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.
The `no_confusion` construction is only generated for inductive
datatypes supported in the kernel.
Before this commit, given `h : T`, `cases h` could leak the internal encoding
used by the inductive compiler WHEN a nested and/or mutual inductive
datatype is used to index the inductive datatype `T`.
The new test exposes the problem.
The solution implemented in this commit uses inj_arrow lemmas
generated by the inductive compiler. We only use the lemmas
if the target is a proposition. If it is not, we sign an error.
The reason for this limitation is documented in the source code.
cc @jroesch @dselsam
Jared: the information leakage has been fixed. So, students will not be
confused by the internal encoding used in the inductive compiler.
I added the example I posted on slack as a new test.
Note that, the workaround I used has been removed.
`{s with ...}` is now `{..., ..s}`, which more clearly expresses that the
result type is not necessarily equal to the type of `s` (in absence of an
expected type and a structure name, we still default to the type of `s`).
Multiple fallback sources can be given: `{..., ..s, ..t}` will fall back to
searching a field in `s`, then in `t`. The last component can also be `..`,
which will replace any missing fields with a placeholder.
The old notation will be removed in the future.
Now, `cmp` is just a fixed helper function.
In the future, we will be able to use (more efficient) specialized
versions during code generation by defining simp rules.
This should match the meaning of "$?" in bash:
"3.7.5 Exit Status
The exit status of an executed command is the value returned by the waitpid system call or equivalent function. Exit statuses fall between 0 and 255."
Fixes#1868
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.
