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Reviewed-by: Zimmi48
Reviewed-by: vbgl
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- to zify the conclusion, we are using Tactics.apply (not rewrite)
Closes #11089
- constrain the arguments of Add Zify X to be GlobRef.t
Unset Primitive Projections so that projections are GlobRef.t.
Closes #14043
Update doc/sphinx/addendum/micromega.rst
Co-authored-by: Théo Zimmermann <theo.zimmi@gmail.com>
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The role of the `zify_saturate` tactic is to augment the goal with
positivity constraints. The premisses were previously obtained from
the context. If they are not present, we instantiate the saturation
lemma anyway.
Also,
- Remove saturation rules for Z.mul, the reasoning is performed by lia/nia
- Run zify_saturate after zify_to_euclidean_division_equations
- Better lemma for Z.power
- Ensure that lemma are generated once
Co-authored-by: Andrej Dudenhefner <mrhaandi>
Closes #12184, #11656
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The vernacular command takes a reference instead of a constr.
Moreover, the head symbol is checked i.e
Add Zify InjTyp ref checks that the referenced term has type
Intyp X1 ... Xn
Closes #14054, #13242
Co-authored-by: Vincent Laporte <vbgl@users.noreply.github.com>
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Closes #13794
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Moved bug_13227.v to complexity/bug_13227_i.v
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- Remove obviously redundant constraints
- Perform (partial) Fourier elimination to detect (easy) cutting-planes
Closes #13227
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Update doc/sphinx/addendum/micromega.rst
Co-authored-by: Jason Gross <jasongross9@gmail.com>
Update theories/micromega/ZifyInt63.v
Co-authored-by: Jason Gross <jasongross9@gmail.com>
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Reviewed-by: vbgl
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zify used to generate many syntactic positivity constraints when translating a goal
from nat to Z. For instance, to state that the product of 2 integers
is positive. Instead, lia performs an interval analysis that is more semantic.
The bug was that the interval analysis was performed after the
elimination of equations. The current workaround is to perform
interval analysis before and after eliminating equations.
bla
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The elimination of let bindings is performing a convertibility check in
order to deal with type aliases.
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Nat.le, Nat.lt and Nat.eq are aliased to le, lt and @eq nat.
The required declarations are now added in ZifyInst.
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Reviewed-by: fajb
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- The cutting plane has been (sometimes) improved to generate stronger
cuts.
- There is now some support for profiling the Simplex
see documentation for Show Lia Profile.
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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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The logic is implemented in OCaml. By induction over the terms,
guided by registered Coq terms in ZifyInst.v, it generates a rewriting
lemma. The rewriting is only performed if there is some progress. If
the rewriting fails (due to dependencies), a novel hypothesis is
generated.
This PR fixes #5155, fixes #8898, fixes #7886, fixes #10707, fixes #9848
ans fixes #10755.
The zify plugin is placed in the micromega directory.
(Though the reason is unclear, having it in a separate directory is
bad for efficiency.) efficiency impact.
There are also a few improvements of lia/lra that are piggybacked.
- more aggressive pruning of useless hypotheses
- slightly optimised conjunctive normal form
- applies exfalso if conclusion is not in Prop
- removal of Timeout in test-suite
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Typeclasses resolution is not used anymore for lia.
Typeclasses resolution is still used by lra but only to access a
database of declared constants.
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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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- 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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esprit d'escalier : is now also fixed for R
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The computed proof term is now more explicit exact (__arith P1 ... Pn X1 ... Xm)
instead of apply (__arith P1 ... Pn) which unification could fail.
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- Assert a purely arihtmetic sub-goal that is proved independently by reflexion.
(This reduces the stress on the conversion test)
- Does not use 'abstract' anymore (more natural proof-term)
- Fix a parsing bug (certain terms in Prop where not recognized)
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If 'abstract' fails e.g. if there are existentials. The tactic runs an abstract-free alternative.
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(Fixed #4985)
Lqa.v defines the tactics lra and nra working over Q.
Lra.v defines the tactics lra and nra working over R.
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default. Interestingly, there is an example where it makes the rest of
the proof less natural.
Goal forall x y:Z, ...
intros [y|p1[|p2|p2]|p1[|p2|p2]].
where case analysis on y is not only in the 2nd and 3rd case, is not
anymore easy to do.
Still, I find the bracketing of intro-patterns a natural property, and
its generalization in all situations a natural expectation for
uniformity. So, what to do? The following is e.g. not as compact and
"one-shot":
intros [|p1|p1]; [intros y|intros [|p2|p2] ..].
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and nia.
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15542 85f007b7-540e-0410-9357-904b9bb8a0f7
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- For instance, refl_equal --> eq_refl
- Npos, Zpos, Zneg now admit more uniform qualified aliases
N.pos, Z.pos, Z.neg.
- A new module BinInt.Pos2Z with results about injections from
positive to Z
- A result about Z.pow pushed in the generic layer
- Zmult_le_compat_{r,l} --> Z.mul_le_mono_nonneg_{r,l}
- Using tactic Z.le_elim instead of Zle_lt_or_eq
- Some cleanup in ring, field, micromega
(use of "Equivalence", "Proper" ...)
- Some adaptions in QArith (for instance changed Qpower.Qpower_decomp)
- In ZMake and ZMake, functor parameters are now named NN and ZZ
instead of N and Z for avoiding confusions
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15515 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15431 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13036 85f007b7-540e-0410-9357-904b9bb8a0f7
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85f007b7-540e-0410-9357-904b9bb8a0f7
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termination bug
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12346 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12337 85f007b7-540e-0410-9357-904b9bb8a0f7
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85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12283 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12253 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12123 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11318 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11211 85f007b7-540e-0410-9357-904b9bb8a0f7
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test-suites is now bounded -- ensure termination
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11200 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11173 85f007b7-540e-0410-9357-904b9bb8a0f7
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"micromega" et "sos" pour les problèmes non linéaires sous-traités à
csdp); mise en place d'un cache pour pouvoir rejouer les preuves
sans avoir besoin de csdp (pour l'instant c'est du bricolage, faudra
affiner cela).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10947 85f007b7-540e-0410-9357-904b9bb8a0f7
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