clang/lib/Sema/SemaConcept.cpp

//===-- SemaConcept.cpp - Semantic Analysis for Constraints and Concepts --===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
//  This file implements semantic analysis for C++ constraints and concepts.
//
//===----------------------------------------------------------------------===//

#include "clang/Sema/Sema.h"
#include "clang/Sema/SemaInternal.h"
#include "clang/Sema/SemaDiagnostic.h"
#include "clang/Sema/TemplateDeduction.h"
#include "clang/Sema/Template.h"
#include "clang/AST/ExprCXX.h"
#include "clang/AST/RecursiveASTVisitor.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/PointerUnion.h"
using namespace clang;
using namespace sema;

bool Sema::CheckConstraintExpression(Expr *ConstraintExpression) {
  // C++2a [temp.constr.atomic]p1
  // ..E shall be a constant expression of type bool.

  ConstraintExpression = ConstraintExpression->IgnoreParenImpCasts();

  if (auto *BinOp = dyn_cast<BinaryOperator>(ConstraintExpression)) {
    if (BinOp->getOpcode() == BO_LAnd || BinOp->getOpcode() == BO_LOr)
      return CheckConstraintExpression(BinOp->getLHS()) &&
             CheckConstraintExpression(BinOp->getRHS());
  } else if (auto *C = dyn_cast<ExprWithCleanups>(ConstraintExpression))
    return CheckConstraintExpression(C->getSubExpr());

  // An atomic constraint!
  if (ConstraintExpression->isTypeDependent())
    return true;

  QualType Type = ConstraintExpression->getType();
  if (!Context.hasSameUnqualifiedType(Type, Context.BoolTy)) {
    Diag(ConstraintExpression->getExprLoc(),
         diag::err_non_bool_atomic_constraint) << Type
        << ConstraintExpression->getSourceRange();
    return false;
  }
  return true;
}

template <typename AtomicEvaluator>
static bool
calculateConstraintSatisfaction(Sema &S, const Expr *ConstraintExpr,
                                ConstraintSatisfaction &Satisfaction,
                                AtomicEvaluator &&Evaluator) {
  ConstraintExpr = ConstraintExpr->IgnoreParenImpCasts();

  if (auto *BO = dyn_cast<BinaryOperator>(ConstraintExpr)) {
    if (BO->getOpcode() == BO_LAnd || BO->getOpcode() == BO_LOr) {
      if (calculateConstraintSatisfaction(S, BO->getLHS(), Satisfaction,
                                          Evaluator))
        return true;

      bool IsLHSSatisfied = Satisfaction.IsSatisfied;

      if (BO->getOpcode() == BO_LOr && IsLHSSatisfied)
        // [temp.constr.op] p3
        //    A disjunction is a constraint taking two operands. To determine if
        //    a disjunction is satisfied, the satisfaction of the first operand
        //    is checked. If that is satisfied, the disjunction is satisfied.
        //    Otherwise, the disjunction is satisfied if and only if the second
        //    operand is satisfied.
        return false;

      if (BO->getOpcode() == BO_LAnd && !IsLHSSatisfied)
        // [temp.constr.op] p2
        //    A conjunction is a constraint taking two operands. To determine if
        //    a conjunction is satisfied, the satisfaction of the first operand
        //    is checked. If that is not satisfied, the conjunction is not
        //    satisfied. Otherwise, the conjunction is satisfied if and only if
        //    the second operand is satisfied.
        return false;

      return calculateConstraintSatisfaction(S, BO->getRHS(), Satisfaction,
          std::forward<AtomicEvaluator>(Evaluator));
    }
  }
  else if (auto *C = dyn_cast<ExprWithCleanups>(ConstraintExpr))
    return calculateConstraintSatisfaction(S, C->getSubExpr(), Satisfaction,
        std::forward<AtomicEvaluator>(Evaluator));

  // An atomic constraint expression
  ExprResult SubstitutedAtomicExpr = Evaluator(ConstraintExpr);

  if (SubstitutedAtomicExpr.isInvalid())
    return true;

  if (!SubstitutedAtomicExpr.isUsable())
    // Evaluator has decided satisfaction without yielding an expression.
    return false;

  EnterExpressionEvaluationContext ConstantEvaluated(
      S, Sema::ExpressionEvaluationContext::ConstantEvaluated);
  SmallVector<PartialDiagnosticAt, 2> EvaluationDiags;
  Expr::EvalResult EvalResult;
  EvalResult.Diag = &EvaluationDiags;
  if (!SubstitutedAtomicExpr.get()->EvaluateAsRValue(EvalResult, S.Context)) {
      // C++2a [temp.constr.atomic]p1
      //   ...E shall be a constant expression of type bool.
    S.Diag(SubstitutedAtomicExpr.get()->getBeginLoc(),
           diag::err_non_constant_constraint_expression)
        << SubstitutedAtomicExpr.get()->getSourceRange();
    for (const PartialDiagnosticAt &PDiag : EvaluationDiags)
      S.Diag(PDiag.first, PDiag.second);
    return true;
  }

  Satisfaction.IsSatisfied = EvalResult.Val.getInt().getBoolValue();
  if (!Satisfaction.IsSatisfied)
    Satisfaction.Details.emplace_back(ConstraintExpr,
                                      SubstitutedAtomicExpr.get());

  return false;
}

template <typename TemplateDeclT>
static bool calculateConstraintSatisfaction(
    Sema &S, TemplateDeclT *Template, ArrayRef<TemplateArgument> TemplateArgs,
    SourceLocation TemplateNameLoc, MultiLevelTemplateArgumentList &MLTAL,
    const Expr *ConstraintExpr, ConstraintSatisfaction &Satisfaction) {
  return calculateConstraintSatisfaction(
      S, ConstraintExpr, Satisfaction, [&](const Expr *AtomicExpr) {
        EnterExpressionEvaluationContext ConstantEvaluated(
            S, Sema::ExpressionEvaluationContext::ConstantEvaluated);

        // Atomic constraint - substitute arguments and check satisfaction.
        ExprResult SubstitutedExpression;
        {
          TemplateDeductionInfo Info(TemplateNameLoc);
          Sema::InstantiatingTemplate Inst(S, AtomicExpr->getBeginLoc(),
              Sema::InstantiatingTemplate::ConstraintSubstitution{}, Template,
              Info, AtomicExpr->getSourceRange());
          if (Inst.isInvalid())
            return ExprError();
          // We do not want error diagnostics escaping here.
          Sema::SFINAETrap Trap(S);
          SubstitutedExpression = S.SubstExpr(const_cast<Expr *>(AtomicExpr),
                                              MLTAL);
          if (SubstitutedExpression.isInvalid() || Trap.hasErrorOccurred()) {
            // C++2a [temp.constr.atomic]p1
            //   ...If substitution results in an invalid type or expression, the
            //   constraint is not satisfied.
            if (!Trap.hasErrorOccurred())
              // A non-SFINAE error has occured as a result of this
              // substitution.
              return ExprError();

            PartialDiagnosticAt SubstDiag{SourceLocation(),
                                          PartialDiagnostic::NullDiagnostic()};
            Info.takeSFINAEDiagnostic(SubstDiag);
            // FIXME: Concepts: This is an unfortunate consequence of there
            //  being no serialization code for PartialDiagnostics and the fact
            //  that serializing them would likely take a lot more storage than
            //  just storing them as strings. We would still like, in the
            //  future, to serialize the proper PartialDiagnostic as serializing
            //  it as a string defeats the purpose of the diagnostic mechanism.
            SmallString<128> DiagString;
            DiagString = ": ";
            SubstDiag.second.EmitToString(S.getDiagnostics(), DiagString);
            unsigned MessageSize = DiagString.size();
            char *Mem = new (S.Context) char[MessageSize];
            memcpy(Mem, DiagString.c_str(), MessageSize);
            Satisfaction.Details.emplace_back(
                AtomicExpr,
                new (S.Context) ConstraintSatisfaction::SubstitutionDiagnostic{
                        SubstDiag.first, StringRef(Mem, MessageSize)});
            Satisfaction.IsSatisfied = false;
            return ExprEmpty();
          }
        }

        if (!S.CheckConstraintExpression(SubstitutedExpression.get()))
          return ExprError();

        return SubstitutedExpression;
      });
}

template<typename TemplateDeclT>
static bool CheckConstraintSatisfaction(Sema &S, TemplateDeclT *Template,
                                        ArrayRef<const Expr *> ConstraintExprs,
                                        ArrayRef<TemplateArgument> TemplateArgs,
                                        SourceRange TemplateIDRange,
                                        ConstraintSatisfaction &Satisfaction) {
  if (ConstraintExprs.empty()) {
    Satisfaction.IsSatisfied = true;
    return false;
  }

  for (auto& Arg : TemplateArgs)
    if (Arg.isInstantiationDependent()) {
      // No need to check satisfaction for dependent constraint expressions.
      Satisfaction.IsSatisfied = true;
      return false;
    }

  Sema::InstantiatingTemplate Inst(S, TemplateIDRange.getBegin(),
      Sema::InstantiatingTemplate::ConstraintsCheck{}, Template, TemplateArgs,
      TemplateIDRange);
  if (Inst.isInvalid())
    return true;

  MultiLevelTemplateArgumentList MLTAL;
  MLTAL.addOuterTemplateArguments(TemplateArgs);

  for (const Expr *ConstraintExpr : ConstraintExprs) {
    if (calculateConstraintSatisfaction(S, Template, TemplateArgs,
                                        TemplateIDRange.getBegin(), MLTAL,
                                        ConstraintExpr, Satisfaction))
      return true;
    if (!Satisfaction.IsSatisfied)
      // [temp.constr.op] p2
      //   [...] To determine if a conjunction is satisfied, the satisfaction
      //   of the first operand is checked. If that is not satisfied, the
      //   conjunction is not satisfied. [...]
      return false;
  }
  return false;
}

bool Sema::CheckConstraintSatisfaction(TemplateDecl *Template,
                                       ArrayRef<const Expr *> ConstraintExprs,
                                       ArrayRef<TemplateArgument> TemplateArgs,
                                       SourceRange TemplateIDRange,
                                       ConstraintSatisfaction &Satisfaction) {
  return ::CheckConstraintSatisfaction(*this, Template, ConstraintExprs,
                                       TemplateArgs, TemplateIDRange,
                                       Satisfaction);
}

bool
Sema::CheckConstraintSatisfaction(ClassTemplatePartialSpecializationDecl* Part,
                                  ArrayRef<const Expr *> ConstraintExprs,
                                  ArrayRef<TemplateArgument> TemplateArgs,
                                  SourceRange TemplateIDRange,
                                  ConstraintSatisfaction &Satisfaction) {
  return ::CheckConstraintSatisfaction(*this, Part, ConstraintExprs,
                                       TemplateArgs, TemplateIDRange,
                                       Satisfaction);
}

bool
Sema::CheckConstraintSatisfaction(VarTemplatePartialSpecializationDecl* Partial,
                                  ArrayRef<const Expr *> ConstraintExprs,
                                  ArrayRef<TemplateArgument> TemplateArgs,
                                  SourceRange TemplateIDRange,
                                  ConstraintSatisfaction &Satisfaction) {
  return ::CheckConstraintSatisfaction(*this, Partial, ConstraintExprs,
                                       TemplateArgs, TemplateIDRange,
                                       Satisfaction);
}

bool Sema::CheckConstraintSatisfaction(const Expr *ConstraintExpr,
                                       ConstraintSatisfaction &Satisfaction) {
  return calculateConstraintSatisfaction(
      *this, ConstraintExpr, Satisfaction,
      [](const Expr *AtomicExpr) -> ExprResult {
        return ExprResult(const_cast<Expr *>(AtomicExpr));
      });
}

bool Sema::EnsureTemplateArgumentListConstraints(
    TemplateDecl *TD, ArrayRef<TemplateArgument> TemplateArgs,
    SourceRange TemplateIDRange) {
  ConstraintSatisfaction Satisfaction;
  llvm::SmallVector<const Expr *, 3> AssociatedConstraints;
  TD->getAssociatedConstraints(AssociatedConstraints);
  if (CheckConstraintSatisfaction(TD, AssociatedConstraints, TemplateArgs,
                                  TemplateIDRange, Satisfaction))
    return true;

  if (!Satisfaction.IsSatisfied) {
    SmallString<128> TemplateArgString;
    TemplateArgString = " ";
    TemplateArgString += getTemplateArgumentBindingsText(
        TD->getTemplateParameters(), TemplateArgs.data(), TemplateArgs.size());

    Diag(TemplateIDRange.getBegin(),
         diag::err_template_arg_list_constraints_not_satisfied)
        << (int)getTemplateNameKindForDiagnostics(TemplateName(TD)) << TD
        << TemplateArgString << TemplateIDRange;
    DiagnoseUnsatisfiedConstraint(Satisfaction);
    return true;
  }
  return false;
}

static void diagnoseWellFormedUnsatisfiedConstraintExpr(Sema &S,
                                                        Expr *SubstExpr,
                                                        bool First = true) {
  SubstExpr = SubstExpr->IgnoreParenImpCasts();
  if (BinaryOperator *BO = dyn_cast<BinaryOperator>(SubstExpr)) {
    switch (BO->getOpcode()) {
    // These two cases will in practice only be reached when using fold
    // expressions with || and &&, since otherwise the || and && will have been
    // broken down into atomic constraints during satisfaction checking.
    case BO_LOr:
      // Or evaluated to false - meaning both RHS and LHS evaluated to false.
      diagnoseWellFormedUnsatisfiedConstraintExpr(S, BO->getLHS(), First);
      diagnoseWellFormedUnsatisfiedConstraintExpr(S, BO->getRHS(),
                                                  /*First=*/false);
      return;
    case BO_LAnd:
      bool LHSSatisfied;
      BO->getLHS()->EvaluateAsBooleanCondition(LHSSatisfied, S.Context);
      if (LHSSatisfied) {
        // LHS is true, so RHS must be false.
        diagnoseWellFormedUnsatisfiedConstraintExpr(S, BO->getRHS(), First);
        return;
      }
      // LHS is false
      diagnoseWellFormedUnsatisfiedConstraintExpr(S, BO->getLHS(), First);

      // RHS might also be false
      bool RHSSatisfied;
      BO->getRHS()->EvaluateAsBooleanCondition(RHSSatisfied, S.Context);
      if (!RHSSatisfied)
        diagnoseWellFormedUnsatisfiedConstraintExpr(S, BO->getRHS(),
                                                    /*First=*/false);
      return;
    case BO_GE:
    case BO_LE:
    case BO_GT:
    case BO_LT:
    case BO_EQ:
    case BO_NE:
      if (BO->getLHS()->getType()->isIntegerType() &&
          BO->getRHS()->getType()->isIntegerType()) {
        Expr::EvalResult SimplifiedLHS;
        Expr::EvalResult SimplifiedRHS;
        BO->getLHS()->EvaluateAsInt(SimplifiedLHS, S.Context);
        BO->getRHS()->EvaluateAsInt(SimplifiedRHS, S.Context);
        if (!SimplifiedLHS.Diag && ! SimplifiedRHS.Diag) {
          S.Diag(SubstExpr->getBeginLoc(),
                 diag::note_atomic_constraint_evaluated_to_false_elaborated)
              << (int)First << SubstExpr
              << SimplifiedLHS.Val.getInt().toString(10)
              << BinaryOperator::getOpcodeStr(BO->getOpcode())
              << SimplifiedRHS.Val.getInt().toString(10);
          return;
        }
      }
      break;

    default:
      break;
    }
  } else if (auto *CSE = dyn_cast<ConceptSpecializationExpr>(SubstExpr)) {
    if (CSE->getTemplateArgsAsWritten()->NumTemplateArgs == 1) {
      S.Diag(
          CSE->getSourceRange().getBegin(),
          diag::
          note_single_arg_concept_specialization_constraint_evaluated_to_false)
          << (int)First
          << CSE->getTemplateArgsAsWritten()->arguments()[0].getArgument()
          << CSE->getNamedConcept();
    } else {
      S.Diag(SubstExpr->getSourceRange().getBegin(),
             diag::note_concept_specialization_constraint_evaluated_to_false)
          << (int)First << CSE;
    }
    S.DiagnoseUnsatisfiedConstraint(CSE->getSatisfaction());
    return;
  }

  S.Diag(SubstExpr->getSourceRange().getBegin(),
         diag::note_atomic_constraint_evaluated_to_false)
      << (int)First << SubstExpr;
}

template<typename SubstitutionDiagnostic>
static void diagnoseUnsatisfiedConstraintExpr(
    Sema &S, const Expr *E,
    const llvm::PointerUnion<Expr *, SubstitutionDiagnostic *> &Record,
    bool First = true) {
  if (auto *Diag = Record.template dyn_cast<SubstitutionDiagnostic *>()){
    S.Diag(Diag->first, diag::note_substituted_constraint_expr_is_ill_formed)
        << Diag->second;
    return;
  }

  diagnoseWellFormedUnsatisfiedConstraintExpr(S,
      Record.template get<Expr *>(), First);
}

void Sema::DiagnoseUnsatisfiedConstraint(
    const ConstraintSatisfaction& Satisfaction) {
  assert(!Satisfaction.IsSatisfied &&
         "Attempted to diagnose a satisfied constraint");
  bool First = true;
  for (auto &Pair : Satisfaction.Details) {
    diagnoseUnsatisfiedConstraintExpr(*this, Pair.first, Pair.second, First);
    First = false;
  }
}

void Sema::DiagnoseUnsatisfiedConstraint(
    const ASTConstraintSatisfaction &Satisfaction) {
  assert(!Satisfaction.IsSatisfied &&
         "Attempted to diagnose a satisfied constraint");
  bool First = true;
  for (auto &Pair : Satisfaction) {
    diagnoseUnsatisfiedConstraintExpr(*this, Pair.first, Pair.second, First);
    First = false;
  }
}

namespace {
struct AtomicConstraint {
  const Expr *ConstraintExpr;
  llvm::Optional<llvm::SmallVector<TemplateArgumentLoc, 3>> ParameterMapping;

  AtomicConstraint(Sema &S, const Expr *ConstraintExpr) :
      ConstraintExpr(ConstraintExpr) { };

  bool hasMatchingParameterMapping(ASTContext &C,
                                   const AtomicConstraint &Other) const {
    if (!ParameterMapping != !Other.ParameterMapping)
      return false;
    if (!ParameterMapping)
      return true;
    if (ParameterMapping->size() != Other.ParameterMapping->size())
      return false;

    for (unsigned I = 0, S = ParameterMapping->size(); I < S; ++I)
      if (!C.getCanonicalTemplateArgument((*ParameterMapping)[I].getArgument())
               .structurallyEquals(C.getCanonicalTemplateArgument(
                  (*Other.ParameterMapping)[I].getArgument())))
        return false;
    return true;
  }

  bool subsumes(ASTContext &C, const AtomicConstraint &Other) const {
    // C++ [temp.constr.order] p2
    //   - an atomic constraint A subsumes another atomic constraint B
    //     if and only if the A and B are identical [...]
    //
    // C++ [temp.constr.atomic] p2
    //   Two atomic constraints are identical if they are formed from the
    //   same expression and the targets of the parameter mappings are
    //   equivalent according to the rules for expressions [...]

    // We do not actually substitute the parameter mappings into the
    // constraint expressions, therefore the constraint expressions are
    // the originals, and comparing them will suffice.
    if (ConstraintExpr != Other.ConstraintExpr)
      return false;

    // Check that the parameter lists are identical
    return hasMatchingParameterMapping(C, Other);
  }
};

/// \brief A normalized constraint, as defined in C++ [temp.constr.normal], is
/// either an atomic constraint, a conjunction of normalized constraints or a
/// disjunction of normalized constraints.
struct NormalizedConstraint {
  enum CompoundConstraintKind { CCK_Conjunction, CCK_Disjunction };

  using CompoundConstraint = llvm::PointerIntPair<
      std::pair<NormalizedConstraint, NormalizedConstraint> *, 1,
      CompoundConstraintKind>;

  llvm::PointerUnion<AtomicConstraint *, CompoundConstraint> Constraint;

  NormalizedConstraint(AtomicConstraint *C): Constraint{C} { };
  NormalizedConstraint(ASTContext &C, NormalizedConstraint LHS,
                       NormalizedConstraint RHS, CompoundConstraintKind Kind)
      : Constraint{CompoundConstraint{
            new (C) std::pair<NormalizedConstraint, NormalizedConstraint>{LHS,
                                                                          RHS},
            Kind}} { };

  CompoundConstraintKind getCompoundKind() const {
    assert(!isAtomic() && "getCompoundKind called on atomic constraint.");
    return Constraint.get<CompoundConstraint>().getInt();
  }

  bool isAtomic() const { return Constraint.is<AtomicConstraint *>(); }

  NormalizedConstraint &getLHS() const {
    assert(!isAtomic() && "getLHS called on atomic constraint.");
    return Constraint.get<CompoundConstraint>().getPointer()->first;
  }

  NormalizedConstraint &getRHS() const {
    assert(!isAtomic() && "getRHS called on atomic constraint.");
    return Constraint.get<CompoundConstraint>().getPointer()->second;
  }

  AtomicConstraint *getAtomicConstraint() const {
    assert(isAtomic() &&
           "getAtomicConstraint called on non-atomic constraint.");
    return Constraint.get<AtomicConstraint *>();
  }

  static llvm::Optional<NormalizedConstraint>
  fromConstraintExprs(Sema &S, NamedDecl *D, ArrayRef<const Expr *> E) {
    assert(E.size() != 0);
    auto First = fromConstraintExpr(S, D, E[0]);
    if (E.size() == 1)
      return First;
    auto Second = fromConstraintExpr(S, D, E[1]);
    if (!Second)
      return llvm::Optional<NormalizedConstraint>{};
    llvm::Optional<NormalizedConstraint> Conjunction;
    Conjunction.emplace(S.Context, std::move(*First), std::move(*Second),
                        CCK_Conjunction);
    for (unsigned I = 2; I < E.size(); ++I) {
      auto Next = fromConstraintExpr(S, D, E[I]);
      if (!Next)
        return llvm::Optional<NormalizedConstraint>{};
      NormalizedConstraint NewConjunction(S.Context, std::move(*Conjunction),
                                          std::move(*Next), CCK_Conjunction);
      *Conjunction = std::move(NewConjunction);
    }
    return Conjunction;
  }

private:
  static llvm::Optional<NormalizedConstraint> fromConstraintExpr(Sema &S,
                                                                 NamedDecl *D,
                                                                 const Expr *E);
};

static bool substituteParameterMappings(Sema &S, NormalizedConstraint &N,
    ConceptDecl *Concept, ArrayRef<TemplateArgument> TemplateArgs,
    const ASTTemplateArgumentListInfo *ArgsAsWritten) {
  if (!N.isAtomic()) {
    if (substituteParameterMappings(S, N.getLHS(), Concept, TemplateArgs,
                                    ArgsAsWritten))
      return true;
    return substituteParameterMappings(S, N.getRHS(), Concept, TemplateArgs,
                                       ArgsAsWritten);
  }
  TemplateParameterList *TemplateParams = Concept->getTemplateParameters();

  AtomicConstraint &Atomic = *N.getAtomicConstraint();
  TemplateArgumentListInfo SubstArgs;
  MultiLevelTemplateArgumentList MLTAL;
  MLTAL.addOuterTemplateArguments(TemplateArgs);
  if (!Atomic.ParameterMapping) {
    llvm::SmallBitVector OccurringIndices(TemplateParams->size());
    S.MarkUsedTemplateParameters(Atomic.ConstraintExpr, /*OnlyDeduced=*/false,
                                 /*Depth=*/0, OccurringIndices);
    Atomic.ParameterMapping.emplace();
    Atomic.ParameterMapping->reserve(OccurringIndices.size());
    for (unsigned I = 0, C = TemplateParams->size(); I != C; ++I)
      if (OccurringIndices[I])
        Atomic.ParameterMapping->push_back(
            S.getIdentityTemplateArgumentLoc(TemplateParams->begin()[I],
                // Here we assume we do not support things like
                // template<typename A, typename B>
                // concept C = ...;
                //
                // template<typename... Ts> requires C<Ts...>
                // struct S { };
                // The above currently yields a diagnostic.
                // We still might have default arguments for concept parameters.
                ArgsAsWritten->NumTemplateArgs > I ?
                ArgsAsWritten->arguments()[I].getLocation() :
                SourceLocation()));
  }
  Sema::InstantiatingTemplate Inst(
      S, ArgsAsWritten->arguments().front().getSourceRange().getBegin(),
      Sema::InstantiatingTemplate::ParameterMappingSubstitution{}, Concept,
      SourceRange(ArgsAsWritten->arguments()[0].getSourceRange().getBegin(),
                  ArgsAsWritten->arguments().back().getSourceRange().getEnd()));
  if (S.SubstTemplateArguments(*Atomic.ParameterMapping, MLTAL, SubstArgs))
    return true;
  std::copy(SubstArgs.arguments().begin(), SubstArgs.arguments().end(),
            N.getAtomicConstraint()->ParameterMapping->begin());
  return false;
}

llvm::Optional<NormalizedConstraint>
NormalizedConstraint::fromConstraintExpr(Sema &S, NamedDecl *D, const Expr *E) {
  assert(E != nullptr);

  // C++ [temp.constr.normal]p1.1
  // [...]
  // - The normal form of an expression (E) is the normal form of E.
  // [...]
  E = E->IgnoreParenImpCasts();
  if (auto *BO = dyn_cast<const BinaryOperator>(E)) {
    if (BO->getOpcode() == BO_LAnd || BO->getOpcode() == BO_LOr) {
      auto LHS = fromConstraintExpr(S, D, BO->getLHS());
      if (!LHS)
        return None;
      auto RHS = fromConstraintExpr(S, D, BO->getRHS());
      if (!RHS)
        return None;

      return NormalizedConstraint(
          S.Context, *LHS, *RHS,
          BO->getOpcode() == BO_LAnd ? CCK_Conjunction : CCK_Disjunction);
    }
  } else if (auto *CSE = dyn_cast<const ConceptSpecializationExpr>(E)) {
    Optional<NormalizedConstraint> SubNF;
    {
      Sema::InstantiatingTemplate Inst(
          S, CSE->getExprLoc(),
          Sema::InstantiatingTemplate::ConstraintNormalization{}, D,
          CSE->getSourceRange());
      // C++ [temp.constr.normal]p1.1
      // [...]
      // The normal form of an id-expression of the form C<A1, A2, ..., AN>,
      // where C names a concept, is the normal form of the
      // constraint-expression of C, after substituting A1, A2, ..., AN for C’s
      // respective template parameters in the parameter mappings in each atomic
      // constraint. If any such substitution results in an invalid type or
      // expression, the program is ill-formed; no diagnostic is required.
      // [...]
      SubNF = fromConstraintExpr(S, CSE->getNamedConcept(),
                                 CSE->getNamedConcept()->getConstraintExpr());
      if (!SubNF)
        return None;
    }

    if (substituteParameterMappings(
            S, *SubNF, CSE->getNamedConcept(),
            CSE->getTemplateArguments(), CSE->getTemplateArgsAsWritten()))
      return None;

    return SubNF;
  }
  return NormalizedConstraint{new (S.Context) AtomicConstraint(S, E)};
}

} // namespace

using NormalForm =
    llvm::SmallVector<llvm::SmallVector<AtomicConstraint *, 2>, 4>;

static NormalForm makeCNF(const NormalizedConstraint &Normalized) {
  if (Normalized.isAtomic())
    return {{Normalized.getAtomicConstraint()}};

  NormalForm LCNF = makeCNF(Normalized.getLHS());
  NormalForm RCNF = makeCNF(Normalized.getRHS());
  if (Normalized.getCompoundKind() == NormalizedConstraint::CCK_Conjunction) {
    LCNF.reserve(LCNF.size() + RCNF.size());
    while (!RCNF.empty())
      LCNF.push_back(RCNF.pop_back_val());
    return LCNF;
  }

  // Disjunction
  NormalForm Res;
  Res.reserve(LCNF.size() * RCNF.size());
  for (auto &LDisjunction : LCNF)
    for (auto &RDisjunction : RCNF) {
      NormalForm::value_type Combined;
      Combined.reserve(LDisjunction.size() + RDisjunction.size());
      std::copy(LDisjunction.begin(), LDisjunction.end(),
                std::back_inserter(Combined));
      std::copy(RDisjunction.begin(), RDisjunction.end(),
                std::back_inserter(Combined));
      Res.emplace_back(Combined);
    }
  return Res;
}

static NormalForm makeDNF(const NormalizedConstraint &Normalized) {
  if (Normalized.isAtomic())
    return {{Normalized.getAtomicConstraint()}};

  NormalForm LDNF = makeDNF(Normalized.getLHS());
  NormalForm RDNF = makeDNF(Normalized.getRHS());
  if (Normalized.getCompoundKind() == NormalizedConstraint::CCK_Disjunction) {
    LDNF.reserve(LDNF.size() + RDNF.size());
    while (!RDNF.empty())
      LDNF.push_back(RDNF.pop_back_val());
    return LDNF;
  }

  // Conjunction
  NormalForm Res;
  Res.reserve(LDNF.size() * RDNF.size());
  for (auto &LConjunction : LDNF) {
    for (auto &RConjunction : RDNF) {
      NormalForm::value_type Combined;
      Combined.reserve(LConjunction.size() + RConjunction.size());
      std::copy(LConjunction.begin(), LConjunction.end(),
                std::back_inserter(Combined));
      std::copy(RConjunction.begin(), RConjunction.end(),
                std::back_inserter(Combined));
      Res.emplace_back(Combined);
    }
  }
  return Res;
}

static bool subsumes(Sema &S, NamedDecl *DP, ArrayRef<const Expr *> P,
                     NamedDecl *DQ, ArrayRef<const Expr *> Q, bool &Subsumes) {
  // C++ [temp.constr.order] p2
  //   In order to determine if a constraint P subsumes a constraint Q, P is
  //   transformed into disjunctive normal form, and Q is transformed into
  //   conjunctive normal form. [...]
  auto PNormalized = NormalizedConstraint::fromConstraintExprs(S, DP, P);
  if (!PNormalized)
    return true;
  const NormalForm PDNF = makeDNF(*PNormalized);

  auto QNormalized = NormalizedConstraint::fromConstraintExprs(S, DQ, Q);
  if (!QNormalized)
    return true;
  const NormalForm QCNF = makeCNF(*QNormalized);

  // C++ [temp.constr.order] p2
  //   Then, P subsumes Q if and only if, for every disjunctive clause Pi in the
  //   disjunctive normal form of P, Pi subsumes every conjunctive clause Qj in
  //   the conjuctive normal form of Q, where [...]
  for (const auto &Pi : PDNF) {
    for (const auto &Qj : QCNF) {
      // C++ [temp.constr.order] p2
      //   - [...] a disjunctive clause Pi subsumes a conjunctive clause Qj if
      //     and only if there exists an atomic constraint Pia in Pi for which
      //     there exists an atomic constraint, Qjb, in Qj such that Pia
      //     subsumes Qjb.
      bool Found = false;
      for (const AtomicConstraint *Pia : Pi) {
        for (const AtomicConstraint *Qjb : Qj) {
          if (Pia->subsumes(S.Context, *Qjb)) {
            Found = true;
            break;
          }
        }
        if (Found)
          break;
      }
      if (!Found) {
        Subsumes = false;
        return false;
      }
    }
  }
  Subsumes = true;
  return false;
}

bool Sema::IsAtLeastAsConstrained(NamedDecl *D1, ArrayRef<const Expr *> AC1,
                                  NamedDecl *D2, ArrayRef<const Expr *> AC2,
                                  bool &Result) {
  if (AC1.empty()) {
    Result = AC2.empty();
    return false;
  }
  if (AC2.empty()) {
    // TD1 has associated constraints and TD2 does not.
    Result = true;
    return false;
  }

  std::pair<NamedDecl *, NamedDecl *> Key{D1, D2};
  auto CacheEntry = SubsumptionCache.find(Key);
  if (CacheEntry != SubsumptionCache.end()) {
    Result = CacheEntry->second;
    return false;
  }
  if (subsumes(*this, D1, AC1, D2, AC2, Result))
    return true;
  SubsumptionCache.try_emplace(Key, Result);
  return false;
}