In obj??, display the docstring if it is not in the source.

Currently, `obj??` does not display obj's docstring because it is likely
redundant with the source (which usually also includes the docstring).
However, when the docstring had been dynamically added, then it should
also be displayed by `obj??` (because it is not redundant in this case).

A reasonable way to check for this condition is to parse the source and
compare the result of `ast.get_docstring()` to the result of
`inspect.getdoc()`, as done by this PR.

IPython/core/oinspect.py

@@ -13,6 +13,7 b' reference the name under which an object is being read.'
 __all__ = ['Inspector','InspectColors']
 
 # stdlib modules
+import ast
 import inspect
 from inspect import signature
 import linecache
@@ -630,10 +631,10 b' class Inspector(Colorable):'
             # Functions, methods, classes
             append_field(_mime, 'Signature', 'definition', code_formatter)
             append_field(_mime, 'Init signature', 'init_definition', code_formatter)
+            append_field(_mime, 'Docstring', 'docstring', formatter)
             if detail_level > 0 and info['source']:
                 append_field(_mime, 'Source', 'source', code_formatter)
             else:
-                append_field(_mime, 'Docstring', 'docstring', formatter)
                 append_field(_mime, 'Init docstring', 'init_docstring', formatter)
 
             append_field(_mime, 'File', 'file')
@@ -821,7 +822,7 b' class Inspector(Colorable):'
                 pass
 
         # Add docstring only if no source is to be shown (avoid repetitions).
-        if ds and out.get('source', None) is None:
+        if ds and not self._source_contains_docstring(out.get('source'), ds):
             out['docstring'] = ds
 
         # Constructor docstring for classes
@@ -936,6 +937,23 b' class Inspector(Colorable):'
 
         return object_info(**out)
 
+    @staticmethod
+    def _source_contains_docstring(src, doc):
+        """
+        Check whether the source *src* contains the docstring *doc*.
+
+        This is is helper function to skip displaying the docstring if the
+        source already contains it, avoiding repetition of information.
+        """
+        try:
+            def_node, = ast.parse(dedent(src)).body
+            return ast.get_docstring(def_node) == doc
+        except Exception:
+            # The source can become invalid or even non-existent (because it
+            # is re-fetched from the source file) so the above code fail in
+            # arbitrary ways.
+            return False
+
     def psearch(self,pattern,ns_table,ns_search=[],
                 ignore_case=False,show_all=False):
         """Search namespaces with wildcards for objects.