(proof-new) Adding rules and proof checker for EUF (#4559)

7 files changed, 318 insertions, 1 deletions

diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 97c352d5d..44b5dfeaf 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -754,6 +754,8 @@ libcvc4_add_sources(
   theory/uf/equality_engine.cpp
   theory/uf/equality_engine.h
   theory/uf/equality_engine_types.h
+  theory/uf/proof_checker.cpp
+  theory/uf/proof_checker.h
   theory/uf/ho_extension.cpp
   theory/uf/ho_extension.h
   theory/uf/symmetry_breaker.cpp
diff --git a/src/expr/node_manager.cpp b/src/expr/node_manager.cpp
index 7bc98f65d..427afd5af 100644
--- a/src/expr/node_manager.cpp
+++ b/src/expr/node_manager.cpp
@@ -865,4 +865,26 @@ void NodeManager::debugHook(int debugFlag){
   // For debugging purposes only, DO NOT CHECK IN ANY CODE!
 }
 
+Kind NodeManager::getKindForFunction(TNode fun)
+{
+  TypeNode tn = fun.getType();
+  if (tn.isFunction())
+  {
+    return kind::APPLY_UF;
+  }
+  else if (tn.isConstructor())
+  {
+    return kind::APPLY_CONSTRUCTOR;
+  }
+  else if (tn.isSelector())
+  {
+    return kind::APPLY_SELECTOR;
+  }
+  else if (tn.isTester())
+  {
+    return kind::APPLY_TESTER;
+  }
+  return kind::UNDEFINED_KIND;
+}
+
 }/* CVC4 namespace */
diff --git a/src/expr/node_manager.h b/src/expr/node_manager.h
index 45d3d5b7d..1fab328e9 100644
--- a/src/expr/node_manager.h
+++ b/src/expr/node_manager.h
@@ -444,6 +444,20 @@ public:
   /** Get a Kind from an operator expression */
   static inline Kind operatorToKind(TNode n);
 
+  /** Get corresponding application kind for function
+   *
+   * Different functional nodes are applied differently, according to their
+   * type. For example, uninterpreted functions (of FUNCTION_TYPE) are applied
+   * via APPLY_UF, while constructors (of CONSTRUCTOR_TYPE) via
+   * APPLY_CONSTRUCTOR. This method provides the correct application according
+   * to which functional type fun has.
+   *
+   * @param fun The functional node
+   * @return the correct application kind for fun. If fun's type is not function
+   * like (see TypeNode::isFunctionLike), then UNDEFINED_KIND is returned.
+   */
+  static Kind getKindForFunction(TNode fun);
+
   // general expression-builders
 
   /** Create a node with one child. */
diff --git a/src/expr/proof_rule.cpp b/src/expr/proof_rule.cpp
index 0e73d8c10..595e1d5f7 100644
--- a/src/expr/proof_rule.cpp
+++ b/src/expr/proof_rule.cpp
@@ -31,7 +31,15 @@ const char* toString(PfRule id)
     case PfRule::MACRO_SR_PRED_INTRO: return "MACRO_SR_PRED_INTRO";
     case PfRule::MACRO_SR_PRED_ELIM: return "MACRO_SR_PRED_ELIM";
     case PfRule::MACRO_SR_PRED_TRANSFORM: return "MACRO_SR_PRED_TRANSFORM";
-
+    //================================================= Equality rules
+    case PfRule::REFL: return "REFL";
+    case PfRule::SYMM: return "SYMM";
+    case PfRule::TRANS: return "TRANS";
+    case PfRule::CONG: return "CONG";
+    case PfRule::TRUE_INTRO: return "TRUE_INTRO";
+    case PfRule::TRUE_ELIM: return "TRUE_ELIM";
+    case PfRule::FALSE_INTRO: return "FALSE_INTRO";
+    case PfRule::FALSE_ELIM: return "FALSE_ELIM";
     //================================================= Boolean rules
     case PfRule::SPLIT: return "SPLIT";
     case PfRule::AND_ELIM: return "AND_ELIM";
diff --git a/src/expr/proof_rule.h b/src/expr/proof_rule.h
index 9dc1d017f..6acccfffd 100644
--- a/src/expr/proof_rule.h
+++ b/src/expr/proof_rule.h
@@ -71,6 +71,56 @@ enum class PfRule : uint32_t
   // has the conclusion (=> F F) and has no free assumptions. More generally, a
   // proof with no free assumptions always concludes a valid formula.
   SCOPE,
+  //================================================= Equality rules
+  // ======== Reflexive
+  // Children: none
+  // Arguments: (t)
+  // ---------------------
+  // Conclusion: (= t t)
+  REFL,
+  // ======== Symmetric
+  // Children: (P:(= t1 t2)) or (P:(not (= t1 t2)))
+  // Arguments: none
+  // -----------------------
+  // Conclusion: (= t2 t1) or (not (= t2 t1))
+  SYMM,
+  // ======== Transitivity
+  // Children: (P1:(= t1 t2), ..., Pn:(= t{n-1} tn))
+  // Arguments: none
+  // -----------------------
+  // Conclusion: (= t1 tn)
+  TRANS,
+  // ======== Congruence  (subsumed by Substitute?)
+  // Children: (P1:(= t1 s1), ..., Pn:(= tn sn))
+  // Arguments: (f)
+  // ---------------------------------------------
+  // Conclusion: (= (f t1 ... tn) (f s1 ... sn))
+  CONG,
+  // ======== True intro
+  // Children: (P:F)
+  // Arguments: none
+  // ----------------------------------------
+  // Conclusion: (= F true)
+  TRUE_INTRO,
+  // ======== True elim
+  // Children: (P:(= F true)
+  // Arguments: none
+  // ----------------------------------------
+  // Conclusion: F
+  TRUE_ELIM,
+  // ======== False intro
+  // Children: (P:(not F))
+  // Arguments: none
+  // ----------------------------------------
+  // Conclusion: (= F false)
+  FALSE_INTRO,
+  // ======== False elim
+  // Children: (P:(= F false)
+  // Arguments: none
+  // ----------------------------------------
+  // Conclusion: (not F)
+  FALSE_ELIM,
+
   //================================================= Boolean rules
   // ======== Split
   // Children: none
diff --git a/src/theory/uf/proof_checker.cpp b/src/theory/uf/proof_checker.cpp
new file mode 100644
index 000000000..28ae34b7b
--- /dev/null
+++ b/src/theory/uf/proof_checker.cpp
@@ -0,0 +1,172 @@
+/*********************                                                        */
+/*! \file proof_checker.cpp
+ ** \verbatim
+ ** Top contributors (to current version):
+ **   Haniel Barbosa, Andrew Reynolds
+ ** This file is part of the CVC4 project.
+ ** Copyright (c) 2009-2019 by the authors listed in the file AUTHORS
+ ** in the top-level source directory) and their institutional affiliations.
+ ** All rights reserved.  See the file COPYING in the top-level source
+ ** directory for licensing information.\endverbatim
+ **
+ ** \brief Implementation of equality proof checker
+ **/
+
+#include "theory/uf/proof_checker.h"
+
+using namespace CVC4::kind;
+
+namespace CVC4 {
+namespace theory {
+namespace uf {
+
+void UfProofRuleChecker::registerTo(ProofChecker* pc)
+{
+  // add checkers
+  pc->registerChecker(PfRule::REFL, this);
+  pc->registerChecker(PfRule::SYMM, this);
+  pc->registerChecker(PfRule::TRANS, this);
+  pc->registerChecker(PfRule::CONG, this);
+  pc->registerChecker(PfRule::TRUE_INTRO, this);
+  pc->registerChecker(PfRule::TRUE_ELIM, this);
+  pc->registerChecker(PfRule::FALSE_INTRO, this);
+  pc->registerChecker(PfRule::FALSE_ELIM, this);
+}
+
+Node UfProofRuleChecker::checkInternal(PfRule id,
+                                       const std::vector<Node>& children,
+                                       const std::vector<Node>& args)
+{
+  // compute what was proven
+  if (id == PfRule::REFL)
+  {
+    Assert(children.empty());
+    Assert(args.size() == 1);
+    return args[0].eqNode(args[0]);
+  }
+  else if (id == PfRule::SYMM)
+  {
+    Assert(children.size() == 1);
+    Assert(args.empty());
+    bool polarity = children[0].getKind() != NOT;
+    Node eqp = polarity ? children[0] : children[0][0];
+    if (eqp.getKind() != EQUAL)
+    {
+      // not a (dis)equality
+      return Node::null();
+    }
+    Node conc = eqp[1].eqNode(eqp[0]);
+    return polarity ? conc : conc.notNode();
+  }
+  else if (id == PfRule::TRANS)
+  {
+    Assert(children.size() > 0);
+    Assert(args.empty());
+    Node first;
+    Node curr;
+    for (size_t i = 0, nchild = children.size(); i < nchild; i++)
+    {
+      Node eqp = children[i];
+      if (eqp.getKind() != EQUAL)
+      {
+        return Node::null();
+      }
+      if (first.isNull())
+      {
+        first = eqp[0];
+      }
+      else if (eqp[0] != curr)
+      {
+        return Node::null();
+      }
+      curr = eqp[1];
+    }
+    return first.eqNode(curr);
+  }
+  else if (id == PfRule::CONG)
+  {
+    Assert(children.size() > 0);
+    Assert(args.size() == 1);
+    // We do congruence over builtin kinds using operatorToKind
+    std::vector<Node> lchildren;
+    std::vector<Node> rchildren;
+    // get the expected kind for args[0]
+    Kind k = NodeManager::getKindForFunction(args[0]);
+    if (k == kind::UNDEFINED_KIND)
+    {
+      k = NodeManager::operatorToKind(args[0]);
+    }
+    if (k == kind::UNDEFINED_KIND)
+    {
+      return Node::null();
+    }
+    Trace("uf-pfcheck") << "congruence for " << args[0] << " uses kind " << k
+                        << ", metakind=" << kind::metaKindOf(k) << std::endl;
+    if (kind::metaKindOf(k) == kind::metakind::PARAMETERIZED)
+    {
+      // parameterized kinds require the operator
+      lchildren.push_back(args[0]);
+      rchildren.push_back(args[0]);
+    }
+    for (size_t i = 0, nchild = children.size(); i < nchild; i++)
+    {
+      Node eqp = children[i];
+      if (eqp.getKind() != EQUAL)
+      {
+        return Node::null();
+      }
+      lchildren.push_back(eqp[0]);
+      rchildren.push_back(eqp[1]);
+    }
+    NodeManager* nm = NodeManager::currentNM();
+    Node l = nm->mkNode(k, lchildren);
+    Node r = nm->mkNode(k, rchildren);
+    return l.eqNode(r);
+  }
+  else if (id == PfRule::TRUE_INTRO)
+  {
+    Assert(children.size() == 1);
+    Assert(args.empty());
+    Node trueNode = NodeManager::currentNM()->mkConst(true);
+    return children[0].eqNode(trueNode);
+  }
+  else if (id == PfRule::TRUE_ELIM)
+  {
+    Assert(children.size() == 1);
+    Assert(args.empty());
+    if (children[0].getKind() != EQUAL || !children[0][1].isConst()
+        || !children[0][1].getConst<bool>())
+    {
+      return Node::null();
+    }
+    return children[0][0];
+  }
+  else if (id == PfRule::FALSE_INTRO)
+  {
+    Assert(children.size() == 1);
+    Assert(args.empty());
+    if (children[0].getKind() != kind::NOT)
+    {
+      return Node::null();
+    }
+    Node falseNode = NodeManager::currentNM()->mkConst(false);
+    return children[0][0].eqNode(falseNode);
+  }
+  else if (id == PfRule::FALSE_ELIM)
+  {
+    Assert(children.size() == 1);
+    Assert(args.empty());
+    if (children[0].getKind() != EQUAL || !children[0][1].isConst()
+        || children[0][1].getConst<bool>())
+    {
+      return Node::null();
+    }
+    return children[0][0].notNode();
+  }
+  // no rule
+  return Node::null();
+}
+
+}  // namespace uf
+}  // namespace theory
+}  // namespace CVC4
diff --git a/src/theory/uf/proof_checker.h b/src/theory/uf/proof_checker.h
new file mode 100644
index 000000000..022574eab
--- /dev/null
+++ b/src/theory/uf/proof_checker.h
@@ -0,0 +1,49 @@
+/*********************                                                        */
+/*! \file proof_checker.h
+ ** \verbatim
+ ** Top contributors (to current version):
+ **   Haniel Barbosa, Andrew Reynolds
+ ** This file is part of the CVC4 project.
+ ** Copyright (c) 2009-2019 by the authors listed in the file AUTHORS
+ ** in the top-level source directory) and their institutional affiliations.
+ ** All rights reserved.  See the file COPYING in the top-level source
+ ** directory for licensing information.\endverbatim
+ **
+ ** \brief Equality proof checker utility
+ **/
+
+#include "cvc4_private.h"
+
+#ifndef CVC4__THEORY__UF__PROOF_CHECKER_H
+#define CVC4__THEORY__UF__PROOF_CHECKER_H
+
+#include "expr/node.h"
+#include "expr/proof_checker.h"
+#include "expr/proof_node.h"
+
+namespace CVC4 {
+namespace theory {
+namespace uf {
+
+/** A checker for builtin proofs */
+class UfProofRuleChecker : public ProofRuleChecker
+{
+ public:
+  UfProofRuleChecker() {}
+  ~UfProofRuleChecker() {}
+
+  /** Register all rules owned by this rule checker into pc. */
+  void registerTo(ProofChecker* pc) override;
+
+ protected:
+  /** Return the conclusion of the given proof step, or null if it is invalid */
+  Node checkInternal(PfRule id,
+                     const std::vector<Node>& children,
+                     const std::vector<Node>& args) override;
+};
+
+}  // namespace uf
+}  // namespace theory
+}  // namespace CVC4
+
+#endif /* CVC4__THEORY__UF__PROOF_CHECKER_H */