This PR changes `bv_decide`'s configuration from lots of `set_option` to
an elaborated config like `simp` or `omega`. The notable exception is
`sat.solver` which is still a `set_option` such that users can configure
a custom SAT solver globally for an entire project or file. Additionally
it introduces the ability to set `maxSteps` for the simp preprocessing
run through the new config.
The latter feature was requested by people using `bv_decide` on SMTLIB
which has ginormous terms that exceed the default.
This is the first step towards fixing the issue of not having mutual
recursion between the `Bool` and `BitVec` fragment of `QF_BV` in
`bv_decide`. This PR adds support for `BitVec.ofBool` by doing the
following:
1. Introduce a new mechanism into the reification engine that allows us
to add additional lemmas to the top level on the fly as we are
traversing the expression tree.
2. If we encounter an expression `BitVec.ofBool boolExpr` we reify
`boolExpr` and then abstract `BitVec.ofBool boolExpr` as some atom `a`
3. We add two lemmas `boolExpr = true -> a = 1#1` and `boolExpr = false
-> a = 0#1`. This mirrors the full behavior of `BitVec.ofBool` and thus
makes our atom `a` correctly interpreted again.
In order to do the reification in step 2 mutual recursion in the
reification engine is required. For this reason I started pulling out
logic from the, now rather large, mutual block into other files and
document the invariants that they assume explicitly.
... while at it also call `trivial` to close goals that can be trivially
closed.
---------
Co-authored-by: Siddharth <siddu.druid@gmail.com>
Co-authored-by: Henrik Böving <hargonix@gmail.com>
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>
