/*********************                                                        */
/*! \file dtype.h
 ** \verbatim
 ** Top contributors (to current version):
 **   Andrew Reynolds, Morgan Deters, Tim King
 ** This file is part of the CVC4 project.
 ** Copyright (c) 2009-2020 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 A class representing a datatype definition
 **/

#include "cvc4_private.h"

#ifndef CVC4__EXPR__DTYPE_H
#define CVC4__EXPR__DTYPE_H

#include <map>
#include <string>
#include <vector>
#include "expr/dtype_cons.h"
#include "expr/dtype_selector.h"
#include "expr/node.h"
#include "expr/node_manager_attributes.h"
#include "expr/type_node.h"

namespace CVC4 {

// ----------------------- datatype attributes
/**
 * Attribute for the index of an expression within a datatype, which is either:
 * (1) If the expression is a constructor, then its index refers to its
 * placement in the constructor list of the datatype that owns it, (2) If the
 * expression is a selector, then its index refers to its placement in the
 * argument list of the constructor that owns it.
 */
struct DTypeIndexTag
{
};
typedef expr::Attribute<DTypeIndexTag, size_t> DTypeIndexAttr;
/**
 * Attribute for the constructor index of a selector. This indicates the index
 * (DTypeIndexAttr) of the constructor that owns this selector.
 */
struct DTypeConsIndexTag
{
};
typedef expr::Attribute<DTypeConsIndexTag, size_t> DTypeConsIndexAttr;
/** Attribute true for datatype types that are finite. */
struct DTypeFiniteTag
{
};
typedef expr::Attribute<DTypeFiniteTag, bool> DTypeFiniteAttr;
/** Attribute true when we have computed whether a datatype type is finite */
struct DTypeFiniteComputedTag
{
};
typedef expr::Attribute<DTypeFiniteComputedTag, bool> DTypeFiniteComputedAttr;
/**
 * Attribute true for datatype types that are interpreted as finite (see
 * TypeNode::isInterpretedFinite).
 */
struct DTypeUFiniteTag
{
};
typedef expr::Attribute<DTypeUFiniteTag, bool> DTypeUFiniteAttr;
/**
 * Attribute true when we have computed whether a datatype type is interpreted
 * as finite.
 */
struct DTypeUFiniteComputedTag
{
};
typedef expr::Attribute<DTypeUFiniteComputedTag, bool> DTypeUFiniteComputedAttr;
// ----------------------- end datatype attributes

class NodeManager;

class Datatype;

/**
 * The Node-level representation of an inductive datatype, which currently
 * resides within the Expr-level Datatype class (expr/datatype.h).
 *
 * Notice that this class is a specification for a datatype, and is not
 * itself a type. The type that this specification corresponds to can be
 * retrieved (after resolution as described in the following) via getTypeNode.
 *
 * This is far more complicated than it first seems.  Consider this
 * datatype definition:
 *
 *   DATATYPE nat =
 *     succ(pred: nat)
 *   | zero
 *   END;
 *
 * You cannot define "nat" until you have a Type for it, but you
 * cannot have a Type for it until you fill in the type of the "pred"
 * selector, which needs the Type.  So we have a chicken-and-egg
 * problem.  It's even more complicated when we have mutual recursion
 * between datatypes, since the CVC presentation language does not
 * require forward-declarations.  Here, we define trees of lists that
 * contain trees of lists (etc):
 *
 *   DATATYPE
 *     tree = node(left: tree, right: tree) | leaf(list),
 *     list = cons(car: tree, cdr: list) | nil
 *   END;
 *
 * We build DType objects to describe "tree" and "list", and their constructors
 * and constructor arguments, but leave any unknown types (including
 * self-references) in an "unresolved" state.  After parsing the whole DATATYPE
 * block, we create a TypeNode through ExprManager::mkMutualDatatypeTypes().
 * The ExprManager creates a Type for each, but before "releasing" this type
 * into the wild, it does a round of in-place "resolution" on each DType by
 * calling DType::resolve() with a map of string -> TypeNode to
 * allow the datatype to construct the necessary testers and selectors.
 *
 * An additional point to make is that we want to ease the burden on
 * both the parser AND the users of the CVC4 API, so this class takes
 * on the task of generating its own selectors and testers, for
 * instance.  That means that, after reifying the DType with the
 * NodeManager, the parser needs to go through the (now-resolved)
 * DType and request the constructor, selector, and tester terms.
 * See src/parser/parser.cpp for how this is done.  For API usage
 * ideas, see test/unit/util/datatype_black.h.
 *
 * DTypes may also be defined parametrically, such as this example:
 *
 *  DATATYPE
 *    list[T] = cons(car : T, cdr : list[T]) | null,
 *    tree = node(children : list[tree]) | leaf
 *  END;
 *
 * Here, the definition of the parametric datatype list, where T is a type
 * variable. In other words, this defines a family of types list[C] where C is
 * any concrete type.  DTypes can be parameterized over multiple type variables
 * using the syntax sym[ T1, ..., Tn ] = ...,
 *
 */
class DType
{
  friend class Datatype;
  friend class DTypeConstructor;
  friend class NodeManager;  // for access to resolve()

 public:
  /**
   * Get the datatype of a constructor, selector, or tester operator.
   */
  static const DType& datatypeOf(Node item);

  /**
   * Get the index of a constructor or tester in its datatype, or the
   * index of a selector in its constructor.  (Zero is always the
   * first index.)
   */
  static size_t indexOf(Node item);

  /**
   * Get the index of constructor corresponding to selector.  (Zero is
   * always the first index.)
   */
  static size_t cindexOf(Node item);

  /**
   * Same as above, but without checks. These methods should be used by
   * internal (Node-level) code.
   */
  static size_t indexOfInternal(Node item);
  static size_t cindexOfInternal(Node item);

  /** Create a new DType of the given name. */
  DType(std::string name, bool isCo = false);

  /**
   * Create a new DType of the given name, with the given
   * parameterization.
   */
  DType(std::string name,
        const std::vector<TypeNode>& params,
        bool isCo = false);

  ~DType();

  /** Add a constructor to this DType.
   *
   * Notice that constructor names need not
   * be unique; they are for convenience and pretty-printing only.
   */
  void addConstructor(std::shared_ptr<DTypeConstructor> c);

  /** set sygus
   *
   * This marks this datatype as a sygus datatype.
   * A sygus datatype is one that represents terms of type st
   * via a deep embedding described in Section 4 of
   * Reynolds et al. CAV 2015. We say that this sygus datatype
   * "encodes" its sygus type st in the following.
   *
   * st : the type this datatype encodes (this can be Int, Bool, etc.),
   * bvl : the list of arguments for the synth-fun
   * allow_const : whether all constants are (implicitly) allowed by the
   * datatype
   * allow_all : whether all terms are (implicitly) allowed by the datatype
   *
   * Notice that allow_const/allow_all do not reflect the constructors
   * for this datatype, and instead are used solely for relaxing constraints
   * when doing solution reconstruction (Figure 5 of Reynolds et al.
   * CAV 2015).
   */
  void setSygus(TypeNode st, Node bvl, bool allowConst, bool allowAll);

  /** set that this datatype is a tuple */
  void setTuple();

  /** Get the name of this DType. */
  std::string getName() const;

  /** Get the number of constructors (so far) for this DType. */
  size_t getNumConstructors() const;

  /** Is this datatype parametric? */
  bool isParametric() const;

  /** Get the number of type parameters */
  size_t getNumParameters() const;

  /** Get parameter */
  TypeNode getParameter(size_t i) const;

  /** Get parameters */
  std::vector<TypeNode> getParameters() const;

  /** is this a co-datatype? */
  bool isCodatatype() const;

  /** is this a sygus datatype? */
  bool isSygus() const;

  /** is this a tuple datatype? */
  bool isTuple() const;

  /**
   * Return the cardinality of this datatype.
   * The DType must be resolved.
   *
   * The version of this method that takes type t is required
   * for parametric datatypes, where t is an instantiated
   * parametric datatype type whose datatype is this class.
   */
  Cardinality getCardinality(TypeNode t) const;
  Cardinality getCardinality() const;

  /**
   * Return true iff this DType has finite cardinality. If the
   * datatype is not well-founded, this method returns false. The
   * DType must be resolved or an assertion is violated.
   *
   * The version of this method that takes type t is required
   * for parametric datatypes, where t is an instantiated
   * parametric datatype type whose datatype is this class.
   */
  bool isFinite(TypeNode t) const;
  bool isFinite() const;

  /**
   * Return true iff this  DType is finite (all constructors are
   * finite, i.e., there  are finitely  many ground terms) under the
   * assumption that unintepreted sorts are finite. If the
   * datatype is  not well-founded, this method returns false.  The
   * DType must be resolved or an assertion is violated.
   *
   * The versions of these methods that takes type t is required
   * for parametric datatypes, where t is an instantiated
   * parametric datatype type whose datatype is this class.
   */
  bool isInterpretedFinite(TypeNode t) const;
  bool isInterpretedFinite() const;

  /** is well-founded
   *
   * Return true iff this datatype is well-founded (there exist finite
   * values of this type). This datatype must be resolved or an assertion is
   * violated.
   */
  bool isWellFounded() const;
  /**
   * Does this datatype have nested recursion? This is true if this datatype
   * definition contains itself as an alien subfield type, or a variant
   * of itself as an alien subfield type (if this datatype is parametric).
   * For details see getAlienSubfieldTypes below.
   *
   * Notice that a type having no nested recursion may have a subfield type that
   * has nested recursion.
   */
  bool hasNestedRecursion() const;

  /** is recursive singleton
   *
   * Return true iff this datatype is a recursive singleton
   * (a recursive singleton is a recursive datatype with only
   * one infinite value). For details, see Reynolds et al. CADE 2015.
   *
   * The versions of these methods that takes type t is required
   * for parametric datatypes, where t is an instantiated
   * parametric datatype type whose datatype is this class.
   */
  bool isRecursiveSingleton(TypeNode t) const;
  bool isRecursiveSingleton() const;

  /** recursive single arguments
   *
   * Get recursive singleton argument types (uninterpreted sorts that the
   * cardinality of this datatype is dependent upon). For example, for :
   *   stream :=  cons( head1 : U1, head2 : U2, tail : stream )
   * Then, the recursive singleton argument types of stream are { U1, U2 },
   * since if U1 and U2 have cardinality one, then stream has cardinality
   * one as well.
   *
   * The versions of these methods that takes Type t is required
   * for parametric datatypes, where t is an instantiated
   * parametric datatype type whose datatype is this class.
   */
  unsigned getNumRecursiveSingletonArgTypes(TypeNode t) const;
  TypeNode getRecursiveSingletonArgType(TypeNode t, size_t i) const;
  unsigned getNumRecursiveSingletonArgTypes() const;
  TypeNode getRecursiveSingletonArgType(size_t i) const;

  /**
   * Construct and return a ground term of this DType.  The
   * DType must be both resolved and well-founded, or else an
   * exception is thrown.
   *
   * This method takes a type t, which is a datatype type whose
   * datatype is this class, which may be an instantiated datatype
   * type if this datatype is parametric.
   */
  Node mkGroundTerm(TypeNode t) const;
  /** Make ground value
   *
   * Same as above, but constructs a constant value instead of a ground term.
   * These two notions typically coincide. However, for uninterpreted sorts,
   * they do not: mkGroundTerm returns a fresh variable whereas mkValue returns
   * an uninterpreted constant. The motivation for mkGroundTerm is that
   * unintepreted constants should never appear in lemmas. The motivation for
   * mkGroundValue is for things like type enumeration and model construction.
   */
  Node mkGroundValue(TypeNode t) const;

  /**
   * Get the TypeNode associated to this DType.  Can only be
   * called post-resolution.
   */
  TypeNode getTypeNode() const;

  /**
   * Get the TypeNode associated to this (parameterized) DType.  Can only be
   * called post-resolution.
   */
  TypeNode getTypeNode(const std::vector<TypeNode>& params) const;

  /** Return true iff this DType has already been resolved. */
  bool isResolved() const;

  /** Get the ith DTypeConstructor. */
  const DTypeConstructor& operator[](size_t index) const;

  /** get sygus type
   * This gets the built-in type associated with
   * this sygus datatype, i.e. the type of the
   * term that this sygus datatype encodes.
   */
  TypeNode getSygusType() const;

  /** get sygus var list
   * This gets the variable list of the function
   * to synthesize using this sygus datatype.
   * For example, if we are synthesizing a binary
   * function f where solutions are of the form:
   *   f = (lambda (xy) t[x,y])
   * In this case, this method returns the
   * bound variable list containing x and y.
   */
  Node getSygusVarList() const;
  /** get sygus allow constants
   *
   * Does this sygus datatype allow constants?
   * Notice that this is not a property of the
   * constructors of this datatype. Instead, it is
   * an auxiliary flag (provided in the call
   * to setSygus).
   */
  bool getSygusAllowConst() const;
  /** get sygus allow all
   *
   * Does this sygus datatype allow all terms?
   * Notice that this is not a property of the
   * constructors of this datatype. Instead, it is
   * an auxiliary flag (provided in the call
   * to setSygus).
   */
  bool getSygusAllowAll() const;

  /** involves external type
   * Get whether this datatype has a subfield
   * in any constructor that is not a datatype type.
   */
  bool involvesExternalType() const;
  /** involves uninterpreted type
   * Get whether this datatype has a subfield
   * in any constructor that is an uninterpreted type.
   */
  bool involvesUninterpretedType() const;

  /**
   * Get the list of constructors.
   */
  const std::vector<std::shared_ptr<DTypeConstructor> >& getConstructors()
      const;

  /** prints this datatype to stream */
  void toStream(std::ostream& out) const;

 private:
  /**
   * DTypes refer to themselves, recursively, and we have a
   * chicken-and-egg problem.  The TypeNode around the DType
   * cannot exist until the DType is finalized, and the DType
   * cannot refer to the TypeNode representing itself until it
   * exists.  resolve() is called by the NodeManager when a type is
   * ultimately requested of the DType specification (that is, when
   * NodeManager::mkTypeNode() or NodeManager::mkMutualTypeNodes()
   * is called).  Has the effect of freezing the object, too; that is,
   * addConstructor() will fail after a call to resolve().
   *
   * The basic goal of resolution is to assign constructors, selectors,
   * and testers.  To do this, any UnresolvedType/SelfType references
   * must be cleared up.  This is the purpose of the "resolutions" map;
   * it includes any mutually-recursive datatypes that are currently
   * under resolution.  The four vectors come in two pairs (so, really
   * they are two maps).  placeholders->replacements give type variables
   * that should be resolved in the case of parametric datatypes.
   *
   * @param em the NodeManager at play
   * @param resolutions a map of strings to TypeNodes currently under
   * resolution
   * @param placeholders the types in these DTypes under resolution that must
   * be replaced
   * @param replacements the corresponding replacements
   * @param paramTypes the sort constructors in these DTypes under resolution
   * that must be replaced
   * @param paramReplacements the corresponding (parametric) TypeNodes
   */
  bool resolve(const std::map<std::string, TypeNode>& resolutions,
               const std::vector<TypeNode>& placeholders,
               const std::vector<TypeNode>& replacements,
               const std::vector<TypeNode>& paramTypes,
               const std::vector<TypeNode>& paramReplacements);

  /** compute the cardinality of this datatype */
  Cardinality computeCardinality(TypeNode t,
                                 std::vector<TypeNode>& processing) const;
  /** compute whether this datatype is a recursive singleton */
  bool computeCardinalityRecSingleton(TypeNode t,
                                      std::vector<TypeNode>& processing,
                                      std::vector<TypeNode>& u_assume) const;
  /** compute whether this datatype is well-founded */
  bool computeWellFounded(std::vector<TypeNode>& processing) const;
  /** compute ground term
   *
   * This method checks if there is a term of this datatype whose type is t
   * that is finitely constructable. As needed, it traverses its subfield types.
   *
   * The argument processing is the set of datatype types we are currently
   * traversing.
   *
   * The argument isValue is whether we are constructing a constant value. If
   * this flag is false, we are constructing a canonical ground term that is
   * not necessarily constant.
   */
  Node computeGroundTerm(TypeNode t,
                         std::vector<TypeNode>& processing,
                         bool isValue) const;
  /** Get the shared selector
   *
   * This returns the index^th (constructor-agnostic)
   * selector for type t. The type dtt is the datatype
   * type whose datatype is this class, where this may
   * be an instantiated parametric datatype.
   *
   * In the terminology of "DTypes with Shared Selectors",
   * this returns the term sel_{dtt}^{t,index}.
   */
  Node getSharedSelector(TypeNode dtt, TypeNode t, size_t index) const;
  /**
   * Helper for mkGroundTerm and mkGroundValue above.
   */
  Node mkGroundTermInternal(TypeNode t, bool isValue) const;
  /**
   * This method is used to get alien subfield types of this datatype.
   *
   * A subfield type T of a datatype type D is a type such that a value of
   * type T may appear as a subterm of a value of type D.
   *
   * An *alien* subfield type T of a datatype type D is a type such that a
   * value v of type T may appear as a subterm of a value of D, and moreover
   * v occurs as a strict subterm of a non-datatype term in that value.
   *
   * For example, the alien subfield types of T in:
   *   T -> Emp | Container(s : (Set List))
   *   List -> nil | cons( head : Int, tail: List)
   * are { List, Int }. Notice that Int is an alien subfield type since it
   * appears as a subfield type of List, and List is an alien subfield type
   * of T. In other words, Int is an alien subfield type due to the above
   * definition due to the term (Container (singleton (cons 0 nil))), where
   * 0 occurs as a subterm of (singleton (cons 0 nil)). The non-strict
   * subfield types of T in this example are { (Set List) }.
   *
   * For example, the alien subfield types of T in:
   *   T -> Emp | Container(s : List)
   *   List -> nil | cons( head : (Set T), tail: List)
   * are { T, List, (Set T) }. Notice that T is an alien subfield type of itself
   * since List is a subfield type of T and T is an alien subfield type of List.
   * Furthermore, List and (Set T) are also alien subfield types of T since
   * List is a subfield type of T and T is an alien subfield type of itself.
   *
   * For example, the alien subfield types of T in:
   *   T -> Emp | Container(s : (Array Int T))
   * are { T, Int }, where we assume that values of (Array U1 U2) are
   * constructed from values of U1 and U2, for all types U1, U2. The non-strict
   * subfield types of T in this example are { (Array Int T) }.
   *
   * @param types The set of types to append the alien subfield types to,
   * @param processed The datatypes (cached using d_self) we have processed. If
   * the range of this map is true, we have processed the datatype with
   * isAlienPos = true.
   * @param isAlienPos Whether we are in an alien subfield type position. This
   * flag is true if we have traversed beneath a non-datatype type constructor.
   */
  void getAlienSubfieldTypes(
      std::unordered_set<TypeNode, TypeNodeHashFunction>& types,
      std::map<TypeNode, bool>& processed,
      bool isAlienPos) const;
  /** name of this datatype */
  std::string d_name;
  /** the type parameters of this datatype (if this is a parametric datatype)
   */
  std::vector<TypeNode> d_params;
  /** whether the datatype is a codatatype. */
  bool d_isCo;
  /** whether the datatype is a tuple */
  bool d_isTuple;
  /** the constructors of this datatype */
  std::vector<std::shared_ptr<DTypeConstructor> > d_constructors;
  /** whether this datatype has been resolved */
  bool d_resolved;
  /** self type */
  mutable TypeNode d_self;
  /** cache for involves external type */
  bool d_involvesExt;
  /** cache for involves uninterpreted type */
  bool d_involvesUt;
  /** the builtin type that this sygus type encodes */
  TypeNode d_sygusType;
  /** the variable list for the sygus function to synthesize */
  Node d_sygusBvl;
  /** whether all constants are allowed as solutions */
  bool d_sygusAllowConst;
  /** whether all terms are allowed as solutions */
  bool d_sygusAllowAll;

  /** the cardinality of this datatype
   * "mutable" because computing the cardinality can be expensive,
   * and so it's computed just once, on demand---this is the cache
   */
  mutable Cardinality d_card;

  /** is this type a recursive singleton type?
   * The range of this map stores
   * 0 if the field has not been computed,
   * 1 if this datatype is a recursive singleton type,
   * -1 if this datatype is not a recursive singleton type.
   * For definition of (co)recursive singleton, see
   * Section 2 of Reynolds et al. CADE 2015.
   */
  mutable std::map<TypeNode, int> d_cardRecSingleton;
  /** if d_cardRecSingleton is true,
   * This datatype has infinite cardinality if at least one of the
   * following uninterpreted sorts having cardinality > 1.
   */
  mutable std::map<TypeNode, std::vector<TypeNode> > d_cardUAssume;
  /**
   * Cache of whether this datatype is well-founded, where 0 means we have
   * not computed this information, 1 means it is well-founded, -1 means it is
   * not.
   */
  mutable int d_wellFounded;
  /**
   * Cache of whether this datatype has nested recursion, where 0 means we have
   * not computed this information, 1 means it has nested recursion, -1 means it
   * does not.
   */
  mutable int d_nestedRecursion;
  /** cache of ground term for this datatype */
  mutable std::map<TypeNode, Node> d_groundTerm;
  /** cache of ground values for this datatype */
  mutable std::map<TypeNode, Node> d_groundValue;
  /** cache of shared selectors for this datatype */
  mutable std::map<TypeNode, std::map<TypeNode, std::map<unsigned, Node> > >
      d_sharedSel;
}; /* class DType */

/**
 * A hash function for DTypes.  Needed to store them in hash sets
 * and hash maps.
 */
struct DTypeHashFunction
{
  size_t operator()(const DType& dt) const
  {
    return std::hash<std::string>()(dt.getName());
  }
  size_t operator()(const DType* dt) const
  {
    return std::hash<std::string>()(dt->getName());
  }
}; /* struct DTypeHashFunction */

/* stores an index to DType residing in NodeManager */
class DTypeIndexConstant
{
 public:
  DTypeIndexConstant(size_t index);

  size_t getIndex() const { return d_index; }
  bool operator==(const DTypeIndexConstant& uc) const
  {
    return d_index == uc.d_index;
  }
  bool operator!=(const DTypeIndexConstant& uc) const { return !(*this == uc); }
  bool operator<(const DTypeIndexConstant& uc) const
  {
    return d_index < uc.d_index;
  }
  bool operator<=(const DTypeIndexConstant& uc) const
  {
    return d_index <= uc.d_index;
  }
  bool operator>(const DTypeIndexConstant& uc) const { return !(*this <= uc); }
  bool operator>=(const DTypeIndexConstant& uc) const { return !(*this < uc); }

 private:
  const size_t d_index;
}; /* class DTypeIndexConstant */

std::ostream& operator<<(std::ostream& out, const DTypeIndexConstant& dic);

struct DTypeIndexConstantHashFunction
{
  size_t operator()(const DTypeIndexConstant& dic) const
  {
    return IntegerHashFunction()(dic.getIndex());
  }
}; /* struct DTypeIndexConstantHashFunction */

std::ostream& operator<<(std::ostream& os, const DType& dt);

}  // namespace CVC4

#endif
