Index: llvm/lib/AsmParser/LLParser.cpp
===================================================================
--- llvm/lib/AsmParser/LLParser.cpp
+++ llvm/lib/AsmParser/LLParser.cpp
@@ -1470,15 +1470,26 @@
 
 Value *LLParser::checkValidVariableType(LocTy Loc, const Twine &Name, Type *Ty,
                                         Value *Val, bool IsCall) {
-  if (Val->getType() == Ty)
+  auto CheckType = [&](Type *Ty) {
+    Type *ValTy = Val->getType();
+    if (ValTy == Ty)
+      return true;
+    // For calls, we also allow opaque pointers.
+    if (IsCall && ValTy == PointerType::get(Ty->getContext(),
+                                            Ty->getPointerAddressSpace()))
+      return true;
+    return false;
+  };
+  if (CheckType(Ty))
     return Val;
+
   // For calls we also accept variables in the program address space.
   Type *SuggestedTy = Ty;
   if (IsCall && isa<PointerType>(Ty)) {
     Type *TyInProgAS = cast<PointerType>(Ty)->getElementType()->getPointerTo(
         M->getDataLayout().getProgramAddressSpace());
     SuggestedTy = TyInProgAS;
-    if (Val->getType() == TyInProgAS)
+    if (CheckType(TyInProgAS))
       return Val;
   }
   if (Ty->isLabelTy())
Index: llvm/lib/Bitcode/Reader/BitcodeReader.cpp
===================================================================
--- llvm/lib/Bitcode/Reader/BitcodeReader.cpp
+++ llvm/lib/Bitcode/Reader/BitcodeReader.cpp
@@ -5266,7 +5266,7 @@
             cast<PointerType>(Callee->getType())->getElementType());
         if (!FTy)
           return error("Callee is not of pointer to function type");
-      } else if (cast<PointerType>(Callee->getType())->getElementType() != FTy)
+      } else if (!OpTy->isOpaqueOrPointeeTypeMatches(FTy))
         return error("Explicit call type does not match pointee type of "
                      "callee operand");
       if (Record.size() < FTy->getNumParams() + OpNum)
Index: llvm/lib/Bitcode/Writer/ValueEnumerator.cpp
===================================================================
--- llvm/lib/Bitcode/Writer/ValueEnumerator.cpp
+++ llvm/lib/Bitcode/Writer/ValueEnumerator.cpp
@@ -467,8 +467,10 @@
         if (auto *GEP = dyn_cast<GetElementPtrInst>(&I))
           EnumerateType(GEP->getSourceElementType());
         EnumerateType(I.getType());
-        if (const auto *Call = dyn_cast<CallBase>(&I))
+        if (const auto *Call = dyn_cast<CallBase>(&I)) {
           EnumerateAttributes(Call->getAttributes());
+          EnumerateType(Call->getFunctionType());
+        }
 
         // Enumerate metadata attached with this instruction.
         MDs.clear();
Index: llvm/lib/IR/Verifier.cpp
===================================================================
--- llvm/lib/IR/Verifier.cpp
+++ llvm/lib/IR/Verifier.cpp
@@ -3124,10 +3124,7 @@
          "Called function must be a pointer!", Call);
   PointerType *FPTy = cast<PointerType>(Call.getCalledOperand()->getType());
 
-  Assert(FPTy->getElementType()->isFunctionTy(),
-         "Called function is not pointer to function type!", Call);
-
-  Assert(FPTy->getElementType() == Call.getFunctionType(),
+  Assert(FPTy->isOpaqueOrPointeeTypeMatches(Call.getFunctionType()),
          "Called function is not the same type as the call!", Call);
 
   FunctionType *FTy = Call.getFunctionType();
Index: llvm/test/Assembler/opaque-ptr.ll
===================================================================
--- llvm/test/Assembler/opaque-ptr.ll
+++ llvm/test/Assembler/opaque-ptr.ll
@@ -98,3 +98,19 @@
     %b = atomicrmw add ptr %a, i32 %i acquire
     ret void
 }
+
+; CHECK: define void @call(ptr %p)
+; CHECK:     call void %p()
+; CHECK:     ret void
+define void @call(ptr %p) {
+  call void %p()
+  ret void
+}
+
+; CHECK: define void @call_arg(ptr %p, i32 %a)
+; CHECK:     call void %p(i32 %a)
+; CHECK:     ret void
+define void @call_arg(ptr %p, i32 %a) {
+  call void %p(i32 %a)
+  ret void
+}