task: metadata: install: pip install -e .[dev]
patch: diff --git a/numba/core/types/functions.py b/numba/core/types/functions.py
index 0c3926a0e..eafe45a3b 100644
--- a/numba/core/types/functions.py
+++ b/numba/core/types/functions.py
@@ -457,6 +457,20 @@ class MakeFunctionLiteral(Literal, Opaque):
     pass
 
 
+class _PickleableWeakRef(weakref.ref):
+    """
+    Allow a weakref to be pickled.
+
+    Note that if the object referred to is not kept alive elsewhere in the
+    pickle, the weakref will immediately expire after being constructed.
+    """
+    def __getnewargs__(self):
+        obj = self()
+        if obj is None:
+            raise ReferenceError("underlying object has vanished")
+        return (obj,)
+
+
 class WeakType(Type):
     """
     Base class for types parametered by a mortal object, to which only
@@ -464,7 +478,7 @@ class WeakType(Type):
     """
 
     def _store_object(self, obj):
-        self._wr = weakref.ref(obj)
+        self._wr = _PickleableWeakRef(obj)
 
     def _get_object(self):
         obj = self._wr()

problem_statement: Cannot cache functions with callable arguments
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## Reporting a bug

<!--

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- [x] I have tried using ~~the latest released version of Numba (most recent is
 visible in the change log (https://github.com/numba/numba/blob/master/CHANGE_LOG)~~ d58a63a870587bf8732038ca5b2229a4de218378.
- [x] I have included below a minimal working reproducer (if you are unsure how
 to write one see http://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports).

<!--

Please include details of the bug here, including, if applicable, what you
expected to happen!

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```python
import numba

@numba.njit(cache=True)
def mul_self(x):
	return x * x

@numba.njit(cache=True)
def compose_self_apply(f, x):
	return f(f(x))

compose_self_apply(mul_self, 2)
```
gives
<details>

<summary>Traceback</summary>

```python
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
c:\users\wiese\repos\ga\numba\numba\core\caching.py in IndexDataCacheFile.save(self, key, data)
    482 try:
    483     # If key already exists, we will overwrite the file
--> 484     data_name = overloads[key]
    485 except KeyError:
    486     # Find an available name for the data file

KeyError: ((type(CPUDispatcher(<function mul_self at 0x0000025918224C10>)), int64), ('x86_64-pc-windows-msvc', 'broadwell', '+64bit,+adx,-aes,+avx,+avx2,-avx512bf16,-avx512bitalg,-avx512bw,-avx512cd,-avx512dq,-avx512er,-avx512f,-avx512ifma,-avx512pf,-avx512vbmi,-avx512vbmi2,-avx512vl,-avx512vnni,-avx512vpopcntdq,+bmi,+bmi2,-cldemote,-clflushopt,-clwb,-clzero,+cmov,+cx16,+cx8,-enqcmd,+f16c,+fma,-fma4,+fsgsbase,+fxsr,-gfni,+invpcid,-lwp,+lzcnt,+mmx,+movbe,-movdir64b,-movdiri,-mpx,-mwaitx,+pclmul,-pconfig,-pku,+popcnt,-prefetchwt1,+prfchw,-ptwrite,-rdpid,+rdrnd,+rdseed,-rtm,+sahf,-sgx,-sha,-shstk,+sse,+sse2,+sse3,+sse4.1,+sse4.2,-sse4a,+ssse3,-tbm,-vaes,-vpclmulqdq,-waitpkg,-wbnoinvd,-xop,+xsave,-xsavec,+xsaveopt,-xsaves'), ('95d9e4857cb9755b29e175e557e615d8467821eb42c66a521b4270d86f6b8c06', 'e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855'))

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
<ipython-input-7-74c10e900da8> in <module>
      7 @numba.njit(cache=True)
      8 def compose_self_apply(f, x):
      9         return f(f(x))
---> 11 compose_self_apply(mul_self, 2)

c:\users\wiese\repos\ga\numba\numba\core\dispatcher.py in _DispatcherBase._compile_for_args(self, *args, **kws)
    431         e.patch_message('\n'.join((str(e).rstrip(), help_msg)))
    432 # ignore the FULL_TRACEBACKS config, this needs reporting!
--> 433 raise e

c:\users\wiese\repos\ga\numba\numba\core\dispatcher.py in _DispatcherBase._compile_for_args(self, *args, **kws)
    364         argtypes.append(self.typeof_pyval(a))
    365 try:
--> 366     return self.compile(tuple(argtypes))
    367 except errors.ForceLiteralArg as e:
    368     # Received request for compiler re-entry with the list of arguments
    369     # indicated by e.requested_args.
    370     # First, check if any of these args are already Literal-ized
    371     already_lit_pos = [i for i in e.requested_args
    372                        if isinstance(args[i], types.Literal)]

c:\users\wiese\repos\ga\numba\numba\core\compiler_lock.py in _CompilerLock.__call__.<locals>._acquire_compile_lock(*args, **kwargs)
     29 @functools.wraps(func)
     30 def _acquire_compile_lock(*args, **kwargs):
     31     with self:
---> 32         return func(*args, **kwargs)

c:\users\wiese\repos\ga\numba\numba\core\dispatcher.py in Dispatcher.compile(self, sig)
    822     raise e.bind_fold_arguments(folded)
    823 self.add_overload(cres)
--> 824 self._cache.save_overload(sig, cres)
    825 return cres.entry_point

c:\users\wiese\repos\ga\numba\numba\core\caching.py in Cache.save_overload(self, sig, data)
    664 """
    665 Save the data for the given signature in the cache.
    666 """
    667 with self._guard_against_spurious_io_errors():
--> 668     self._save_overload(sig, data)

c:\users\wiese\repos\ga\numba\numba\core\caching.py in Cache._save_overload(self, sig, data)
    676 key = self._index_key(sig, _get_codegen(data))
    677 data = self._impl.reduce(data)
--> 678 self._cache_file.save(key, data)

c:\users\wiese\repos\ga\numba\numba\core\caching.py in IndexDataCacheFile.save(self, key, data)
    491             break
    492     overloads[key] = data_name
--> 493     self._save_index(overloads)
    494 self._save_data(data_name, data)

c:\users\wiese\repos\ga\numba\numba\core\caching.py in IndexDataCacheFile._save_index(self, overloads)
    537 def _save_index(self, overloads):
    538     data = self._source_stamp, overloads
--> 539     data = self._dump(data)
    540     with self._open_for_write(self._index_path) as f:
    541         pickle.dump(self._version, f, protocol=-1)

c:\users\wiese\repos\ga\numba\numba\core\caching.py in IndexDataCacheFile._dump(self, obj)
    566 def _dump(self, obj):
--> 567     return pickle.dumps(obj, protocol=-1)

TypeError: cannot pickle 'weakref' object
```

</details>

repo: numba/numba
test_cmd: pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
test_patch: diff --git a/numba/tests/cache_usecases.py b/numba/tests/cache_usecases.py
index 27517f3d4..68602852c 100644
--- a/numba/tests/cache_usecases.py
+++ b/numba/tests/cache_usecases.py
@@ -163,6 +163,21 @@ class _TestModule(TestCase):
         raise NotImplementedError
 
 
+@jit(cache=True)
+def first_class_function_mul(x):
+    return x * x
+
+
+@jit(cache=True)
+def first_class_function_add(x):
+    return x + x
+
+
+@jit(cache=True)
+def first_class_function_usecase(f, x):
+    return f(x)
+
+
 def self_test():
     mod = sys.modules[__name__]
     _TestModule().check_module(mod)
diff --git a/numba/tests/test_dispatcher.py b/numba/tests/test_dispatcher.py
index b70c6804a..65f4c07ed 100644
--- a/numba/tests/test_dispatcher.py
+++ b/numba/tests/test_dispatcher.py
@@ -1266,6 +1266,17 @@ class TestCache(BaseCacheUsecasesTest):
             self.assertPreciseEqual(f(3), 12) # 3 + 9 = 12
             self.check_pycache(5) # 1 nbi, 4 nbc
 
+    def test_first_class_function(self):
+        mod = self.import_module()
+        f = mod.first_class_function_usecase
+        self.assertEqual(f(mod.first_class_function_mul, 1), 1)
+        self.assertEqual(f(mod.first_class_function_mul, 10), 100)
+        self.assertEqual(f(mod.first_class_function_add, 1), 2)
+        self.assertEqual(f(mod.first_class_function_add, 10), 20)
+        # 1 + 1 + 1 nbi, 1 + 1 + 2 nbc - a separate cache for each call to `f`
+        # with a different callback.
+        self.check_pycache(7)
+
     def test_cache_reuse(self):
         mod = self.import_module()
         mod.add_usecase(2, 3)