The new test exposes the problem. Before this commit, the common
subexpressions at
```
def tst : tree → nat
| (tree.leaf v) := v
| (tree.node v l r) :=
match f v with
| tt := tst l + tst l - tst l -- <<< HERE
| ff := tst r
end
```
were not converted into a let-exprs.
We use the auxiliary procedure pull_nested_rec_fn to pull recursive
application in nested match expressions. This is needed because the
nested match expression is compiled before we process the recursive
procedure that contains it. This transformation may produce
performance problems if the recursive application does not depend on
the data being matched. Here is an example from the new test:
```
def tst : tree → nat
| (tree.leaf v) := v
| (tree.node v l r) :=
match f v with
| tt := tst l
| ff := tst r
end
```
pull_nested_rec_fn will convert it into
```
def tst : tree → nat
| (tree.leaf v) := v
| (tree.node v l r) := tst._match_1 (f v) (tst l) (tst r)
```
Since our interpreter uses eager evaluation, both `(tst l)` and `(tst r)`
are executed. This commit fixes this issue by expanding `tst._match_1`
during code generation.
@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.
The equation compiler uses different strategies for processing
recursive equations. Some of them may produce unclear runtime cost
model. For example, the following fibonacci functions was running in
linear time instead of exponential time because the equation compiler
used the brec_on recursor.
def fib : nat → nat
| 0 := 1
| 1 := 1
| (n+2) := fib (n+1) + fib n
@dselsam and @jroesch have reported examples were the equation compiler
produces a negative performance impact. The new test (`eval` function)
captures the problem reported by @jroesch. In this example, the runtime
should not depend on the "amount of fuel".
This commit addresses this issue.
Motivations:
- Clear execution cost semantics for recursive functions.
- Auxiliary meta definition may assist recursive definition unfolding in the type_context object.
Next step: use meta auxiliary definition at code generation.
Comment from parser.h
This commit makes sure that all declaration parameters must be surrounded with some kind of bracket. (e.g., '()', '{}', '[]').
The goal is to avoid counter-intuitive declarations such as:
example p : false := trivial
def main proof : false := trivial
which would be parsed as
example (p : false) : _ := trivial
def main (proof : false) : _ := trivial
where `_` in both cases is elaborated into `true`. This issue was raised by @gebner in the slack channel.
Remark: we still want implicit delimiters for lambda/pi expressions. That is, we want to write
fun x : t, s
or
fun x, s
instead of
fun (x : t), s
To make the equation compiler more convenient to use, we will add a
couple of preprocessing steps.
This commit adds the first one of them. In this step, we use
type inference to refine pattern variables, and we relax the
restrictions on inaccessible annotations.
We will also add a preprocessing step that implements the "complete
transition" step before we execute the elim_match step.
