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

 * Top contributors (to current version):

 *   Andrew Reynolds, Mathias Preiner, Fabian Wolff

 *

 * 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.

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

 *

 * sygus_sampler

 */

#include "cvc5_private.h"

#ifndef CVC5__THEORY__QUANTIFIERS__SYGUS_SAMPLER_H

#define CVC5__THEORY__QUANTIFIERS__SYGUS_SAMPLER_H

#include <map>

#include "theory/evaluator.h"

#include "theory/quantifiers/lazy_trie.h"

#include "theory/quantifiers/sygus/term_database_sygus.h"

#include "theory/quantifiers/term_enumeration.h"

namespace cvc5 {

namespace theory {

namespace quantifiers {

/** SygusSampler

 *

 * This class can be used to test whether two expressions are equivalent

 * by random sampling. We use this class for the following options:

 *

 * sygus-rr-synth: synthesize candidate rewrite rules by finding two terms

 * t1 and t2 do not rewrite to the same term, but are identical when considering

 * a set of sample points, and

 *

 * sygus-rr-verify: detect unsound rewrite rules by finding two terms t1 and

 * t2 that rewrite to the same term, but not identical when considering a set

 * of sample points.

 *

 * To use this class:

 * (1) Call initialize( tds, f, nsamples) where f is sygus datatype term.

 * (2) For terms n1....nm enumerated that correspond to builtin analog of sygus

 * term f, we call registerTerm( n1 )....registerTerm( nm ). It may be the case

 * that registerTerm( ni ) returns nj for some j < i. In this case, we have that

 * ni and nj are equivalent under the sample points in this class.

 *

 * For example, say the grammar for f is:

 *   A = 0 | 1 | x | y | A+A | ite( B, A, A )

 *   B = A <= A

 * If we call initialize( tds, f, 5 ), this class will generate 5 random sample

 * points for (x,y), say (0,0), (1,1), (0,1), (1,0), (2,2). The return values

 * of successive calls to registerTerm are listed below.

 *   registerTerm( 0 ) -> 0

 *   registerTerm( x ) -> x

 *   registerTerm( x+y ) -> x+y

 *   registerTerm( y+x ) -> x+y

 *   registerTerm( x+ite(x <= 1+1, 0, y ) ) -> x

 * Notice that the number of sample points can be configured for the above

 * options using sygus-samples=N.

 */

class SygusSampler : public LazyTrieEvaluator

{

 public:

  SygusSampler();

  /** initialize

   *

   * tn : the return type of terms we will be testing with this class,

   * vars : the variables we are testing substitutions for,

   * nsamples : number of sample points this class will test,

   * unique_type_ids : if this is set to true, then we consider each variable

   * in vars to have a unique "type id". A type id is a finer-grained notion of

   * type that is used to determine when a rewrite rule is redundant.

   */

  virtual void initialize(TypeNode tn,

                          const std::vector<Node>& vars,

                          unsigned nsamples,

                          bool unique_type_ids = false);

  /** initialize sygus

   *

   * qe : pointer to quantifiers engine,

   * f : a term of some SyGuS datatype type whose values we will be

   * testing under the free variables in the grammar of f,

   * nsamples : number of sample points this class will test,

   * useSygusType : whether we will register terms with this sampler that have

   * the same type as f. If this flag is false, then we will be registering

   * terms of the analog of the type of f, that is, the builtin type that

   * f's type encodes in the deep embedding.

   */

  virtual void initializeSygus(TermDbSygus* tds,

                               Node f,

                               unsigned nsamples,

                               bool useSygusType);

  /** register term n with this sampler database

   *

   * forceKeep is whether we wish to force that n is chosen as a representative

   * value in the trie.

   */

  virtual Node registerTerm(Node n, bool forceKeep = false);

  /** get number of sample points */

  /** get variables, adds d_vars to vars */

  void getVariables(std::vector<Node>& vars) const;

  /** get sample point

   *

   * Appends sample point #index to the vector pt, d_vars to vars.

   */

  void getSamplePoint(unsigned index,

                      std::vector<Node>& pt);

  /** Add pt to the set of sample points considered by this sampler */

  void addSamplePoint(std::vector<Node>& pt);

  /** evaluate n on sample point index */

  Node evaluate(Node n, unsigned index) override;

  /**

   * Compute the variables from the domain of d_var_index that occur in n,

   * store these in the vector fvs.

   */

  void computeFreeVariables(Node n, std::vector<Node>& fvs);

  /**

   * Returns the index of a sample point such that the evaluation of a and b

   * diverge, or -1 if no such sample point exists.

   */

  int getDiffSamplePointIndex(Node a, Node b);

  //--------------------------queries about terms

  /** is contiguous

   *

   * This returns whether n's free variables (terms occurring in the range of

   * d_type_vars) are a prefix of the list of variables in d_type_vars for each

   * type id. For instance, if d_type_vars[id] = { x, y } for some id, then

   * 0, x, x+y, y+x are contiguous but y is not. This is useful for excluding

   * terms from consideration that are alpha-equivalent to others.

   */

  bool isContiguous(Node n);

  /** is ordered

   *

   * This returns whether n's free variables are in order with respect to

   * variables in d_type_vars for each type. For instance, if

   * d_type_vars[id] = { x, y } for some id, then 0, x, x+y are ordered but

   * y and y+x are not.

   */

  bool isOrdered(Node n);

  /** is linear

   *

   * This returns whether n contains at most one occurrence of each free

   * variable. For example, x, x+y are linear, but x+x, (x-y)+y, (x+0)+(x+0) are

   * non-linear.

   */

  bool isLinear(Node n);

  /** check variables

   *

   * This returns false if !isOrdered(n) and checkOrder is true or !isLinear(n)

   * if checkLinear is true, or false otherwise.

   */

  bool checkVariables(Node n, bool checkOrder, bool checkLinear);

  /** contains free variables

   *

   * Returns true if the free variables of b are a subset of those in a, where

   * we require a strict subset if strict is true. Free variables are those that

   * occur in the range d_type_vars.

   */

  bool containsFreeVariables(Node a, Node b, bool strict = false);

  //--------------------------end queries about terms

  /** check equivalent

   *

   * Check whether bv and bvr are equivalent on all sample points, print

   * an error if not. Used with --sygus-rr-verify.

   */

  void checkEquivalent(Node bv, Node bvr);

 protected:

  /** sygus term database of d_qe */

  TermDbSygus* d_tds;

  /** term enumerator object (used for random sampling) */

  TermEnumeration d_tenum;

  /** samples */

  std::vector<std::vector<Node> > d_samples;

  /** evaluator class */

  Evaluator d_eval;

  /** data structure to check duplication of sample points */

  {

   public:

    /** add pt to this trie, returns true if pt is not a duplicate. */

    bool add(std::vector<Node>& pt);

   private:

    /** the children of this node */

    std::map<Node, PtTrie> d_children;

  };

  /** a trie for samples */

  PtTrie d_samples_trie;

  /** the sygus type for this sampler (if applicable). */

  TypeNode d_ftn;

  /** whether we are registering terms of sygus types with this sampler */

  bool d_use_sygus_type;

  /**

   * For each (sygus) type, a map from builtin terms to the sygus term they

   * correspond to.

   */

  std::map<TypeNode, std::map<Node, Node> > d_builtin_to_sygus;

  /** all variables we are sampling values for */

  std::vector<Node> d_vars;

  /** type variables

   *

   * We group variables according to "type ids". Two variables have the same

   * type id if they have indistinguishable status according to this sampler.

   * This is a finer-grained grouping than types. For example, two variables

   * of the same type may have different type ids if they occur as constructors

   * of a different set of sygus types in the grammar we are considering.

   * For instance, we assign x and y different type ids in this grammar:

   *   A -> B + C

   *   B -> x | 0 | 1

   *   C -> y

   * Type ids are computed for each variable in d_vars during initialize(...).

   *

   * For each type id, a list of variables in the grammar we are considering,

   * for that type. These typically correspond to the arguments of the

   * function-to-synthesize whose grammar we are considering.

   */

  std::map<unsigned, std::vector<Node> > d_type_vars;

  /**

   * A map all variables in the grammar we are considering to their index in

   * d_type_vars.

   */

  std::map<Node, unsigned> d_var_index;

  /**  Map from variables to the id (the domain of d_type_vars). */

  std::map<Node, unsigned> d_type_ids;

  /** constants

   *

   * For each type, a list of constants in the grammar we are considering, for

   * that type.

   */

  std::map<TypeNode, std::vector<Node> > d_type_consts;

  /** a lazy trie for each type

   *

   * This stores the evaluation of all terms registered to this class.

   *

   * Notice if we are registering sygus terms with this class, then terms

   * are grouped into this trie according to their sygus type, and not their

   * builtin type. For example, for grammar:

   *   A -> x | B+1

   *   B -> x | 0 | 1 | B+B

   * If we register C^B_+( C^B_x(), C^B_0() ) and C^A_x() with this class,

   * then x+0 is registered to d_trie[B] and x is registered to d_trie[A],

   * and no rewrite rule is reported. The reason for this is that otherwise

   * we would end up reporting many useless rewrites since the same builtin

   * term can be generated by multiple sygus types (e.g. C^B_x() and C^A_x()).

   */

  std::map<TypeNode, LazyTrie> d_trie;

  /** is this sampler valid?

   *

   * A sampler can be invalid if sample points cannot be generated for a type

   * of an argument to function f.

   */

  bool d_is_valid;

  /** initialize samples

   *

   * Adds nsamples sample points to d_samples.

   */

  void initializeSamples(unsigned nsamples);

  /** get random value for a type

   *

   * Returns a random value for the given type based on the random number

   * generator. Currently, supported types:

   *

   * Bool, Bitvector : returns a random value in the range of that type.

   * Int, String : returns a random string of values in (base 10) of random

   * length, currently by a repeated coin flip.

   * Real : returns the division of two random integers, where the denominator

   * is omitted if it is zero.

   */

  Node getRandomValue(TypeNode tn);

  /** get sygus random value

   *

   * Returns a random value based on the sygus type tn. The return value is

   * a constant in the analog type of tn. This function chooses either to

   * return a random value, or otherwise will construct a constant based on

   * a random constructor of tn whose builtin operator is not a variable.

   *

   * rchance: the chance that the call to this function will be forbidden

   * from making recursive calls and instead must return a value based on

   * a nullary constructor of tn or based on getRandomValue above.

   * rinc: the percentage to increment rchance on recursive calls.

   *

   * For example, consider the grammar:

   *   A -> x | y | 0 | 1 | +( A, A ) | ite( B, A, A )

   *   B -> A = A

   * If we call this function on A and rchance is 0.0, there are five evenly

   * chosen possibilities, either we return a random value via getRandomValue

   * above, or we choose one of the four non-variable constructors of A.

   * Say we choose ite, then we recursively call this function for

   * B, A, and A, which return constants c1, c2, and c3. Then, this function

   * returns the rewritten form of ite( c1, c2, c3 ).

   * If on the other hand, rchance was 0.5 and rand() < 0.5. Then, we force

   * this call to terminate by either selecting a random value via

   * getRandomValue, 0 or 1.

   */

  Node getSygusRandomValue(TypeNode tn,

                           double rchance,

                           double rinc,

                           unsigned depth = 0);

  /** map from sygus types to non-variable constructors */

  std::map<TypeNode, std::vector<unsigned> > d_rvalue_cindices;

  /** map from sygus types to non-variable nullary constructors */

  std::map<TypeNode, std::vector<unsigned> > d_rvalue_null_cindices;

  /** the random string alphabet */

  std::vector<unsigned> d_rstring_alphabet;

  /** map from variables to sygus types that include them */

  std::map<Node, std::vector<TypeNode> > d_var_sygus_types;

  /** map from constants to sygus types that include them */

  std::map<Node, std::vector<TypeNode> > d_const_sygus_types;

  /** register sygus type, initializes the above two data structures */

  void registerSygusType(TypeNode tn);

};

}  // namespace quantifiers

}  // namespace theory

}  // namespace cvc5

#endif /* CVC5__THEORY__QUANTIFIERS__SYGUS_SAMPLER_H */