/******************************************************************************

 * Top contributors (to current version):

 *   Andrew Reynolds, Haniel Barbosa, Gereon Kremer

 *

 * This file is part of the cvc5 project.

 *

 * Copyright (c) 2009-2021 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.

 * ****************************************************************************

 *

 * The module for processing proof nodes.

 */

#include "cvc5_private.h"

#ifndef CVC5__SMT__PROOF_POST_PROCESSOR_H

#define CVC5__SMT__PROOF_POST_PROCESSOR_H

#include <map>

#include <sstream>

#include <unordered_set>

#include "proof/proof_node_updater.h"

#include "smt/proof_final_callback.h"

#include "smt/witness_form.h"

#include "theory/inference_id.h"

#include "util/statistics_stats.h"

namespace cvc5 {

class Env;

namespace rewriter {

class RewriteDb;

}

namespace smt {

/**

 * A callback class used by SmtEngine for post-processing proof nodes by

 * connecting proofs of preprocessing, and expanding macro PfRule applications.

 */

class ProofPostprocessCallback : public ProofNodeUpdaterCallback

{

 public:

  ProofPostprocessCallback(Env& env,

                           ProofGenerator* pppg,

                           rewriter::RewriteDb* rdb,

                           bool updateScopedAssumptions);

  /**

   * Initialize, called once for each new ProofNode to process. This initializes

   * static information to be used by successive calls to update.

   */

  void initializeUpdate();

  /**

   * Set eliminate rule, which adds rule to the list of rules we will eliminate

   * during update. This adds rule to d_elimRules. Supported rules for

   * elimination include MACRO_*, SUBS and REWRITE. Otherwise, this method

   * has no effect.

   */

  void setEliminateRule(PfRule rule);

  /** Should proof pn be updated? */

  bool shouldUpdate(std::shared_ptr<ProofNode> pn,

                    const std::vector<Node>& fa,

                    bool& continueUpdate) override;

  /** Update the proof rule application. */

  bool update(Node res,

              PfRule id,

              const std::vector<Node>& children,

              const std::vector<Node>& args,

              CDProof* cdp,

              bool& continueUpdate) override;

 private:

  /** Common constants */

  Node d_true;

  /** Reference to the env */

  Env& d_env;

  /** Pointer to the proof node manager */

  ProofNodeManager* d_pnm;

  /** The preprocessing proof generator */

  ProofGenerator* d_pppg;

  /** The witness form proof generator */

  WitnessFormGenerator d_wfpm;

  /** The witness form assumptions used in the proof */

  std::vector<Node> d_wfAssumptions;

  /** Kinds of proof rules we are eliminating */

  std::unordered_set<PfRule, PfRuleHashFunction> d_elimRules;

  /** Whether we post-process assumptions in scope. */

  bool d_updateScopedAssumptions;

  //---------------------------------reset at the begining of each update

  /** Mapping assumptions to their proof from preprocessing */

  std::map<Node, std::shared_ptr<ProofNode> > d_assumpToProof;

  //---------------------------------end reset at the begining of each update

  /**

   * Expand rules in the given application, add the expanded proof to cdp.

   * The set of rules we expand is configured by calls to setEliminateRule

   * above. This method calls update to perform possible post-processing in the

   * rules it introduces as a result of the expansion.

   *

   * @param id The rule of the application

   * @param children The children of the application

   * @param args The arguments of the application

   * @param cdp The proof to add to

   * @return The conclusion of the rule, or null if this rule is not eliminated.

   */

  Node expandMacros(PfRule id,

                    const std::vector<Node>& children,

                    const std::vector<Node>& args,

                    CDProof* cdp);

  /**

   * Update the proof rule application, called during expand macros when

   * we wish to apply the update method. This method has the same behavior

   * as update apart from ignoring the continueUpdate flag.

   */

  bool updateInternal(Node res,

                      PfRule id,

                      const std::vector<Node>& children,

                      const std::vector<Node>& args,

                      CDProof* cdp);

  /**

   * Add proof for witness form. This returns the equality t = toWitness(t)

   * and ensures that the proof of this equality has been added to cdp.

   * Notice the proof of this fact may have open assumptions of the form:

   *   k = toWitness(k)

   * where k is a skolem. Furthermore, note that all open assumptions of this

   * form are available via d_wfpm.getWitnessFormEqs() in the remainder of

   * the lifetime of this class.

   */

  Node addProofForWitnessForm(Node t, CDProof* cdp);

  /**

   * Apply transivity if necessary for the arguments. The nodes in

   * tchildren have been ordered such that they are legal arguments to TRANS.

   *

   * Returns the conclusion of the transitivity step, which is null if

   * tchildren is empty. Also note if tchildren contains a single element,

   * then no TRANS step is necessary to add to cdp.

   *

   * @param tchildren The children of a TRANS step

   * @param cdp The proof to add the TRANS step to

   * @return The conclusion of the TRANS step.

   */

  Node addProofForTrans(const std::vector<Node>& tchildren, CDProof* cdp);

  /**

   * Add proof for substitution step. Some substitutions are derived based

   * on viewing a formula as a Boolean assignment (see MethodId::SB_LITERAL for

   * example). This method ensures that the proof of var == subs exists

   * in cdp, where var, subs were derived from BuiltinProofRuleChecker's

   * getSubstitution method.

   *

   * @param var The variable of the substitution

   * @param subs The substituted term

   * @param assump The formula the substitution was derived from

   * @param cdp The proof to add to

   * @return var == subs, the conclusion of the substitution step.

   */

  Node addProofForSubsStep(Node var, Node subs, Node assump, CDProof* cdp);

  /** Add eq (or its symmetry) to transivity children, if not reflexive */

  bool addToTransChildren(Node eq,

                          std::vector<Node>& tchildren,

                          bool isSymm = false);

  /**

   * When given children and args lead to different sets of literals in a

   * conclusion depending on whether macro resolution or chain resolution is

   * applied, the literals that appear in the chain resolution result, but not

   * in the macro resolution result, from now on "crowding literals", are

   * literals removed implicitly by macro resolution. For example

   *

   *      l0 v l0 v l0 v l1 v l2    ~l0 v l1   ~l1

   * (1)  ----------------------------------------- MACRO_RES

   *                 l2

   *

   * but

   *

   *      l0 v l0 v l0 v l1 v l2    ~l0 v l1   ~l1

   * (2)  ---------------------------------------- CHAIN_RES

   *                l0 v l0 v l1 v l2

   *

   * where l0 and l1 are crowding literals in the second proof.

   *

   * There are two views for how MACRO_RES implicitly removes the crowding

   * literal, i.e., how MACRO_RES can be expanded into CHAIN_RES so that

   * crowding literals are removed. The first is that (1) becomes

   *

   *  l0 v l0 v l0 v l1 v l2  ~l0 v l1  ~l0 v l1  ~l0 v l1  ~l1  ~l1  ~l1  ~l1

   *  ---------------------------------------------------------------- CHAIN_RES

   *                                 l2

   *

   * via the repetition of the premise responsible for removing more than one

   * occurrence of the crowding literal. The issue however is that this

   * expansion is exponential. Note that (2) has two occurrences of l0 and one

   * of l1 as crowding literals. However, by repeating ~l0 v l1 two times to

   * remove l0, the clause ~l1, which would originally need to be repeated only

   * one time, now has to be repeated two extra times on top of that one. With

   * multiple crowding literals and their elimination depending on premises that

   * themselves add crowding literals one can easily end up with resolution

   * chains going from dozens to thousands of premises. Such examples do occur

   * in practice, even in our regressions.

   *

   * The second way of expanding MACRO_RES, which avoids this exponential

   * behavior, is so that (1) becomes

   *

   *      l0 v l0 v l0 v l1 v l2

   * (4)  ---------------------- FACTORING

   *      l0 v l1 v l2                       ~l0 v l1

   *      ------------------------------------------- CHAIN_RES

   *                   l1 v l1 v l2

   *                  ------------- FACTORING

   *                     l1 v l2                   ~l1

   *                    ------------------------------ CHAIN_RES

   *                                 l2

   *

   * This method first determines what are the crowding literals by checking

   * what literals occur in clauseLits that do not occur in targetClauseLits

   * (the latter contains the literals from the original MACRO_RES conclusion

   * while the former the literals from a direct application of CHAIN_RES). Then

   * it builds a proof such as (4) and adds the steps to cdp. The final

   * conclusion is returned.

   *

   * Note that in the example the CHAIN_RES steps introduced had only two

   * premises, and could thus be replaced by a RESOLUTION step, but since we

   * general there can be more than two premises we always use CHAIN_RES.

   *

   * @param clauseLits literals in the conclusion of a CHAIN_RESOLUTION step

   * with children and args[1:]

   * @param clauseLits literals in the conclusion of a MACRO_RESOLUTION step

   * with children and args

   * @param children a list of clauses

   * @param args a list of arguments to a MACRO_RESOLUTION step

   * @param cdp a CDProof

   * @return The resulting node of transforming MACRO_RESOLUTION into

   * CHAIN_RESOLUTION according to the above idea.

   */

  Node eliminateCrowdingLits(const std::vector<Node>& clauseLits,

                             const std::vector<Node>& targetClauseLits,

                             const std::vector<Node>& children,

                             const std::vector<Node>& args,

                             CDProof* cdp);

};

/**

 * The proof postprocessor module. This postprocesses the final proof

 * produced by an SmtEngine. Its main two tasks are to:

 * (1) Connect proofs of preprocessing,

 * (2) Expand macro PfRule applications.

 */

class ProofPostproccess

{

 public:

  /**

   * @param env The environment we are using

   * @param pppg The proof generator for pre-processing proofs

   * @param updateScopedAssumptions Whether we post-process assumptions in

   * scope. Since doing so is sound and only problematic depending on who is

   * consuming the proof, it's true by default.

   */

  ProofPostproccess(Env& env,

                    ProofGenerator* pppg,

                    rewriter::RewriteDb* rdb,

                    bool updateScopedAssumptions = true);

  ~ProofPostproccess();

  /** post-process */

  void process(std::shared_ptr<ProofNode> pf);

  /** set eliminate rule */

  void setEliminateRule(PfRule rule);

 private:

  /** The post process callback */

  ProofPostprocessCallback d_cb;

  /**

   * The updater, which is responsible for expanding macros in the final proof

   * and connecting preprocessed assumptions to input assumptions.

   */

  ProofNodeUpdater d_updater;

  /** The post process callback for finalization */

  ProofFinalCallback d_finalCb;

  /**

   * The finalizer, which is responsible for taking stats and checking for

   * (lazy) pedantic failures.

   */

  ProofNodeUpdater d_finalizer;

};

}  // namespace smt

}  // namespace cvc5

#endif