gh-37004: Fixes in save_session()
    
1. fix test for cython functions in save_session()
   This fixes #37003
2. fix handling of lazy import variables in save_session()
   This fixes #37002
3. remove unused `extra_globals` attribute in class DocTestTask
   This was introduced for the transition from python 2 to 3, no longer
used
4. don't sort the output of `sage.misc.session.show_identifiers()`
   There's no need to sort here... sorting was introduced in baedc41
in order to fix doctest errors, but dictionaries now keep the insertion
order. Thus `show_identifiers()` will return the variables in the order
they were introduced for the first time which seems reasonable and it's
fine to test.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.

Fixes: #37002, #37003
    
URL: #37004
Reported by: Gonzalo Tornaría
Reviewer(s): Frédéric Chapoton

Author: Release Manager

src/sage/doctest/forker.py

@@ -2489,19 +2489,6 @@ class DocTestTask():
         ['cputime', 'err', 'failures', 'optionals', 'tests', 'walltime', 'walltime_skips']
     """
 
-    extra_globals = {}
-    """
-    Extra objects to place in the global namespace in which tests are run.
-    Normally this should be empty but there are special cases where it may
-    be useful.
-
-    For example, in Sage versions 9.1 and earlier, on Python 3 add
-    ``long`` as an alias for ``int`` so that tests that use the
-    ``long`` built-in (of which there are many) still pass.  We did
-    this so that the test suite could run on Python 3 while Python 2
-    was still the default.
-    """
-
     def __init__(self, source):
         """
         Initialization.
@@ -2630,10 +2617,6 @@ def _run(self, runner, options, results):
         # Remove '__package__' item from the globals since it is not
         # always in the globals in an actual Sage session.
         dict_all.pop('__package__', None)
-
-        # Add any other special globals for testing purposes only
-        dict_all.update(self.extra_globals)
-
         sage_namespace = RecordingDict(dict_all)
         sage_namespace['__name__'] = '__main__'
         doctests, extras = self.source.create_doctests(sage_namespace)

src/sage/misc/session.pyx

@@ -27,7 +27,7 @@ This saves a dictionary with ``w`` as one of the keys::
 
     sage: z = load(os.path.join(d.name, 'session'))
     sage: list(z)
-    ['d', 'w']
+    ['w', 'd']
     sage: z['w']
     2/3
 
@@ -68,19 +68,19 @@ AUTHOR:
 import builtins
 import types
 
-# We want the caller's locals, but locals() is emulated in Cython
-cdef caller_locals = builtins.locals
-
 # Sage imports
 from sage.misc.persist import load, save, loads, dumps
+from sage.misc.lazy_import import LazyImport
+
+# We want the caller's locals, but locals() is emulated in Cython
+cdef caller_locals = builtins.locals
 
 # This module-scope variables is used to save the
 # global state of the sage environment at the moment
 # before the user starts typing or running code.
 
 state_at_init = None
 
-CythonFunctionType = type(lambda: None)
 
 def init(state=None):
     """
@@ -163,9 +163,13 @@ def _is_new_var(x, v, hidden):
     # definitely new.
     if x not in state_at_init:
         return True
+    # A lazy import that was there at init time is not new
+    if isinstance(v, LazyImport):
+        return False
     # A variable could also be new even if it was there at init, say if
     # its value changed.
-    return x not in state_at_init or state_at_init[x] is not v
+    return state_at_init[x] is not v
+
 
 def show_identifiers(hidden=False):
     r"""
@@ -196,7 +200,7 @@ def show_identifiers(hidden=False):
         sage: a = 10
         sage: factor = 20
         sage: show_identifiers()
-        ['a', 'factor']
+        ['factor', 'a']
 
     To get the actual value of a variable from the list, use the
     :func:`globals()` function.::
@@ -210,27 +214,21 @@ def show_identifiers(hidden=False):
 
         sage: _hello = 10
         sage: show_identifiers()
-        ['a', 'factor']
+        ['factor', 'a']
         sage: '_hello' in show_identifiers(hidden=True)
         True
 
     Many of the hidden variables are part of the IPython command history, at
     least in command line mode.::
 
         sage: show_identifiers(hidden=True)        # random output
-        ['__', '_i', '_6', '_4', '_3', '_1', '_ii', '__doc__', '__builtins__', '___', '_9', '__name__', '_', 'a', '_i12', '_i14', 'factor', '__file__', '_hello', '_i13', '_i11', '_i10', '_i15', '_i5', '_13', '_10', '_iii', '_i9', '_i8', '_i7', '_i6', '_i4', '_i3', '_i2', '_i1', '_init_cmdline', '_14']
+        ['__builtin__', '_ih', '_oh', '_dh', 'exit', 'quit', '_', '__', '___',
+        '_i', '_ii', '_iii', '_i1', 'factor', '_i2', '_2', '_i3', 'a', '_i4',
+        '_i5', '_5', '_i6', '_6', '_i7', '_hello', '_i8', '_8', '_i9', '_9',
+        '_i10']
     """
-    from sage.doctest.forker import DocTestTask
     state = caller_locals()
-    # Ignore extra variables injected into the global namespace by the doctest
-    # runner
-    _none = object()
-
-    def _in_extra_globals(name, val):
-        return val == DocTestTask.extra_globals.get(name, _none)
-
-    return sorted([x for x, v in state.items() if _is_new_var(x, v, hidden)
-                   and not _in_extra_globals(x, v)])
+    return [x for x, v in state.items() if _is_new_var(x, v, hidden)]
 
 
 def save_session(name='sage_session', verbose=False):
@@ -293,28 +291,44 @@ def save_session(name='sage_session', verbose=False):
         sage: f = lambda x : x^2
         sage: save_session(tmp_f)
         sage: save_session(tmp_f, verbose=True)
-        Saving...
-        Not saving f: f is a function, method, class or type
         ...
+        Not saving f: f is a function or method
 
     Something similar happens for cython-defined functions::
 
         sage: g = cython_lambda('double x', 'x*x + 1.5')
         sage: save_session(tmp_f, verbose=True)
-        Saving...
-        Not saving g: g is a function, method, class or type
         ...
+        Not saving g: g is a cython function or method
+
+    And the same for a lazy import::
+
+        sage: from sage.misc.lazy_import import LazyImport
+        sage: lazy_ZZ = LazyImport('sage.rings.integer_ring', 'ZZ')
+        sage: save_session(tmp_f, verbose=True)
+        ...
+        Not saving lazy_ZZ: lazy_ZZ is a lazy import
     """
     state = caller_locals()
     # This dict D will contain the session -- as a dict -- that we will save to disk.
     D = {}
     # We iterate only over the new variables that were defined in this
     # session, since those are the only ones we will save.
-    for k in show_identifiers(hidden = True):
+    for k in show_identifiers(hidden=True):
         try:
             x = state[k]
-            if isinstance(x, (types.FunctionType, types.BuiltinFunctionType, types.BuiltinMethodType, CythonFunctionType, type)):
-                raise TypeError('{} is a function, method, class or type'.format(k))
+
+            if isinstance(x, type):
+                raise TypeError('{} is a class or type'.format(k))
+
+            if isinstance(x, (types.FunctionType, types.BuiltinFunctionType, types.BuiltinMethodType)):
+                raise TypeError('{} is a function or method'.format(k))
+
+            if getattr(type(x), '__name__', None) == 'cython_function_or_method':
+                raise TypeError('{} is a cython function or method'.format(k))
+
+            if isinstance(x, LazyImport):
+                raise TypeError('{} is a lazy import'.format(k))
 
             # We attempt to pickle *and* unpickle every variable to
             # make *certain* that we can pickled D at the end below.