This is a follow up to 'https://github.com/leanprover/std4/pull/645',
where the simp lemmas were requested:
https://github.com/leanprover/std4/pull/645#issuecomment-1944862251
---
Note that @semorrison asked to use `(Fin.last _)` to index. Now that we
use a `Nat` to index `msb` , the pattern `(Fin.last _)` would not have
the width be automatically inferred. Therefore, I've changed the
definitions to use `Nat` for indexing.
---------
Co-authored-by: Siddharth Bhat Mala <sb2743@cl.cam.ac.uk>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This PR is an effort to improve reasoning at the Nat level about
bitvectors and reduce of Fin and Nat.
It slightly tightens some proofs, but is generally aimed at reducing
inconsistencies between definitions at the Nat and Fin types in favor of
more consistently using Nat operations.
This ports leanprover/std4#664 to Lean core.
Here was the rational I provided in the discussion for
leanprover/std4#664:
It's mostly about consistency. If we use the same types and style in
definitions and proofs, there is less surprise when unfolding or
otherwise using definitions. We use some Nat based operations that
haven't been extended to Fin such as the bitwise operations, and I don't
want to pay the overhead of introducing a Fin version of every Bitvector
operation.
So this basically means Nat is preferred.
One argument potentially in favor of Fin is that we could reuse results
proven there, but that doesn't really seem to be the case so far.
A second argument is that we want to simplify expression to use more
canonical forms and we currently can pretty-print those operations
better using ofNat than ofFin. We could define the notations using ofFin
of course though, but that's additional operators that will show up in
expressions.
Adds a simple error-recovery mechanism to Lean's parser, similar to
those used in other combinator parsing libraries.
Lean itself isn't very amenable to error recovery with this mechanism,
as it requires global knowledge of the grammar in question to write
recovery rules that don't break backtracking or `<|>`. I only found a
few opportunities.
But for DSLs, this is really important. In particular, Verso parse
errors interacted very badly with Lean parse errors in a way that
required frequent "restart file" commands, but this mechanism allows me
to both recover from Verso parse errors and to have Lean skip the rest
of the file rather than repeatedly trying to parse it as Lean commands.
#3408 was somewhat large and didn't properly test the symm and label
attribute code after edits to the builtin versions.
This migrates the code for generating labeled attributes from Init back
to Lean so that the required definitions are in scope.
This also addresses a mistake in the symm elaborator that prevented symm
without location information from elaborating.
Both fixes have been tested on the Std test suite and successfully
passed.
Adds documentation to the `String.Iterator` API, mentored by
@eric-wieser and @david-christiansen
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
This is a quite substantial tactic.
It also includes the infamour `NatCast` typeclass (which I've equipped
with a module-doc). I wasn't at all sure where that should live, so it
is currently randomly in `Lean/Elan/Tactic/NatCast.lean`: presumably if
we're doing this it will go somewhere in `Init`.
---------
Co-authored-by: Leonardo de Moura <leomoura@amazon.com>
