Introduce recursive_container_traits (#4623)

* Testing

* Similar fix for std::vector

* Fix infinite recursion check:

1) Apply to is_copy_assignable additionally
2) Check infinite recursion for map-like types

* style: pre-commit fixes

* Optional commit that demonstrates the limitations of this PR

* Fix positioning of container bindings

The bindings were previously in a block that was only activated if numpy
was available.

* Suggestions from code review: API side

* Suggestions from code review: Test side

* Suggestions from code review

1) Renaming: is_recursive_container and
   MutuallyRecursiveContainerPair(MV|VM)
2) Avoid ambiguous specializations of is_recursive_container

* Some little fixes

* Reordering of structs

* Add recursive checks for is_move_constructible

* Static testing for pybind11 type traits

* More precise checking of recursive types

Instead of a trait `is_recursive_container`, use a trait
`recursive_container_traits` with dependent type
`recursive_container_traits::type_to_check_recursively`.
So, instead of just checking if a type is recursive and then trying to
somehow deal with it, recursively-defined traits such as
is_move_constructible can now directly ask this trait where the
recursion should proceed.

* Review suggestions

1. Use std::conditional
2. Fix typo

* Remove leftover include from test

---------

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

include/pybind11/detail/type_caster_base.h

@@ -822,26 +822,179 @@ using movable_cast_op_type
                                   typename std::add_rvalue_reference<intrinsic_t<T>>::type,
                                   typename std::add_lvalue_reference<intrinsic_t<T>>::type>>;
 
-// std::is_copy_constructible isn't quite enough: it lets std::vector<T> (and similar) through when
-// T is non-copyable, but code containing such a copy constructor fails to actually compile.
-template <typename T, typename SFINAE = void>
-struct is_copy_constructible : std::is_copy_constructible<T> {};
+// Does the container have a mapped type and is it recursive?
+// Implemented by specializations below.
+template <typename Container, typename SFINAE = void>
+struct container_mapped_type_traits {
+    static constexpr bool has_mapped_type = false;
+    static constexpr bool has_recursive_mapped_type = false;
+};
+
+template <typename Container>
+struct container_mapped_type_traits<
+    Container,
+    typename std::enable_if<
+        std::is_same<typename Container::mapped_type, Container>::value>::type> {
+    static constexpr bool has_mapped_type = true;
+    static constexpr bool has_recursive_mapped_type = true;
+};
+
+template <typename Container>
+struct container_mapped_type_traits<
+    Container,
+    typename std::enable_if<
+        negation<std::is_same<typename Container::mapped_type, Container>>::value>::type> {
+    static constexpr bool has_mapped_type = true;
+    static constexpr bool has_recursive_mapped_type = false;
+};
+
+// Does the container have a value type and is it recursive?
+// Implemented by specializations below.
+template <typename Container, typename SFINAE = void>
+struct container_value_type_traits : std::false_type {
+    static constexpr bool has_value_type = false;
+    static constexpr bool has_recursive_value_type = false;
+};
+
+template <typename Container>
+struct container_value_type_traits<
+    Container,
+    typename std::enable_if<
+        std::is_same<typename Container::value_type, Container>::value>::type> {
+    static constexpr bool has_value_type = true;
+    static constexpr bool has_recursive_value_type = true;
+};
+
+template <typename Container>
+struct container_value_type_traits<
+    Container,
+    typename std::enable_if<
+        negation<std::is_same<typename Container::value_type, Container>>::value>::type> {
+    static constexpr bool has_value_type = true;
+    static constexpr bool has_recursive_value_type = false;
+};
+
+/*
+ * Tag to be used for representing the bottom of recursively defined types.
+ * Define this tag so we don't have to use void.
+ */
+struct recursive_bottom {};
+
+/*
+ * Implementation detail of `recursive_container_traits` below.
+ * `T` is the `value_type` of the container, which might need to be modified to
+ * avoid recursive types and const types.
+ */
+template <typename T, bool is_this_a_map>
+struct impl_type_to_check_recursively {
+    /*
+     * If the container is recursive, then no further recursion should be done.
+     */
+    using if_recursive = recursive_bottom;
+    /*
+     * Otherwise yield `T` unchanged.
+     */
+    using if_not_recursive = T;
+};
+
+/*
+ * For pairs - only as value type of a map -, the first type should remove the `const`.
+ * Also, if the map is recursive, then the recursive checking should consider
+ * the first type only.
+ */
+template <typename A, typename B>
+struct impl_type_to_check_recursively<std::pair<A, B>, /* is_this_a_map = */ true> {
+    using if_recursive = typename std::remove_const<A>::type;
+    using if_not_recursive = std::pair<typename std::remove_const<A>::type, B>;
+};
 
-template <typename T, typename SFINAE = void>
-struct is_move_constructible : std::is_move_constructible<T> {};
+/*
+ * Implementation of `recursive_container_traits` below.
+ */
+template <typename Container, typename SFINAE = void>
+struct impl_recursive_container_traits {
+    using type_to_check_recursively = recursive_bottom;
+};
 
-// Specialization for types that appear to be copy constructible but also look like stl containers
-// (we specifically check for: has `value_type` and `reference` with `reference = value_type&`): if
-// so, copy constructability depends on whether the value_type is copy constructible.
 template <typename Container>
-struct is_copy_constructible<
+struct impl_recursive_container_traits<
     Container,
-    enable_if_t<
-        all_of<std::is_copy_constructible<Container>,
-               std::is_same<typename Container::value_type &, typename Container::reference>,
-               // Avoid infinite recursion
-               negation<std::is_same<Container, typename Container::value_type>>>::value>>
-    : is_copy_constructible<typename Container::value_type> {};
+    typename std::enable_if<container_value_type_traits<Container>::has_value_type>::type> {
+    static constexpr bool is_recursive
+        = container_mapped_type_traits<Container>::has_recursive_mapped_type
+          || container_value_type_traits<Container>::has_recursive_value_type;
+    /*
+     * This member dictates which type Pybind11 should check recursively in traits
+     * such as `is_move_constructible`, `is_copy_constructible`, `is_move_assignable`, ...
+     * Direct access to `value_type` should be avoided:
+     * 1. `value_type` might recursively contain the type again
+     * 2. `value_type` of STL map types is `std::pair<A const, B>`, the `const`
+     *    should be removed.
+     *
+     */
+    using type_to_check_recursively = typename std::conditional<
+        is_recursive,
+        typename impl_type_to_check_recursively<
+            typename Container::value_type,
+            container_mapped_type_traits<Container>::has_mapped_type>::if_recursive,
+        typename impl_type_to_check_recursively<
+            typename Container::value_type,
+            container_mapped_type_traits<Container>::has_mapped_type>::if_not_recursive>::type;
+};
+
+/*
+ * This trait defines the `type_to_check_recursively` which is needed to properly
+ * handle recursively defined traits such as `is_move_constructible` without going
+ * into an infinite recursion.
+ * Should be used instead of directly accessing the `value_type`.
+ * It cancels the recursion by returning the `recursive_bottom` tag.
+ *
+ * The default definition of `type_to_check_recursively` is as follows:
+ *
+ * 1. By default, it is `recursive_bottom`, so that the recursion is canceled.
+ * 2. If the type is non-recursive and defines a `value_type`, then the `value_type` is used.
+ *    If the `value_type` is a pair and a `mapped_type` is defined,
+ *    then the `const` is removed from the first type.
+ * 3. If the type is recursive and `value_type` is not a pair, then `recursive_bottom` is returned.
+ * 4. If the type is recursive and `value_type` is a pair and a `mapped_type` is defined,
+ *    then `const` is removed from the first type and the first type is returned.
+ *
+ * This behavior can be extended by the user as seen in test_stl_binders.cpp.
+ *
+ * This struct is exactly the same as impl_recursive_container_traits.
+ * The duplication achieves that user-defined specializations don't compete
+ * with internal specializations, but take precedence.
+ */
+template <typename Container, typename SFINAE = void>
+struct recursive_container_traits : impl_recursive_container_traits<Container> {};
+
+template <typename T>
+struct is_move_constructible
+    : all_of<std::is_move_constructible<T>,
+             is_move_constructible<
+                 typename recursive_container_traits<T>::type_to_check_recursively>> {};
+
+template <>
+struct is_move_constructible<recursive_bottom> : std::true_type {};
+
+// Likewise for std::pair
+// (after C++17 it is mandatory that the move constructor not exist when the two types aren't
+// themselves move constructible, but this can not be relied upon when T1 or T2 are themselves
+// containers).
+template <typename T1, typename T2>
+struct is_move_constructible<std::pair<T1, T2>>
+    : all_of<is_move_constructible<T1>, is_move_constructible<T2>> {};
+
+// std::is_copy_constructible isn't quite enough: it lets std::vector<T> (and similar) through when
+// T is non-copyable, but code containing such a copy constructor fails to actually compile.
+template <typename T>
+struct is_copy_constructible
+    : all_of<std::is_copy_constructible<T>,
+             is_copy_constructible<
+                 typename recursive_container_traits<T>::type_to_check_recursively>> {};
+
+template <>
+struct is_copy_constructible<recursive_bottom> : std::true_type {};
 
 // Likewise for std::pair
 // (after C++17 it is mandatory that the copy constructor not exist when the two types aren't
@@ -852,14 +1005,16 @@ struct is_copy_constructible<std::pair<T1, T2>>
     : all_of<is_copy_constructible<T1>, is_copy_constructible<T2>> {};
 
 // The same problems arise with std::is_copy_assignable, so we use the same workaround.
-template <typename T, typename SFINAE = void>
-struct is_copy_assignable : std::is_copy_assignable<T> {};
-template <typename Container>
-struct is_copy_assignable<Container,
-                          enable_if_t<all_of<std::is_copy_assignable<Container>,
-                                             std::is_same<typename Container::value_type &,
-                                                          typename Container::reference>>::value>>
-    : is_copy_assignable<typename Container::value_type> {};
+template <typename T>
+struct is_copy_assignable
+    : all_of<
+          std::is_copy_assignable<T>,
+          is_copy_assignable<typename recursive_container_traits<T>::type_to_check_recursively>> {
+};
+
+template <>
+struct is_copy_assignable<recursive_bottom> : std::true_type {};
+
 template <typename T1, typename T2>
 struct is_copy_assignable<std::pair<T1, T2>>
     : all_of<is_copy_assignable<T1>, is_copy_assignable<T2>> {};

include/pybind11/stl_bind.h

@@ -61,9 +61,11 @@ struct is_comparable<
 /* For a vector/map data structure, recursively check the value type
    (which is std::pair for maps) */
 template <typename T>
-struct is_comparable<T, enable_if_t<container_traits<T>::is_vector>> {
-    static constexpr const bool value = is_comparable<typename T::value_type>::value;
-};
+struct is_comparable<T, enable_if_t<container_traits<T>::is_vector>>
+    : is_comparable<typename recursive_container_traits<T>::type_to_check_recursively> {};
+
+template <>
+struct is_comparable<recursive_bottom> : std::true_type {};
 
 /* For pairs, recursively check the two data types */
 template <typename T>