Add anyset & frozenset, enable copying (cast) to std::set (#3901)

* Add frozenset, and allow it cast to std::set

For the reverse direction, std::set still casts to set. This is in concordance with the behavior for sequence containers, where e.g. tuple casts to std::vector but std::vector casts to list.

Extracted from #3886.

* Rename set_base to any_set to match Python C API

since this will be part of pybind11 public API

* PR: static_cast, anyset

* Add tests for frozenset

and rename anyset methods

* Remove frozenset default ctor, add tests

Making frozenset non-default constructible means that we need to adjust pyobject_caster to not require that its value is default constructible, by initializing value to a nil handle.  This also allows writing C++ functions taking anyset, and is arguably a performance improvement, since there is no need to allocate an object that will just be replaced by load.

Add some more tests, including anyset::empty, anyset::size, set::add and set::clear.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Add rationale to `pyobject_caster` default ctor

* Remove ineffectual protected: access control

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

include/pybind11/cast.h

@@ -908,6 +908,14 @@ struct handle_type_name<kwargs> {
 
 template <typename type>
 struct pyobject_caster {
+    template <typename T = type, enable_if_t<std::is_same<T, handle>::value, int> = 0>
+    pyobject_caster() : value() {}
+
+    // `type` may not be default constructible (e.g. frozenset, anyset).  Initializing `value`
+    // to a nil handle is safe since it will only be accessed if `load` succeeds.
+    template <typename T = type, enable_if_t<std::is_base_of<object, T>::value, int> = 0>
+    pyobject_caster() : value(reinterpret_steal<type>(handle())) {}
+
     template <typename T = type, enable_if_t<std::is_same<T, handle>::value, int> = 0>
     bool load(handle src, bool /* convert */) {
         value = src;

include/pybind11/pytypes.h

@@ -1784,25 +1784,35 @@ class kwargs : public dict {
     PYBIND11_OBJECT_DEFAULT(kwargs, dict, PyDict_Check)
 };
 
-class set : public object {
+class anyset : public object {
 public:
-    PYBIND11_OBJECT_CVT(set, object, PySet_Check, PySet_New)
-    set() : object(PySet_New(nullptr), stolen_t{}) {
+    PYBIND11_OBJECT(anyset, object, PyAnySet_Check)
+    size_t size() const { return static_cast<size_t>(PySet_Size(m_ptr)); }
+    bool empty() const { return size() == 0; }
+    template <typename T>
+    bool contains(T &&val) const {
+        return PySet_Contains(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 1;
+    }
+};
+
+class set : public anyset {
+public:
+    PYBIND11_OBJECT_CVT(set, anyset, PySet_Check, PySet_New)
+    set() : anyset(PySet_New(nullptr), stolen_t{}) {
         if (!m_ptr) {
             pybind11_fail("Could not allocate set object!");
         }
     }
-    size_t size() const { return (size_t) PySet_Size(m_ptr); }
-    bool empty() const { return size() == 0; }
     template <typename T>
     bool add(T &&val) /* py-non-const */ {
         return PySet_Add(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 0;
     }
     void clear() /* py-non-const */ { PySet_Clear(m_ptr); }
-    template <typename T>
-    bool contains(T &&val) const {
-        return PySet_Contains(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 1;
-    }
+};
+
+class frozenset : public anyset {
+public:
+    PYBIND11_OBJECT_CVT(frozenset, anyset, PyFrozenSet_Check, PyFrozenSet_New)
 };
 
 class function : public object {

include/pybind11/stl.h

@@ -55,10 +55,10 @@ struct set_caster {
     using key_conv = make_caster<Key>;
 
     bool load(handle src, bool convert) {
-        if (!isinstance<pybind11::set>(src)) {
+        if (!isinstance<anyset>(src)) {
             return false;
         }
-        auto s = reinterpret_borrow<pybind11::set>(src);
+        auto s = reinterpret_borrow<anyset>(src);
         value.clear();
         for (auto entry : s) {
             key_conv conv;