How are C# Local Functions Implemented

AddFive.cs

public static int AddFive(int a)
{
    // object of a compiler-generated type is created
    // reference to a compiler-generated method
    return Program.<AddFive>g__InnerAdd1_0(5, ref new Program.<>c__DisplayClass1_0()
    {
        a = a
    });
}

AddFive.Decompiled.cs

public static int AddFive(int a)
{
   // object of a compiler-generated type is created
   Program.<>c__DisplayClass1_0 cDisplayClass10 = new Program.<>c__DisplayClass1_0();
   // reference to a compiler-generated field
   cDisplayClass10.a = a;
   // reference to a compiler-generated method
   Program.<AddFive>g__InnerAdd1_0(5, ref cDisplayClass10);
   // reference to a compiler-generated field
   return cDisplayClass10.a;
}

AddFive.WithMutation.cs

public static int AddFive(int a)
{
    void InnerAdd(int b) => a += b;

    InnerAdd(5);

    return a;
}

GeneratedMethod.cs

.method assembly hidebysig static int32
    '<AddFive>g__InnerAdd1_0'(
      int32 b,
      [in] valuetype Demo.Program/'<>c__DisplayClass1_0'& obj1
    ) cil managed
  {
    .custom instance void
      [mscorlib]System.Runtime.CompilerServices.CompilerGeneratedAttribute::.ctor()
      = (01 00 00 00 )
    .maxstack 8

    IL_0000: ldarg.1      // obj1
    IL_0001: ldfld        int32 Demo.Program/'<>c__DisplayClass1_0'::a
    IL_0006: ldarg.0      // b
    IL_0007: add
    IL_0008: ret

  } // end of method Program::'<AddFive>g__InnerAdd1_0'

GeneratedType.cs

.class nested private sealed auto ansi beforefieldinit
  '<>c__DisplayClass1_0'
    extends [mscorlib]System.ValueType
{
  .custom instance void
    [mscorlib]System.Runtime.CompilerServices.CompilerGeneratedAttribute::.ctor()
    = (01 00 00 00 )

  .field public int32 a
}

Program.cs

class Program
{
    static void Main(string[] args)
    {
        Console.WriteLine(AddFive(7));
    }

    static int AddFive(int a)
    {
        // the local function declaration
        int InnerAdd(int b) => a + b;

        return InnerAdd(5);
    }
}