The new `partial def`s allow us to define `fix` in Lean, but the Lean
implementation is not as efficient as the native one. The native one
in C++ use weak pointers to prevent a closure allocation at every
recursive invocation.
This commit also fixes the `fixCore` helper functions that were broken
after we switched to camelCase.
We have updated the test `fix1.lean` to demonstrate the native
implementation is faster. Here are the numbers on my desktop.
```
./run.sh fix1.lean 24
721420279
Time for 'native fix': 816ms
721420279
Time for 'fix in lean': 1.34s
```
The idea is to avoid allocating tuples when creating the fixpoint of
nary functions. For example, consider the new tests:
- tests/playground/fix.lean
- tests/playground/fix_with_tuples.lean
The second one (`fix_with_tuples`) uses the `fix` operator and tuples. For input = 20,
it creates more than 1 million extra objects. The first implementation
(`fix.lean`) using `fix₂` avoids this overhead.
TODO: Add support for pattern #N with N > 9 at
```
def expand_extern_pattern_aux (args : list string) : nat → string.iterator → string → string
```
