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       1                 :            : /******************************************************************************
       2                 :            :  * This file is part of the cvc5 project.
       3                 :            :  *
       4                 :            :  * Copyright (c) 2009-2026 by the authors listed in the file AUTHORS
       5                 :            :  * in the top-level source directory and their institutional affiliations.
       6                 :            :  * All rights reserved.  See the file COPYING in the top-level source
       7                 :            :  * directory for licensing information.
       8                 :            :  * ****************************************************************************
       9                 :            :  *
      10                 :            :  * Alpha equivalence checking.
      11                 :            :  */
      12                 :            : 
      13                 :            : #include "cvc5_private.h"
      14                 :            : 
      15                 :            : #ifndef CVC5__ALPHA_EQUIVALENCE_H
      16                 :            : #define CVC5__ALPHA_EQUIVALENCE_H
      17                 :            : 
      18                 :            : #include "expr/term_canonize.h"
      19                 :            : #include "proof/eager_proof_generator.h"
      20                 :            : #include "smt/env_obj.h"
      21                 :            : #include "theory/quantifiers/quant_util.h"
      22                 :            : 
      23                 :            : namespace cvc5::internal {
      24                 :            : namespace theory {
      25                 :            : namespace quantifiers {
      26                 :            : 
      27                 :            : /**
      28                 :            :  * This trie stores a trie for each multi-set of types. For each term t
      29                 :            :  * registered to this node, we store t in the appropriate
      30                 :            :  * AlphaEquivalenceTypeNode trie. For example, if t contains 2 free variables of
      31                 :            :  * type T1 and 3 free variables of type T2, then it is stored at
      32                 :            :  * d_children[T1][2].d_children[T2][3].
      33                 :            :  */
      34                 :            : class AlphaEquivalenceTypeNode
      35                 :            : {
      36                 :            :   using NodeMap = context::CDHashMap<Node, Node>;
      37                 :            : 
      38                 :            :  public:
      39                 :            :   AlphaEquivalenceTypeNode(context::Context* c);
      40                 :            :   /** children of this node */
      41                 :            :   std::map<std::pair<TypeNode, size_t>,
      42                 :            :            std::unique_ptr<AlphaEquivalenceTypeNode>>
      43                 :            :       d_children;
      44                 :            :   /**
      45                 :            :    * map from canonized quantifier bodies to a quantified formula whose
      46                 :            :    * canonized body is that term.
      47                 :            :    */
      48                 :            :   NodeMap d_quant;
      49                 :            :   /** register node
      50                 :            :    *
      51                 :            :    * This registers term q to this trie. The term t is the canonical form of
      52                 :            :    * q, typs/typCount represent a multi-set of types of free variables in t.
      53                 :            :    */
      54                 :            :   Node registerNode(context::Context* c,
      55                 :            :                     Node q,
      56                 :            :                     Node t,
      57                 :            :                     std::vector<TypeNode>& typs,
      58                 :            :                     std::map<TypeNode, size_t>& typCount);
      59                 :            : };
      60                 :            : 
      61                 :            : /**
      62                 :            :  * Stores a database of quantified formulas, which computes alpha-equivalence.
      63                 :            :  */
      64                 :            : class AlphaEquivalenceDb
      65                 :            : {
      66                 :            :  public:
      67                 :            :   AlphaEquivalenceDb(context::Context* c,
      68                 :            :                      expr::TermCanonize* tc,
      69                 :            :                      bool sortCommChildren);
      70                 :            :   /** adds quantified formula q to this database
      71                 :            :    *
      72                 :            :    * This function returns a quantified formula q' that is alpha-equivalent to
      73                 :            :    * q. If q' != q, then q' was previously added to this database via a call
      74                 :            :    * to addTerm.
      75                 :            :    */
      76                 :            :   Node addTerm(Node q);
      77                 :            :   /**
      78                 :            :    * Add term with substitution, which additionally finds a set of terms such
      79                 :            :    * that q' * subs is alpha-equivalent (possibly modulo rewriting) to q, where
      80                 :            :    * q' is the return quantified formula.
      81                 :            :    */
      82                 :            :   Node addTermWithSubstitution(Node q,
      83                 :            :                                std::vector<Node>& vars,
      84                 :            :                                std::vector<Node>& subs);
      85                 :            : 
      86                 :            :  private:
      87                 :            :   /**
      88                 :            :    * Add term to the trie, where t is the canonized form of the body of
      89                 :            :    * quantified formula q. Returns the quantified formula, if any, that already
      90                 :            :    * had been added to this class, or q otherwise.
      91                 :            :    */
      92                 :            :   Node addTermToTypeTrie(Node t, Node q);
      93                 :            :   /** The context we depend on */
      94                 :            :   context::Context* d_context;
      95                 :            :   /** a trie per # of variables per type */
      96                 :            :   AlphaEquivalenceTypeNode d_ae_typ_trie;
      97                 :            :   /** pointer to the term canonize utility */
      98                 :            :   expr::TermCanonize* d_tc;
      99                 :            :   /** whether to sort children of commutative operators during canonization. */
     100                 :            :   bool d_sortCommutativeOpChildren;
     101                 :            :   /**
     102                 :            :    * Maps quantified formulas to variables map, used for tracking substitutions
     103                 :            :    * in addTermWithSubstitution. The range in d_bvmap[q] contains the mapping
     104                 :            :    * from canonical free variables to variables in q.
     105                 :            :    */
     106                 :            :   std::map<Node, std::map<Node, TNode>> d_bvmap;
     107                 :            : };
     108                 :            : 
     109                 :            : /**
     110                 :            :  * A quantifiers module that computes reductions based on alpha-equivalence,
     111                 :            :  * using the above utilities.
     112                 :            :  */
     113                 :            : class AlphaEquivalence : protected EnvObj
     114                 :            : {
     115                 :            :  public:
     116                 :            :   AlphaEquivalence(Env& env);
     117                 :      87978 :   ~AlphaEquivalence() {}
     118                 :            :   /** reduce quantifier
     119                 :            :    *
     120                 :            :    * If non-null, its return value is a trust node containing the lemma
     121                 :            :    * justifying why q is reducible.  This lemma is of the form ( q = q' ) where
     122                 :            :    * q' is a quantified formula that was previously registered to this class via
     123                 :            :    * a call to reduceQuantifier, and q and q' are alpha-equivalent.
     124                 :            :    */
     125                 :            :   TrustNode reduceQuantifier(Node q);
     126                 :            : 
     127                 :            :  private:
     128                 :            :   /**
     129                 :            :    * Add the alpha equivalence step f = f { vars -> subs } to cdp, where we
     130                 :            :    * ensure that f does not contain vars. Return the conclusion of this step.
     131                 :            :    */
     132                 :            :   Node addAlphaEquivStep(CDProof& cdp,
     133                 :            :                          const Node& f,
     134                 :            :                          const std::vector<Node>& vars,
     135                 :            :                          const std::vector<Node>& subs);
     136                 :            :   /** a term canonizer */
     137                 :            :   expr::TermCanonize d_termCanon;
     138                 :            :   /** the database of quantified formulas registered to this class */
     139                 :            :   AlphaEquivalenceDb d_aedb;
     140                 :            :   /** An eager proof generator storing alpha equivalence proofs.*/
     141                 :            :   std::unique_ptr<EagerProofGenerator> d_pfAlpha;
     142                 :            :   /** Are proofs enabled for this object? */
     143                 :            :   bool isProofEnabled() const;
     144                 :            : };
     145                 :            : 
     146                 :            : }  // namespace quantifiers
     147                 :            : }  // namespace theory
     148                 :            : }  // namespace cvc5::internal
     149                 :            : 
     150                 :            : #endif