This PR changes the signature of `Array.get` to take a Nat and a proof,
rather than a `Fin`, for consistency with the rest of the (planned)
Array API. Note that because of bootstrapping issues we can't provide
`get_elem_tactic` as an autoparameter for the proof. As users will
mostly use the `xs[i]` notation provided by `GetElem`, this hopefully
isn't a problem.
We may restore `Fin` based versions, either here or downstream, as
needed, but they won't be the "main" functions.
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
I made a few choices so far that can probably be discussed:
- got rid of `modn` on `UInt`, nobody seems to use it apart from the
definition of `shift` which can use normal `mod`
- removed the previous defeq optimized definition of `USize.size` in
favor for a normal one. The motivation was to allow `OfNat` to work
which doesn't seem to be necessary anymore afaict.
- Minimized uses of `.val`, should we maybe mark it deprecated?
- Mostly got rid of `.val` in basically all theorems as the proper next
level of API would now be `.toBitVec`. We could probably re-prove them
but it would be more annoying given the change of definition.
- Did not yet redefine `log2` in terms of `BitVec` as this would require
a `log2` in `BitVec` as well, do we want this?
- I added a couple of theorems around the relation of `<` on `UInt` and
`Nat`. These were previously not needed because defeq was used all over
the place to save us. I did not yet generalize these to all types as I
wasn't sure if they are the appropriate lemma that we want to have.
Given the derived `Repr` instance for types with parameters, the absence
of `Repr Empty` can cause `Repr` instance synthesis to fail. For
example, given
```lean
inductive Prim (special : Type) where
| plus
| other : special → Prim special
deriving Repr
```
this works:
```lean
#eval (Prim.plus : Prim Int)
```
but this fails:
```lean
#eval (Prim.plus : Prim Empty)
```
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
`Nat.repr` was implemented by generating a list of `Chars`, each created
by a 10-way if-then-else. This can cause significant slow down in some
particular use cases.
Now `Nat.repr` is `implemented_by` a faster implementation that uses
C++’s `std::to_string` on small numbers (< USize.size) and maintains an
array of pre-allocated strings for the first 128 numbers.
The handling of big numbers (≥ USize.size) remains as before.
while trying to help a user who was facing an unhelpful
```
omega did not find a contradiction:
[0, 0, 0, 0, 1, -1] ∈ [1, ∞)
[0, 0, 0, 0, 0, 1] ∈ [0, ∞)
[0, 0, 0, 0, 1] ∈ [0, ∞)
[1, -1] ∈ [1, ∞)
[0, 0, 0, 1] ∈ [0, ∞)
[0, 1] ∈ [0, ∞)
[1] ∈ [0, ∞)
[0, 0, 0, 1, 1] ∈ [-1, ∞)
```
I couldn’t resist and wrote a pretty-printer for these problem that
shows the linear combination as such, and includes the recognized atoms.
This is especially useful since oftem `omega` failures stem from failure
to recognize atoms as equal. In this case, we now get:
```
omega-failure.lean:19:2-19:7: error: omega could not prove the goal:
a possible counterexample may satisfy the constraints
d - e ≥ 1
e ≥ 0
d ≥ 0
a - b ≥ 1
c ≥ 0
b ≥ 0
a ≥ 0
c + d ≥ -1
where
a := ↑(sizeOf xs)
b := ↑(sizeOf x)
c := ↑(sizeOf x.fst)
d := ↑(sizeOf x.snd)
e := ↑(sizeOf xs)
```
and this might help the user make progress (e.g. by using `case x`
first, and investingating why `sizeOf xs` shows up twice)
Part of the retreat Hackathon.
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
`charToHex` is an auxiliary function used at `Char.quoteCore` for
converting ASCII control characters into `\x` notation.
Its name was misleading.
Closes#1404
@Kha this is a fix for the example that @gebner posted on Zulip.
There are other possible workarounds, but I think this one is
"intuitive".
Here is the problem description and workaround.
We currently use the `withPosition` combinator at `matchAlts`. The
original motivation was nested `match`-expressions without
parenthesis.
We also have the `checkColGt` in the application parser.
Thus, `frob 5` is not parsed as an application. That is, the term
parser after the `then` keyword stops at `frob`.
Then, we get the weird "expected 'else'" error message at `5` :)
In this commit, I add a `checkColGe` check at the beginning of each
alternative right-hand-side.
The effect on the stdlib was minimal. It basically affected old code
that used the Lean 3 workaround for partial functions
```
partial def f : N -> N | i =>
...
```
In Lean 4, we can use the more natural
```
partial def f (i : N) : N :=
...
```
or
```
partial def f : N -> N := fun i =>
...
```
It also affected code such as
```
instance : Repr String.Iterator where
reprPrec | ⟨s, pos⟩, prec =>
Repr.addAppParen ("String.Iterator.mk " ++ reprArg s ++ " " ++ reprArg pos) prec
```
This is a workaround for a missing feature. We really wanted to write
```
instance : Repr String.Iterator where
reprPrec ⟨s, pos⟩ prec :=
Repr.addAppParen ("String.Iterator.mk " ++ reprArg s ++ " " ++ reprArg pos) prec
```
@Kha The old `= true` workarounds are not needed anymore, they were
due to another issue and are not related to yesterday's issue.
That is, the one exposed by the `ForIn` typeclass.
