This renames `BitVec.getLsb` to `getLsbD` (`D` for "default" value, i.e.
false), and introduces `getLsb?` and `getLsb'` (which we can rename to
`getLsb` after a deprecation cycle).
(Similarly for `getMsb`.)
Also adds a `GetElem` class so we can use `x[i]` and `x[i]?` notation.
Later, we will turn
```
theorem getLsbD_eq_getElem?_getD (x : BitVec w) (i : Nat) (h : i < w) :
x.getLsbD i = x[i]?.getD false
```
on as a `@[simp]` lemma.
This PR doesn't attempt to demonstrate the benefits, but I think both
arguments are going to get easier, and this will bring the BitVec API
closer in line to List/Array, etc.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This change canonicalizes the BitVec variable names to `x y z : BitVec`
instead of alternative namings such as `s t : BitVec` or `a b : BitVec`.
Variable names that carry semantic meaning such as `(msbs : BitVec w)
(lsb : Bool)` remain untouched.
This is purely a naming change to make our bitvector proofs more
consistent and polish the (auto-generated) documentation as a very small
step towards polishing the documentation of the BitVec library in Lean.
---------
Co-authored-by: AnotherAlexHere <153999274+AnotherAlexHere@users.noreply.github.com>
This implements the recurrence theorems `getLsb_mul`, `mulRec_zero_eq`,
`mulRec_succ_eq` to allow bitblasting multiplication.
---------
Co-authored-by: Kim Morrison <scott@tqft.net>
This PR adds theorems that relate unsigned bitvector comparisons
`BitVec.ult` and `BitVec.ule` to `BitVec.carry`. These lemmas are a
prerequisite to bit-blasting these comparisons in LeanSAT.
Every usage of `carry` followed the pattern: `carry _ x.toNat y.toNat`,
so we've refactorod `carry` to take the `BitVec`s as arguments, and made
the `toNat` part of its definition.
