit(0);
-    // Scaffold example (no-ops for now):
-    // levelwise_proof pr;
-    // for (auto* p : ps) { pr.add_axiom(property_inst::of(p, polynom_property::an_del, /*level*/0)); }
-    // std::cout << pr.dump();
     }
+  } I(ps, max_x, s);
+  I.run();
 }
+
+} // namespace nlsat

src/nlsat/levelwise.h

@@ -1,6 +1,26 @@
 #pragma once
 #include "nlsat_types.h"
+
 namespace nlsat {
-    void lewelwise_project(polynomial_ref_vector & ps, var max_x);
+
+class assignment; // forward declared in nlsat_types.h
+
+// Levelwise driver (PIMPL). Orchestrates property-based projection/proof.
+class levelwise {
+    struct impl;
+    impl* m_impl;
+public:
+    // Construct with polynomials ps, maximal variable max_x, and current sample s (assignment of vars < max_x)
+    levelwise(polynomial_ref_vector const& ps, var max_x, assignment const& s);
+    ~levelwise();
+
+    levelwise(levelwise const&) = delete;
+    levelwise& operator=(levelwise const&) = delete;
+    levelwise(levelwise&&) noexcept;
+    levelwise& operator=(levelwise&&) noexcept;
+};
+
+// Convenience free-function driver prototype
+void levelwise_project(polynomial_ref_vector const& ps, var max_x, assignment const& s);
 
 } // namespace nlsat

src/nlsat/nlsat_explain.cpp

@@ -1246,7 +1246,7 @@ namespace nlsat {
             
             polynomial_ref_vector samples(m_pm);
 
-            lewelwise_project(ps, max_x);
+            levelwise_project(ps, max_x, this->m_assignment);
             if (x < max_x)
                 cac_add_cell_lits(ps, x, samples);