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Closes #13794
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This will be more predictable. In case there are several possible
substitution, the "simplest" is prefered.
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- Remove obviously redundant constraints
- Perform (partial) Fourier elimination to detect (easy) cutting-planes
Closes #13227
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IMHO it is a bit more logical, WDYT?
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Add headers to a few files which were missing them.
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Only significant change is in gcd / lcm which now are typed in `Z.t`
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- zify_iter_specs is entirely in OCaml
- zify_op has been improved
* The generation of proof-terms is more direct
* It does not `rewrite` but instead either performs
a `pose proof` or a `change`
* The support for `and`, `or`, `not`, arrow is hardcoded
* Avoid generating duplicate hypotheses such as 0 <= Z.of_nat x
- zify_elim_let is entirely in OCaml (no Ltac callback)
[micromega] fix stack overflow
Less naive computation of bounds (online elimination of duplicates)
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- Add an instance to ZifyInst to instruct zify that
0 < x -> 0 < y -> 0 < Z.pow x y
- More aggressive interval analysis to bound non-linear monomials.
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PR #9725 fixes completness bugs introduces some inefficiency. The
current PR intends to fix the inefficiency while retaining
completness. The fix removes a pre-processing step and instead relies
on a more elaborate proof format introducing positivity constraints on
the fly.
Solve bootstrapping issues: RMicromega <-> Rbase <-> lia.
Fixes #11063 and fixes #11242 and fixes #11270
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- Improved reification for Micromega (support for #8764)
- Fixes #9268: Do not take universes into account in lia reification
Improve #9291 by threading the evar_map during reification.
Universes are unified.
- Remove (potentially cyclic) dependency over lra for Rle_abs
- Towards a complete simplex-based lia
fixes #9615
Lia is now exclusively using cutting plane proofs.
For this to always work, all the variables need to be positive.
Therefore, lia is pre-processing the goal for each variable x
it introduces the constraints x = y - z , y>=0 , z >= 0
for some fresh variable y and z.
For scalability, nia is currently NOT performing this pre-processing.
- Lia is using the FSet library
manual merge of commit #230899e87c51c12b2f21b6fedc414d099a1425e4
to work around a "leaked" hint breaking compatibility of eauto
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This is a pre-requisite to use automated formatting tools such as
`ocamlformat`, also, there were quite a few places where the comments
had basically no effect, thus it was confusing for the developer.
p.s: Reading some comments was a lot of fun :)
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- Simplex based linear prover
Unset Simplex to get Fourier elimination
For lia and nia, do not enumerate but generate cutting planes.
- Better non-linear support
Factorisation of the non-linear pre-processing
Careful handling of equation x=e, x is only eliminated if x is used linearly
- More opaque interfaces
(Linear solvers Simplex and Mfourier are independent)
- Set Dump Arith "file" so that lia,nia calls generate Coq goals
in filexxx.v. Used to collect benchmarks and regressions.
- Rationalise the test-suite
example.v only tests psatz Z
example_nia.v only tests lia, nia
In both files, the tests are in essence the same.
In particular, if a test is solved by psatz but not by nia,
we finish the goal by an explicit Abort.
There are additional tests in example_nia.v which require specific
integer reasoning out of scope of psatz.
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We add .mli files, removed dead code and use standard combinators
instead of redefined ad-hoc ones in a few places.
A lot of cleaning still has to be done on this code: documenting the
interfaces, resolving the many abstraction leaks. I suspect there is
still a lot of code duplication.
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