Implement IEquatable<> and IComparable<> for paths

src/Spectre.IO/DirectoryPath.cs

@@ -8,7 +8,7 @@ namespace Spectre.IO;
 /// <summary>
 /// Represents a directory path.
 /// </summary>
-public sealed class DirectoryPath : Path
+public sealed class DirectoryPath : Path, IEquatable<DirectoryPath>, IComparable<DirectoryPath>
 {
     /// <summary>
     /// Gets a value indicating whether or not the current
@@ -240,4 +240,29 @@ public FilePath GetRelativePath(FilePath to)
 
         return GetRelativePath(to.GetDirectory()).GetFilePath(to.GetFilename());
     }
+
+    /// <inheritdoc />
+    public int CompareTo(DirectoryPath? other)
+    {
+        return PathComparer.Default.Compare(this, other);
+    }
+
+    /// <inheritdoc />
+    public bool Equals(DirectoryPath? other)
+    {
+        return PathComparer.Default.Equals(this, other);
+    }
+
+    /// <inheritdoc />
+    public override bool Equals(object? obj)
+    {
+        return ReferenceEquals(this, obj)
+               || (obj is DirectoryPath other && Equals(other));
+    }
+
+    /// <inheritdoc />
+    public override int GetHashCode()
+    {
+        return PathComparer.Default.GetHashCode(this);
+    }
 }

src/Spectre.IO/FilePath.cs

@@ -6,7 +6,7 @@ namespace Spectre.IO;
 /// <summary>
 /// Represents a file path.
 /// </summary>
-public sealed class FilePath : Path
+public sealed class FilePath : Path, IEquatable<FilePath>, IComparable<FilePath>
 {
     /// <summary>
     /// Gets a value indicating whether this path has a file extension.
@@ -240,4 +240,29 @@ public FilePath GetRelativePath(FilePath to)
     {
         return GetDirectory().GetRelativePath(to);
     }
+
+    /// <inheritdoc />
+    public int CompareTo(FilePath? other)
+    {
+        return PathComparer.Default.Compare(this, other);
+    }
+
+    /// <inheritdoc />
+    public bool Equals(FilePath? other)
+    {
+        return PathComparer.Default.Equals(this, other);
+    }
+
+    /// <inheritdoc />
+    public override bool Equals(object? obj)
+    {
+        return ReferenceEquals(this, obj)
+               || (obj is FilePath other && Equals(other));
+    }
+
+    /// <inheritdoc />
+    public override int GetHashCode()
+    {
+        return PathComparer.Default.GetHashCode(this);
+    }
 }

src/Spectre.IO/Path.cs

@@ -8,7 +8,7 @@ namespace Spectre.IO;
 /// Provides properties and instance methods for working with paths.
 /// This class must be inherited.
 /// </summary>
-public abstract class Path
+public abstract class Path : IEquatable<Path>, IComparable<Path>
 {
     private readonly string[] _segments;
 
@@ -135,4 +135,43 @@ public override string ToString()
     {
         return FullPath;
     }
+
+    /// <inheritdoc />
+    public int CompareTo(Path? other)
+    {
+        return PathComparer.Default.Compare(this, other);
+    }
+
+    /// <inheritdoc />
+    public bool Equals(Path? other)
+    {
+        return PathComparer.Default.Equals(this, other);
+    }
+
+    /// <inheritdoc />
+    public override bool Equals(object? obj)
+    {
+        if (ReferenceEquals(null, obj))
+        {
+            return false;
+        }
+
+        if (ReferenceEquals(this, obj))
+        {
+            return true;
+        }
+
+        if (obj.GetType() != this.GetType())
+        {
+            return false;
+        }
+
+        return Equals((Path)obj);
+    }
+
+    /// <inheritdoc />
+    public override int GetHashCode()
+    {
+        return PathComparer.Default.GetHashCode(this);
+    }
 }

src/Spectre.IO/PathComparer.cs

@@ -55,7 +55,7 @@ public int Compare(Path? x, Path? y)
         }
 
         // This might look strange,
-        // but for some reason, null reference tracking
+        // but for some reason, nullable reference tracking
         // does not work correctly otherwise.
         if (x == null || y == null)
         {
@@ -67,6 +67,11 @@ public int Compare(Path? x, Path? y)
             return 1;
         }
 
+        if (x.GetType() != y.GetType())
+        {
+            return -1;
+        }
+
         if (x.Segments.Count != y.Segments.Count)
         {
             return x.Segments.Count
@@ -102,6 +107,11 @@ public bool Equals(Path? x, Path? y)
             return false;
         }
 
+        if (x.GetType() != y.GetType())
+        {
+            return false;
+        }
+
         if (x.Segments.Count != y.Segments.Count)
         {
             return false;