(proof-new) Rename ProofSkolemCache to SkolemManager (#4556)

This PR changes the design of ProofSkolemCache so that it has facilities for tracking proofs. This is required so that the term formula removal pass can be made proof-producing.

This makes it so that ProofSkolemCache is renamed to SkolemManager, which lives in NodeManager. Creating (most) skolems must be accompanied by a corresponding ProofGenerator that can provide the proof for the existential corresponding to their witness form.

Further updates will include refactoring the mkSkolemExists method of SkolemManager so that its contract wrt proofs is simpler.

Once all calls to mkSkolem go through the standard interface, then NodeManager::mkSkolem will be moved to SkolemManager::mkSkolemInternal.

1 files changed, 163 insertions, 0 deletions

diff --git a/src/expr/skolem_manager.h b/src/expr/skolem_manager.h
new file mode 100644
index 000000000..eaf74bcce
--- /dev/null
+++ b/src/expr/skolem_manager.h
@@ -0,0 +1,163 @@
+/*********************                                                        */
+/*! \file skolem_manager.h
+ ** \verbatim
+ ** Top contributors (to current version):
+ **   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 Skolem manager utility
+ **/
+
+#include "cvc4_private.h"
+
+#ifndef CVC4__EXPR__SKOLEM_MANAGER_H
+#define CVC4__EXPR__SKOLEM_MANAGER_H
+
+#include <string>
+
+#include "expr/node.h"
+
+namespace CVC4 {
+
+class ProofGenerator;
+
+/**
+ * A manager for skolems that can be used in proofs. This is designed to be
+ * a trusted interface to NodeManager::mkSkolem, where one
+ * must provide a definition for the skolem they create in terms of a
+ * predicate that the introduced variable is intended to witness.
+ *
+ * It is implemented by mapping terms to an attribute corresponding to their
+ * "witness form" as described below. Hence, this class does not impact the
+ * reference counting of skolem variables which may be deleted if they are not
+ * used.
+ */
+class SkolemManager
+{
+ public:
+  SkolemManager() {}
+  ~SkolemManager() {}
+  /**
+   * This makes a skolem of same type as bound variable v, (say its type is T),
+   * whose definition is (witness ((v T)) pred). This definition is maintained
+   * by this class.
+   *
+   * Notice that (exists ((v T)) pred) should be a valid formula. This fact
+   * captures the reason for why the returned Skolem was introduced.
+   *
+   * Take as an example extensionality in arrays:
+   *
+   * (declare-fun a () (Array Int Int))
+   * (declare-fun b () (Array Int Int))
+   * (assert (not (= a b)))
+   *
+   * To witness the index where the arrays a and b are disequal, it is intended
+   * we call this method on:
+   *   Node k = mkSkolem( x, F )
+   * where F is:
+   *   (=> (not (= a b)) (not (= (select a x) (select b x))))
+   * and x is a fresh bound variable of integer type. Internally, this will map
+   * k to the term:
+   *   (witness ((x Int)) (=> (not (= a b))
+   *                          (not (= (select a x) (select b x)))))
+   * A lemma generated by the array solver for extensionality may safely use
+   * the skolem k in the standard way:
+   *   (=> (not (= a b)) (not (= (select a k) (select b k))))
+   * Furthermore, notice that the following lemma does not involve fresh
+   * skolem variables and is valid according to the theory of arrays extended
+   * with support for witness:
+   *   (let ((w (witness ((x Int)) (=> (not (= a b))
+   *                                   (not (= (select a x) (select b x)))))))
+   *     (=> (not (= a b)) (not (= (select a w) (select b w)))))
+   * This version of the lemma, which requires no explicit tracking of free
+   * Skolem variables, can be obtained by a call to getWitnessForm(...)
+   * below. We call this the "witness form" of the lemma above.
+   *
+   * @param v The bound variable of the same type of the Skolem to create.
+   * @param pred The desired property of the Skolem to create, in terms of bound
+   * variable v.
+   * @param prefix The prefix of the name of the Skolem
+   * @param comment Debug information about the Skolem
+   * @param flags The flags for the Skolem (see NodeManager::mkSkolem)
+   * @param pg The proof generator for this skolem. If non-null, this proof
+   * generator must respond to a call to getProofFor(exists x. pred) during
+   * the lifetime of the current node manager.
+   * @return The skolem whose witness form is registered by this class.
+   */
+  Node mkSkolem(Node v,
+                Node pred,
+                const std::string& prefix,
+                const std::string& comment = "",
+                int flags = NodeManager::SKOLEM_DEFAULT,
+                ProofGenerator* pg = nullptr);
+  /**
+   * Same as above, but where pred is an existential quantified formula
+   * whose bound variable list contains v. For example, calling this method on:
+   *   x, (exists ((x Int) (y Int)) (P x y))
+   * will return:
+   *   (witness ((x Int)) (exists ((y Int)) (P x y)))
+   * If the variable v is not in the bound variable list of q, then null is
+   * returned and an assertion failure is thrown.
+   */
+  Node mkSkolemExists(Node v,
+                      Node q,
+                      const std::string& prefix,
+                      const std::string& comment = "",
+                      int flags = NodeManager::SKOLEM_DEFAULT,
+                      ProofGenerator* pg = nullptr);
+  /**
+   * Same as above, but for special case of (witness ((x T)) (= x t))
+   * where T is the type of t. This skolem is unique for each t, which we
+   * implement via an attribute on t. This attribute is used to ensure to
+   * associate a unique skolem for each t.
+   *
+   * Notice that a purification skolem is trivial to justify, and hence it
+   * does not require a proof generator.
+   */
+  Node mkPurifySkolem(Node t,
+                      const std::string& prefix,
+                      const std::string& comment = "",
+                      int flags = NodeManager::SKOLEM_DEFAULT);
+  /**
+   * Get proof generator for witness term t. This returns the proof generator
+   * that was provided in a call to mkSkolem above.
+   */
+  ProofGenerator* getProofGenerator(Node t);
+  /** convert to witness form
+   *
+   * @param n The term or formula to convert to witness form described above
+   * @return n in witness form.
+   */
+  static Node getWitnessForm(Node n);
+  /** convert to Skolem form
+   *
+   * @param n The term or formula to convert to Skolem form described above
+   * @return n in Skolem form.
+   */
+  static Node getSkolemForm(Node n);
+  /** convert to witness form vector */
+  static void convertToWitnessFormVec(std::vector<Node>& vec);
+  /** convert to Skolem form vector */
+  static void convertToSkolemFormVec(std::vector<Node>& vec);
+
+ private:
+  /**
+   * Mapping from witness terms to proof generators.
+   */
+  std::map<Node, ProofGenerator*> d_gens;
+  /** Convert to witness or skolem form */
+  static Node convertInternal(Node n, bool toWitness);
+  /** Get or make skolem attribute for witness term w */
+  static Node getOrMakeSkolem(Node w,
+                              const std::string& prefix,
+                              const std::string& comment,
+                              int flags);
+};
+
+}  // namespace CVC4
+
+#endif /* CVC4__EXPR__PROOF_SKOLEM_CACHE_H */