The `induction h` tactic tries to clear hypothesis `h` after it is
applied. But, before this commit, `cases h` would only try to clear `h`
when performing non-dependent elimination. This was problematic when
writing tactic scripts for automating proofs.
@kha I added the `d_array` type that we discussed today.
However, the VM implemantion is still using persistent arrays.
If we remove the persistent array support, then code using
hash_map will only be efficient if the hash_map is used linearly.
This is not the case in the reader module because we are planning
to support backtracking.
On the other hand, it is awkward we currently don't have a vanilla
array implementation in the VM. I suspect this will be a problem in
the future.
So, I see the following possibilities:
1- We implement a map data-structure using red-black trees in Lean.
We use this new data-structure to implement all maps in the new reader and
macro expander.
2- We implement a very simple map as a list of pairs.
Then, we replace it in the VM with an efficient implementation.
The VM implementation may use our internal red-black trees.
We may also use a persistent hash table implemented in C++,
but it would be awkward to ask the user to provide a hash function in the reference
implementation (i.e., the one using list of pairs), but not use it
anywhere :)
In contrast, if we use the red-black tree implementation we
would have to ask the user to provide a total order.
It is overkill for the list of pair reference implementation because
we just need an equality test, but, at least, the comparison function
will be used in the implementation.
3- Add types `d_parray` (dependent persistent array) and
`parray` (persistent array). In Lean, they would just wrap the
`d_array` and `array` types. In the VM, `d_array` and `array` would
be implemented using vanilla arrays and `d_parray` and `parray` would
be implemented using persistent arrays. Then, we could have
`d_hash_map`, `hash_map`, `d_phash_map` and `phash_map`. Argh, so many
versions :(
We would use `phash_map` to implement our reader and macro expander.
4- Add a `(persistent : bool := ff)` parameter to `d_array` and
`array` types. The disadvantage of this approach is that it has
a performance impact. The VM implementation would have to check
the `persisent` flag at runtime. The value of this flag is known
at compilation time, but we currently don't have a mechanism
for specializing native builtin C++ implementations for VM functions.
Reason: vector in in init folder was introducing an overload (`::`) for
all Lean users. The workaround (use `local infix ::`) was
counterintuitive.
We currently have no special support for bitvectors in the code
generator. Thus, there is no need to have vector and bitvec in the init
folder right now. Moreover, the new parser and elaborator (issue #1674) should
provide better ways of managing overloaded symbols.
