//===--- CSRanking.cpp - Constraint System Ranking ------------------------===//
//
// This source file is part of the Swift.org open source project
//
// Copyright (c) 2014 - 2015 Apple Inc. and the Swift project authors
// Licensed under Apache License v2.0 with Runtime Library Exception
//
// See http://swift.org/LICENSE.txt for license information
// See http://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
//
//===----------------------------------------------------------------------===//
//
// This file implements solution ranking heuristics for the
// constraint-based type checker.
//
//===----------------------------------------------------------------------===//
#include "ConstraintSystem.h"
#include "swift/AST/ArchetypeBuilder.h"
#include "llvm/ADT/Statistic.h"

using namespace swift;
using namespace constraints;

//===--------------------------------------------------------------------===//
// Statistics
//===--------------------------------------------------------------------===//
#define DEBUG_TYPE "Constraint solver overall"
STATISTIC(NumDiscardedSolutions, "# of solutions discarded");

void ConstraintSystem::increaseScore(ScoreKind kind) {
  unsigned index = static_cast<unsigned>(kind);
  ++CurrentScore.Data[index];

  if (TC.getLangOpts().DebugConstraintSolver) {
    auto &log = getASTContext().TypeCheckerDebug->getStream();
    if (solverState)
      log.indent(solverState->depth * 2);
    log << "(increasing score due to ";
    switch (kind) {
      case SK_Fix:
      log << "attempting to fix the source";
      break;

    case SK_ForceUnchecked:
      log << "force of an implicitly unwrapped optional";
      break;

    case SK_UserConversion:
      log << "user conversion";
      break;

    case SK_FunctionConversion:
      log << "function conversion";
      break;

    case SK_NonDefaultLiteral:
      log << "non-default literal";
      break;
        
    case SK_ArrayUpcastConversion:
      log << "array upcast conversion";
      break;
    case SK_ArrayBridgedConversion:
      log << "array bridged conversion";
      break;
    }
    log << ")\n";
  }
}

bool ConstraintSystem::worseThanBestSolution() const {
  if (!solverState || !solverState->BestScore ||
      CurrentScore <= *solverState->BestScore)
    return false;

  if (TC.getLangOpts().DebugConstraintSolver) {
    auto &log = getASTContext().TypeCheckerDebug->getStream();
    log.indent(solverState->depth * 2)
      << "(solution is worse than the best solution)\n";
  }

  return true;
}

llvm::raw_ostream &constraints::operator<<(llvm::raw_ostream &out,
                                           const Score &score) {
  for (unsigned i = 0; i != NumScoreKinds; ++i) {
    if (i) out << ' ';
    out << score.Data[i];
  }
  return out;
}

/// \brief Remove the initializers from any tuple types within the
/// given type.
static Type stripInitializers(Type origType) {
  return origType.transform([&](Type type) -> Type {
             if (auto tupleTy = type->getAs<TupleType>()) {
               SmallVector<TupleTypeElt, 4> fields;
               for (const auto &field : tupleTy->getFields()) {
                 fields.push_back(TupleTypeElt(field.getType(),
                                               field.getName(),
                                               DefaultArgumentKind::None,
                                               field.isVararg()));
                                               
               }
               return TupleType::get(fields, type->getASTContext());
             }
             return type;
           });
}

///\ brief Compare two declarations for equality when they are used.
///
static bool sameDecl(Decl *decl1, Decl *decl2) {
  if (decl1 == decl2)
    return true;

  // All types considered identical.
  // FIXME: This is a hack. What we really want is to have substituted the
  // base type into the declaration reference, so that we can compare the
  // actual types to which two type declarations resolve. If those types are
  // equivalent, then it doesn't matter which declaration is chosen.
  if (isa<TypeDecl>(decl1) && isa<TypeDecl>(decl2))
    return true;
  
  if (decl1->getKind() != decl2->getKind())
    return false;

  return false;
}

/// \brief Compare two overload choices for equality.
static bool sameOverloadChoice(const OverloadChoice &x,
                               const OverloadChoice &y) {
  if (x.getKind() != y.getKind())
    return false;

  switch (x.getKind()) {
  case OverloadChoiceKind::BaseType:
    // FIXME: Compare base types after substitution?
    return true;

  case OverloadChoiceKind::Decl:
  case OverloadChoiceKind::DeclViaDynamic:
    return sameDecl(x.getDecl(), y.getDecl());

  case OverloadChoiceKind::TypeDecl:
    // FIXME: Compare types after substitution?
    return sameDecl(x.getDecl(), y.getDecl());

  case OverloadChoiceKind::TupleIndex:
    return x.getTupleIndex() == y.getTupleIndex();
  }
}

/// Compare two declarations to determine whether one is a witness of the other.
static Comparison compareWitnessAndRequirement(TypeChecker &tc, DeclContext *dc,
                                               ValueDecl *decl1,
                                               ValueDecl *decl2) {
  // We only have a witness/requirement pair if exactly one of the declarations
  // comes from a protocol.
  auto proto1 = dyn_cast<ProtocolDecl>(decl1->getDeclContext());
  auto proto2 = dyn_cast<ProtocolDecl>(decl2->getDeclContext());
  if ((bool)proto1 == (bool)proto2)
    return Comparison::Unordered;

  // Figure out the protocol, requirement, and potential witness.
  ProtocolDecl *proto;
  ValueDecl *req;
  ValueDecl *potentialWitness;
  if (proto1) {
    proto = proto1;
    req = decl1;
    potentialWitness = decl2;
  } else {
    proto = proto2;
    req = decl2;
    potentialWitness = decl1;
  }

  // Cannot compare type declarations this way.
  // FIXME: Use the same type-substitution approach as lookupMemberType.
  if (isa<TypeDecl>(req))
    return Comparison::Unordered;

  if (!potentialWitness->getDeclContext()->isTypeContext())
    return Comparison::Unordered;

  // Determine whether the type of the witness's context conforms to the
  // protocol.
  auto owningType
    = potentialWitness->getDeclContext()->getDeclaredTypeInContext();
  ProtocolConformance *conformance = nullptr;
  if (!tc.conformsToProtocol(owningType, proto, dc, &conformance) ||
      !conformance->isComplete())
    return Comparison::Unordered;

  // If the witness and the potential witness are not the same, there's no
  // ordering here.
  if (conformance->getWitness(req, &tc).getDecl() != potentialWitness)
    return Comparison::Unordered;

  // We have a requirement/witness match.
  return proto1? Comparison::Worse : Comparison::Better;
}

namespace {
  /// Dependent type opener that maps from a dependent type to its corresponding
  /// archetype in the given context.
  class ArchetypeOpener : public constraints::DependentTypeOpener {
    DeclContext *DC;
    llvm::DenseMap<TypeVariableType *, Type> Mapped;

  public:
    explicit ArchetypeOpener(DeclContext *dc) : DC(dc) { }

    virtual void openedGenericParameter(GenericTypeParamType *param,
                                        TypeVariableType *typeVar,
                                        Type &replacementType) {
      replacementType = ArchetypeBuilder::mapTypeIntoContext(DC, param);

      Mapped[typeVar] = param;
    }

    virtual bool shouldBindAssociatedType(Type baseType,
                                          TypeVariableType *baseTypeVar,
                                          AssociatedTypeDecl *assocType,
                                          TypeVariableType *memberTypeVar,
                                          Type &replacementType) {
      assert(Mapped.count(baseTypeVar) && "Missing base mapping?");
      auto memberType = DependentMemberType::get(Mapped[baseTypeVar],
                                                 assocType,
                                                 DC->getASTContext());
      replacementType = ArchetypeBuilder::mapTypeIntoContext(DC, memberType);

      // Record this mapping.
      Mapped[memberTypeVar] = memberType;
      return true;
    }
  };
}

namespace {
  /// Describes the relationship between the context types for two declarations.
  enum class SelfTypeRelationship {
    /// The types are unrelated; ignore the bases entirely.
    Unrelated,
    /// The types are equivalent.
    Equivalent,
    /// The first type is a subclass of the second.
    Subclass,
    /// The second type is a subclass of the first.
    Superclass,
    /// The first type conforms to the second
    ConformsTo,
    /// The second type conforms to the first.
    ConformedToBy
  };
}

/// Determines whether the first type is nominally a superclass of the second
/// type, ignore generic arguments.
static bool isNominallySuperclassOf(TypeChecker &tc, Type type1, Type type2) {
  auto nominal1 = type1->getAnyNominal();
  if (!nominal1)
    return false;

  for (auto super2 = type2; super2; super2 = super2->getSuperclass(&tc)) {
    if (super2->getAnyNominal() == nominal1)
      return true;
  }

  return false;
}

/// Determine the relationship between the self types of the given declaration
/// contexts..
static SelfTypeRelationship computeSelfTypeRelationship(TypeChecker &tc,
                                                        DeclContext *dc,
                                                        DeclContext *dc1,
                                                        DeclContext *dc2){
  // If at least one of the contexts is a non-type context, the two are
  // unrelated.
  if (!dc1->isTypeContext() || !dc2->isTypeContext())
    return SelfTypeRelationship::Unrelated;

  Type type1 = dc1->getDeclaredTypeInContext();
  Type type2 = dc2->getDeclaredTypeInContext();

  // If the types are equal, the answer is simple.
  if (type1->isEqual(type2))
    return SelfTypeRelationship::Equivalent;

  // If both types can have superclasses, which whether one is a superclass
  // of the other. The subclass is the common base type.
  if (type1->mayHaveSuperclass() && type2->mayHaveSuperclass()) {
    if (isNominallySuperclassOf(tc, type1, type2))
      return SelfTypeRelationship::Superclass;

    if (isNominallySuperclassOf(tc, type2, type1))
      return SelfTypeRelationship::Subclass;

    return SelfTypeRelationship::Unrelated;
  }

  // If neither or both are protocol types, consider the bases unrelated.
  bool isProtocol1 = type1->is<ProtocolType>();
  bool isProtocol2 = type2->is<ProtocolType>();
  if (isProtocol1 == isProtocol2)
    return SelfTypeRelationship::Unrelated;

  // Just one of the two is a protocol. Check whether the other conforms to
  // that protocol.
  Type protoTy = isProtocol1? type1 : type2;
  Type modelTy = isProtocol1? type2 : type1;
  auto proto = protoTy->castTo<ProtocolType>()->getDecl();

  // If the model type does not conform to the protocol, the bases are
  // unrelated.
  if (!tc.conformsToProtocol(modelTy, proto, dc))
    return SelfTypeRelationship::Unrelated;

  return isProtocol1? SelfTypeRelationship::ConformedToBy
                    : SelfTypeRelationship::ConformsTo;
}

// Given a type and a declaration context, return a type with a curried
// 'self' type as input if the declaration context describes a type.
static Type addCurriedSelfType(ASTContext &ctx, Type type, DeclContext *dc) {
  if (!dc->isTypeContext())
    return type;

  auto nominal = dc->getDeclaredTypeOfContext()->getAnyNominal();
  auto selfTy = nominal->getInterfaceType()->castTo<MetatypeType>()
                  ->getInstanceType();
  if (nominal->isGenericContext())
    return GenericFunctionType::get(nominal->getGenericSignature(),
                                    selfTy, type, AnyFunctionType::ExtInfo());
  return FunctionType::get(selfTy, type);
}

/// \brief Determine whether the first declaration is as "specialized" as
/// the second declaration.
///
/// "Specialized" is essentially a form of subtyping, defined below.
static bool isDeclAsSpecializedAs(TypeChecker &tc, DeclContext *dc,
                                  ValueDecl *decl1, ValueDecl *decl2) {
  // If the kinds are different, there's nothing we can do.
  // FIXME: This is wrong for type declarations, which we're skipping
  // entirely.
  if (decl1->getKind() != decl2->getKind() || isa<TypeDecl>(decl1))
    return false;

  // A non-generic declaration is more specialized than a generic declaration.
  if (auto func1 = dyn_cast<AbstractFunctionDecl>(decl1)) {
    auto func2 = cast<AbstractFunctionDecl>(decl2);
    if (static_cast<bool>(func1->getGenericParams()) !=
          static_cast<bool>(func2->getGenericParams()))
      return func2->getGenericParams();
  }

  // A witness is always more specialized than the requirement it satisfies.
  switch (compareWitnessAndRequirement(tc, dc, decl1, decl2)) {
  case Comparison::Unordered:
    break;

  case Comparison::Better:
    return true;

  case Comparison::Worse:
    return false;
  }

  Type type1 = decl1->getInterfaceType();
  Type type2 = decl2->getInterfaceType();

  /// What part of the type should we check?
  enum {
    CheckAll,
    CheckInput,
    CheckResult
  } checkKind;
  if (isa<AbstractFunctionDecl>(decl1) || isa<EnumElementDecl>(decl1)) {
    // Nothing to do: these have the curried 'self' already.
    checkKind = CheckInput;

    // Only check the result type for conversion functions.
    if (auto func = dyn_cast<FuncDecl>(decl1)) {
      if (func->getAttrs().isConversion())
        checkKind = CheckResult;
    }
  } else {
    // Add a curried 'self' type.
    assert(!type1->is<GenericFunctionType>() && "Odd generic function type?");
    assert(!type2->is<GenericFunctionType>() && "Odd generic function type?");
    type1 = addCurriedSelfType(tc.Context, type1, decl1->getDeclContext());
    type2 = addCurriedSelfType(tc.Context, type2, decl2->getDeclContext());

    // For a subscript declaration, only look at the input type (i.e., the
    // indices).
    if (isa<SubscriptDecl>(decl1))
      checkKind = CheckInput;
    else
      checkKind = CheckAll;
  }

  // Construct a constraint system to compare the two declarations.
  ConstraintSystem cs(tc, dc, ConstraintSystemOptions());

  // Get the type of a reference to the second declaration.
  Type openedType2 = cs.openType(type2,decl2->getPotentialGenericDeclContext());

  // Get the type of a reference to the first declaration, swapping in
  // archetypes for the dependent types.
  ArchetypeOpener opener(decl1->getPotentialGenericDeclContext());
  Type openedType1 = cs.openType(type1, decl1->getPotentialGenericDeclContext(),
                                 /*skipProtocolSelfConstraint=*/false,
                                 &opener);

  // Extract the self types from the declarations, if they have them.
  Type selfTy1;
  Type selfTy2;
  if (decl1->getDeclContext()->isTypeContext()) {
    auto funcTy1 = openedType1->castTo<FunctionType>();
    selfTy1 = funcTy1->getInput()->getRValueInstanceType();
    openedType1 = funcTy1->getResult();
  }
  if (decl2->getDeclContext()->isTypeContext()) {
    auto funcTy2 = openedType2->castTo<FunctionType>();
    selfTy2 = funcTy2->getInput()->getRValueInstanceType();
    openedType2 = funcTy2->getResult();
  }

  // Determine the relationship between the 'self' types and add the
  // appropriate constraints. The constraints themselves never fail, but
  // they help deduce type variables that were opened.
  switch (computeSelfTypeRelationship(tc, dc, decl1->getDeclContext(),
                                      decl2->getDeclContext())) {
  case SelfTypeRelationship::Unrelated:
    // Skip the self types parameter entirely.
    break;

  case SelfTypeRelationship::Equivalent:
    cs.addConstraint(ConstraintKind::Equal, selfTy1, selfTy2);
    break;

  case SelfTypeRelationship::Subclass:
    cs.addConstraint(ConstraintKind::Subtype, selfTy1, selfTy2);
    break;

  case SelfTypeRelationship::Superclass:
    cs.addConstraint(ConstraintKind::Subtype, selfTy2, selfTy1);
    break;

  case SelfTypeRelationship::ConformsTo:
    cs.addConstraint(ConstraintKind::ConformsTo, selfTy1, selfTy2);
    break;

  case SelfTypeRelationship::ConformedToBy:
    cs.addConstraint(ConstraintKind::ConformsTo, selfTy2, selfTy1);
    break;
  }

  switch (checkKind) {
  case CheckAll:
    // Check whether the first type is a subtype of the second.
    cs.addConstraint(ConstraintKind::Subtype, openedType1, openedType2);
    break;

  case CheckInput: {
    // Check whether the first function type's input is a subtype of the second
    // type's inputs, i.e., can we forward the arguments?
    auto funcTy1 = openedType1->castTo<FunctionType>();
    auto funcTy2 = openedType2->castTo<FunctionType>();
    cs.addConstraint(ConstraintKind::Subtype,
                     funcTy1->getInput(),
                     funcTy2->getInput());
    break;
  }

  case CheckResult: {
    // Check whether the first function type's input is a subtype of the second
    // type's inputs, i.e., can we forward the arguments?
    auto funcTy1 = openedType1->castTo<FunctionType>();
    auto funcTy2 = openedType2->castTo<FunctionType>();
    cs.addConstraint(ConstraintKind::Subtype,
                     funcTy1->getResult(),
                     funcTy2->getResult());
    break;
  }
  }

  // Solve the system.
  SmallVector<Solution, 1> solutions;
  return !cs.solve(solutions, FreeTypeVariableBinding::Allow);
}

Comparison TypeChecker::compareDeclarations(DeclContext *dc,
                                            ValueDecl *decl1,
                                            ValueDecl *decl2){
  bool decl1Better = isDeclAsSpecializedAs(*this, dc, decl1, decl2);
  bool decl2Better = isDeclAsSpecializedAs(*this, dc, decl2, decl1);

  if (decl1Better == decl2Better)
    return Comparison::Unordered;

  return decl1Better? Comparison::Better : Comparison::Worse;
}

SolutionCompareResult ConstraintSystem::compareSolutions(
                        ConstraintSystem &cs,
                        ArrayRef<Solution> solutions,
                        const SolutionDiff &diff,
                        unsigned idx1,
                        unsigned idx2) {
  // Whether the solutions are identical.
  bool identical = true;

  // Compare the fixed scores by themselves.
  if (solutions[idx1].getFixedScore() != solutions[idx2].getFixedScore()) {
    return solutions[idx1].getFixedScore() < solutions[idx2].getFixedScore()
             ? SolutionCompareResult::Better
             : SolutionCompareResult::Worse;
  }

  // Compute relative score.
  unsigned score1 = 0;
  unsigned score2 = 0;

  // Compare overload sets.
  for (auto &overload : diff.overloads) {
    auto choice1 = overload.choices[idx1];
    auto choice2 = overload.choices[idx2];

    // If the systems made the same choice, there's nothing interesting here.
    if (sameOverloadChoice(choice1, choice2))
      continue;
    
    auto decl1 = choice1.getDecl();
    auto dc1 = decl1->getDeclContext();
    auto decl2 = choice2.getDecl();
    auto dc2 = decl2->getDeclContext();

    // The two systems are not identical. If the decls in question are distinct
    // protocol members, let the checks below determine if the two choices are
    // 'identical' or not. This allows us to structurally unify disparate
    // protocol members during overload resolution.
    if ((dc1->getContextKind() == DeclContextKind::NominalTypeDecl) &&
        (dc1->getContextKind() == dc2->getContextKind())) {
      
        auto ntd1 = dyn_cast<NominalTypeDecl>(dc1);
        auto ntd2 = dyn_cast<NominalTypeDecl>(dc2);
        
        identical = (ntd1 != ntd2) &&
                    (ntd1->getKind() == DeclKind::Protocol) &&
                    (ntd2->getKind() == DeclKind::Protocol);
      
    } else {
      identical = false;
    }
    
    // If the kinds of overload choice don't match...
    if (choice1.getKind() != choice2.getKind()) {
      identical = false;
      
      // A declaration found directly beats any declaration found via dynamic
      // lookup.
      if (choice1.getKind() == OverloadChoiceKind::Decl &&
          choice2.getKind() == OverloadChoiceKind::DeclViaDynamic) {
        ++score1;
        continue;
      }
      if (choice1.getKind() == OverloadChoiceKind::DeclViaDynamic &&
          choice2.getKind() == OverloadChoiceKind::Decl) {
        ++score2;
        continue;
      }

      continue;
    }

    // The kinds of overload choice match, but the contents don't.
    auto &tc = cs.getTypeChecker();
    switch (choice1.getKind()) {
    case OverloadChoiceKind::TupleIndex:
      break;

    case OverloadChoiceKind::BaseType:
      llvm_unreachable("Never considered different");

    case OverloadChoiceKind::TypeDecl:
      break;

    case OverloadChoiceKind::DeclViaDynamic:
    case OverloadChoiceKind::Decl:
      // Determine whether one declaration is more specialized than the other.
      if (isDeclAsSpecializedAs(tc, cs.DC, decl1, decl2))
        ++score1;
      if (isDeclAsSpecializedAs(tc, cs.DC, decl2, decl1))
        ++score2;

      // If both declarations come from Clang, and one is a type and the other
      // is a function, prefer the function.
      if (decl1->hasClangNode() &&
          decl2->hasClangNode() &&
          ((isa<TypeDecl>(decl1) &&
            isa<AbstractFunctionDecl>(decl2)) ||
           (isa<AbstractFunctionDecl>(decl1) &&
            isa<TypeDecl>(decl2)))) {
        if (isa<TypeDecl>(decl1))
          ++score2;
        else
          ++score1;
      }

      // A class member is always better than a curried instance member.
      // If the members agree on instance-ness, a property is better than a
      // method (because a method is usually immediately invoked).
      if (!decl1->isInstanceMember() && decl2->isInstanceMember())
        ++score1;
      else if (!decl2->isInstanceMember() && decl1->isInstanceMember())
        ++score2;
      else if (isa<VarDecl>(decl1) && isa<FuncDecl>(decl2))
        ++score1;
      else if (isa<VarDecl>(decl2) && isa<FuncDecl>(decl1))
        ++score2;

      break;
    }
  }

  // Compare the type variable bindings.
  auto &tc = cs.getTypeChecker();
  for (auto &binding : diff.typeBindings) {
    // If the type variable isn't one for which we should be looking at the
    // bindings, don't.
    if (!binding.typeVar->getImpl().prefersSubtypeBinding())
      continue;

    auto type1 = binding.bindings[idx1];
    auto type2 = binding.bindings[idx2];

    // Strip any initializers from tuples in the type; they aren't
    // to be compared.
    type1 = stripInitializers(type1);
    type2 = stripInitializers(type2);

    // If the types are equivalent, there's nothing more to do.
    if (type1->isEqual(type2))
      continue;
    
    // If either of the types still contains type variables, we can't
    // compare them.
    // FIXME: This is really unfortunate. More type variable sharing
    // (when it's sane) would help us do much better here.
    if (type1->hasTypeVariable() || type2->hasTypeVariable()) {
      identical = false;
      continue;
    }

    // If one type is a subtype of the other, but not vice-verse,
    // we prefer the system with the more-constrained type.
    // FIXME: Collapse this check into the second check.
    bool type1Better = tc.isSubtypeOf(type1, type2, cs.DC);
    bool type2Better = tc.isSubtypeOf(type2, type1, cs.DC);
    if (type1Better || type2Better) {
      if (type1Better)
        ++score1;
      if (type2Better)
        ++score2;

      // Prefer the unlabeled form of a type.
      auto unlabeled1 = type1->getUnlabeledType(cs.getASTContext());
      auto unlabeled2 = type2->getUnlabeledType(cs.getASTContext());
      if (unlabeled1->isEqual(unlabeled2)) {
        if (type1->isEqual(unlabeled1)) {
          ++score1;
          continue;
        }
        if (type2->isEqual(unlabeled2)) {
          ++score2;
          continue;
        }
      }

      identical = false;
      continue;
    }

    // The systems are not considered equivalent.
    identical = false;

    // If one type is convertible to of the other, but not vice-versa.
    type1Better = tc.isConvertibleTo(type1, type2, cs.DC);
    type2Better = tc.isConvertibleTo(type2, type1, cs.DC);
    if (type1Better || type2Better) {
      if (type1Better)
        ++score1;
      if (type2Better)
        ++score2;
      continue;
    }

    // A concrete type is better than an archetype.
    // FIXME: Total hack.
    if (type1->is<ArchetypeType>() != type2->is<ArchetypeType>()) {
      if (type1->is<ArchetypeType>())
        ++score2;
      else
        ++score1;
      continue;
    }
  }

  // FIXME: There are type variables and overloads not common to both solutions
  // that haven't been considered. They make the systems different, but don't
  // affect ranking. We need to handle this.

  // If the scores are different, we have a winner.
  if (score1 != score2) {
    return score1 > score2? SolutionCompareResult::Better
                          : SolutionCompareResult::Worse;
  }

  // Neither system wins; report whether they were identical or not.
  return identical? SolutionCompareResult::Identical
                  : SolutionCompareResult::Incomparable;
}

Optional<unsigned>
ConstraintSystem::findBestSolution(SmallVectorImpl<Solution> &viable,
                                   bool minimize) {
  if (viable.empty())
    return Nothing;
  if (viable.size() == 1)
    return 0;

  SolutionDiff diff(viable);

  // Find a potential best.
  SmallVector<bool, 16> losers(viable.size(), false);
  unsigned bestIdx = 0;
  for (unsigned i = 1, n = viable.size(); i != n; ++i) {
    switch (compareSolutions(*this, viable, diff, i, bestIdx)) {
    case SolutionCompareResult::Identical:
      // FIXME: Might want to warn about this in debug builds, so we can
      // find a way to eliminate the redundancy in the search space.
    case SolutionCompareResult::Incomparable:
        break;

    case SolutionCompareResult::Worse:
      losers[i] = true;
      break;

    case SolutionCompareResult::Better:
      losers[bestIdx] = true;
      bestIdx = i;
      break;
    }
  }

  // Make sure that our current best is better than all of the solved systems.
  bool ambiguous = false;
  for (unsigned i = 0, n = viable.size(); i != n && !ambiguous; ++i) {
    if (i == bestIdx)
      continue;

    switch (compareSolutions(*this, viable, diff, bestIdx, i)) {
    case SolutionCompareResult::Identical:
      // FIXME: Might want to warn about this in debug builds, so we can
      // find a way to eliminate the redundancy in the search space.
      break;

    case SolutionCompareResult::Better:
      losers[i] = true;
      break;

    case SolutionCompareResult::Worse:
      losers[bestIdx] = true;
      SWIFT_FALLTHROUGH;

    case SolutionCompareResult::Incomparable:
      // If we're not supposed to minimize the result set, just return eagerly.
      if (!minimize)
        return Nothing;

      ambiguous = true;
      break;
    }
  }

  // If the result was not ambiguous, we're done.
  if (!ambiguous) {
    NumDiscardedSolutions += viable.size() - 1;
    return bestIdx;
  }

  // The comparison was ambiguous. Identify any solutions that are worse than
  // any other solution.
  for (unsigned i = 0, n = viable.size(); i != n; ++i) {
    // If the first solution has already lost once, don't bother looking
    // further.
    if (losers[i])
      continue;

    for (unsigned j = i + 1; j != n; ++j) {
      // If the second solution has already lost once, don't bother looking
      // further.
      if (losers[j])
        continue;

      switch (compareSolutions(*this, viable, diff, i, j)) {
      case SolutionCompareResult::Identical:
        // FIXME: Dub one of these the loser arbitrarily?
        break;

      case SolutionCompareResult::Better:
        losers[j] = true;
        break;

      case SolutionCompareResult::Worse:
        losers[i] = true;
        break;

      case SolutionCompareResult::Incomparable:
        break;
      }
    }
  }

  // Remove any solution that is worse than some other solution.
  unsigned outIndex = 0;
  for (unsigned i = 0, n = viable.size(); i != n; ++i) {
    // Skip over the losing solutions.
    if (losers[i])
      continue;

    // If we have skipped any solutions, move this solution into the next
    // open position.
    if (outIndex < i)
      viable[outIndex] = std::move(viable[i]);

    ++outIndex;
  }
  viable.erase(viable.begin() + outIndex, viable.end());
  NumDiscardedSolutions += viable.size() - outIndex;

  return Nothing;
}

SolutionDiff::SolutionDiff(ArrayRef<Solution> solutions)  {
  if (solutions.size() <= 1)
    return;

  // Populate the type bindings with the first solution.
  llvm::DenseMap<TypeVariableType *, SmallVector<Type, 2>> typeBindings;
  for (auto binding : solutions[0].typeBindings) {
    typeBindings[binding.first].push_back(binding.second);
  }

  // Populate the overload choices with the first solution.
  llvm::DenseMap<ConstraintLocator *, SmallVector<OverloadChoice, 2>>
    overloadChoices;
  for (auto choice : solutions[0].overloadChoices) {
    overloadChoices[choice.first].push_back(choice.second.choice);
  }

  // Find the type variables and overload locators common to all of the
  // solutions.
  for (auto &solution : solutions.slice(1)) {
    // For each type variable bound in all of the previous solutions, check
    // whether we have a binding for this type variable in this solution.
    SmallVector<TypeVariableType *, 4> removeTypeBindings;
    for (auto &binding : typeBindings) {
      auto known = solution.typeBindings.find(binding.first);
      if (known == solution.typeBindings.end()) {
        removeTypeBindings.push_back(binding.first);
        continue;
      }

      // Add this solution's binding to the results.
      binding.second.push_back(known->second);
    }

    // Remove those type variables for which this solution did not have a
    // binding.
    for (auto typeVar : removeTypeBindings) {
      typeBindings.erase(typeVar);
    }
    removeTypeBindings.clear();

    // For each overload locator for which we have an overload choice in
    // all of the previous solutions. Check whether we have an overload choice
    // in this solution.
    SmallVector<ConstraintLocator *, 4> removeOverloadChoices;
    for (auto &overloadChoice : overloadChoices) {
      auto known = solution.overloadChoices.find(overloadChoice.first);
      if (known == solution.overloadChoices.end()) {
        removeOverloadChoices.push_back(overloadChoice.first);
        continue;
      }

      // Add this solution's overload choice to the results.
      overloadChoice.second.push_back(known->second.choice);
    }

    // Remove those overload locators for which this solution did not have
    // an overload choice.
    for (auto overloadChoice : removeOverloadChoices) {
      overloadChoices.erase(overloadChoice);
    }
  }

  // Look through the type variables that have bindings in all of the
  // solutions, and add those that have differences to the diff.
  for (auto &binding : typeBindings) {
    Type singleType;
    for (auto type : binding.second) {
      if (!singleType)
        singleType = type;
      else if (!singleType->isEqual(type)) {
        // We have a difference. Add this binding to the diff.
        this->typeBindings.push_back(
          SolutionDiff::TypeBindingDiff{
            binding.first,
            std::move(binding.second)
          });

        break;
      }
    }
  }

  // Look through the overload locators that have overload choices in all of
  // the solutions, and add those that have differences to the diff.
  for (auto &overloadChoice : overloadChoices) {
    OverloadChoice singleChoice = overloadChoice.second[0];
    for (auto choice : overloadChoice.second) {
      if (!sameOverloadChoice(singleChoice, choice)) {
        // We have a difference. Add this set of overload choices to the diff.
        this->overloads.push_back(
          SolutionDiff::OverloadDiff{
            overloadChoice.first,
            overloadChoice.second
          });
        
      }
    }
  }
}