std::filesystem::path::lexically_normal, std::filesystem::path::lexically_relative, std::filesystem::path::lexically_proximate

path lexically_normal() const;	(1)	(since C++17)
path lexically_relative(const path& base) const;	(2)	(since C++17)
path lexically_proximate(const path& base) const;	(3)	(since C++17)

1) Returns *this converted to normal form in its generic format

2) Returns *this made relative to base.

First, if root_name() != base.root_name() || is_absolute() != base.is_absolute() || (!has_root_directory() && base.has_root_directory()), returns a default-constructed path.
Otherwise, first determines the first mismatched element of *this and base as if by auto [a, b] = mismatch(begin(), end(), base.begin(), base.end()), then

if a == end() and b == base.end(), returns path(".");
otherwise, define $N$ as the number of nonempty filename elements that are neither dot nor dot-dot in [b, base.end()), minus the number of dot-dot filename elements, If $N < 0$ , returns a default-constructed path.
otherwise, if $N = 0$ and a == end() || a->empty(), returns path(".").
otherwise returns an object composed from

a default-constructed path() followed by
$N$ applications of operator/=(path("..")), followed by
one application of operator/= for each element in the half-open range [a, end())

3) If the value of lexically_relative(base) is not an empty path, return it. Otherwise return *this.

Parameters

(none)

Return value

1) The normal form of the path

2) The relative form of the path

3) The proximate form of the path

Exceptions

(none)

Notes

These conversions are purely lexical. They do not check that the paths exist, do not follow symlinks, and do not access the filesystem at all. For symlink-following counterparts of lexically_relative and lexically_proximate, see relative and proximate.

On Windows, the returned path has backslashes (the preferred separators),

Example

Run this code

#include <iostream>
#include <filesystem>
#include <cassert>
namespace fs = std::filesystem;
 
int main()
{
    assert(fs::path("foo/./bar/..").lexically_normal() == "foo/");
    assert(fs::path("foo/.///bar/../").lexically_normal() == "foo/");
 
    assert(fs::path("/a/d").lexically_relative("/a/b/c") == "../../d");
    assert(fs::path("/a/b/c").lexically_relative("/a/d") == "../b/c");
    assert(fs::path("a/b/c").lexically_relative("a") == "b/c");
    assert(fs::path("a/b/c").lexically_relative("a/b/c/x/y") == "../..");
    assert(fs::path("a/b/c").lexically_relative("a/b/c") == ".");
    assert(fs::path("a/b").lexically_relative("c/d") == "../../a/b");
}

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 3096	C++17	trailing "/" and "/." are handled incorrectly	corrected

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications