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
```
Prevent assertion violation when processing examples such as:
```
@[pattern] def badPattern (x : Nat) : Nat := 0
def tst (y : Nat) : Nat :=
match y with
| (@badPattern _) := 1
| _ := 2
```
The `x` is not used in `badPattern`. Thus, the elaborator fails to
synthesize the metavariable corresponding to `_` at `@badPattern _`.
The fix detects this kind of instance, but I commented the code the
throws the error because we would prevent us from compiling `term.lean`.
The assertion violation was originally triggered by the pattern definition
```
@[pattern] def «explicitBinderContent» (requireType : optParam.{1} Bool Bool.false) :=
{SyntaxNodeKind . name := `Lean.Parser.Term.explicitBinderContent}
at
...
view := fun stx, let (stx, i) := match stx.asNode : _ -> Prod Syntax Nat with
| some {kind := @«explicitBinderContent» requireType, -- << HERE
args := [stx], ..} := ...
```
These definitions were generated by the node choice macro.
cc @kha
@kha I added this example as a template for what the equation compiler
will have to do. The plan is:
- We can use `partial` to define any function if the result type is
inhabited.
- If the result type is of the form `Partial a`, the equation compiler
generates lemmas of the form:
```
theorem fooEq args : terminates (foo args) → foo args = lhs
```
The new test contains an example.
@kha: I initially planned to use the UTF8 API only in very special
cases, but I found them to be super useful. They allow us to implement
an efficient String library mostly in Lean.
However, the there was a problem: `abbrev String.Pos := USize`.
This definition is fine for a low level API, but this is not the case
anymore. By having `String.Pos := USize`, we will not be able to
prove natural theorems for the `String` API. For example,
`String.map id s = s` did not hold. We would have to include the
artificial antecedent `s.length <= usizeMax` (or something like this).
I suspect it would be very painful.
So, this commit defines `String.Pos` as `Nat`. The performance
overhead seems to be very small.
In 64-bit machines, the max small nat value should now be (2^63 - 1), and on 32-bit
machines (2^32 - 1).
The main motivation for this modification are the array indexing
operations. With the new representation, if a Nat index is not small,
then it must not be a valid index. This was not true in 64-bit
machines. Example: an array of size 2^33 would fit in memory, and but
an index `i` > 2^32 - 1 would not be a small nat value.
