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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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Signed primitive integers defined on top of the existing unsigned ones
with two's complement.
The module Sint63 includes the theory of signed primitive integers that
differs from the unsigned case.
Additions to the kernel:
les (signed <=), lts (signed <), compares (signed compare),
divs (signed division), rems (signed remainder),
asr (arithmetic shift right)
(The s suffix is not used when importing the Sint63 module.)
The printing and parsing of primitive ints was updated and the
int63_syntax_plugin was removed (we use Number Notation instead).
A primitive int is parsed / printed as unsigned or signed depending on
the scope. In the default (Set Printing All) case, it is printed in
hexadecimal.
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Ack-by: SkySkimmer
Reviewed-by: ppedrot
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We deprecate unspecified locality as was done for Hint.
Close #13724
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Also works for simpl.
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Ack-by: SkySkimmer
Ack-by: ppedrot
Reviewed-by: vbgl
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Following a request from Pierre-Marie Pédrot in #13258
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By default Coq stdlib warnings raise an error, so this is really required.
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Keep Numeral Notation wit a deprecation warning.
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Added user overlay for bignums
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We also put them in a module, so users can `Require Int63. Import
Int63.Int63Notations` without needing to unqualify the primitives.
In particular, we change
- `a \% m` into `a mod m` to correspond with the notation in ZArith
- `m == n` into `m =? n` to correspond with the eqb notations elsewhere
- `m < n` into `m <? n` to correspond with the ltb notations elsewhere
- `m <= n` into `m <=? n` to correspond with the leb notations elsewhere
- `m ≤ n` into `m ≤? n` for consistency with the non-unicode notation
The old notations are still accessible as deprecated notations.
Fixes #12454
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Ack-by: SkySkimmer
Reviewed-by: maximedenes
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Reviewed-by: anton-trunov
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Fixes #11905
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Add headers to a few files which were missing them.
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We avoid redundant notations for the same concepts and make sure
notations do not break Ltac parsing for users of these libraries.
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Ack-by: fajb
Reviewed-by: ppedrot
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This could be Prop (for compat with usual Coq), Set (for HoTT),
or actually an arbitrary "i".
Take lower bound of universes into account in pretyping/engine
Reinstate proper elaboration of SProp <= l constraints:
replacing is_small with equality with lbound is _not_ semantics preserving!
lbound = Set
Elaborate template polymorphic inductives with lower bound Prop
This will make more constraints explicit
Check univ constraints with Prop as lower bound for template inductives
Restrict template polymorphic universes to those not bounded from below
Fixes #9294
fix suggested by Matthieu
Try second fix suggested by Matthieu
Take care of modifying elaboration for record declarations as well.
Rebase and export functions for debug
Remove exported functions used while debugging
Add a new typing flag "check_template" and option "-no-template-checl"
This parameterizes the new criterion on template polymorphic inductives
to allow bypassing it (necessary for backward compatibility).
Update checker to the new typing flags structure
Switch on the new template_check flag to allow old unsafe behavior in
indTyping.
This is the only change of code really impacting the kernel, together
with the commit implementing unbounded from below and parameterization
by the lower bound on universes.
Add deprecated option `Unset Template Check` allowing to make proof
scripts work with both 8.9 and 8.10 for a while
Fix `Template Check` option name and test it
Add `Unset Template Check` to Coq89.v
Cooking of inductives and template-check tests
Cleanup test-suite file for template check / universes(template) flags
cookind tests
Move test of `Unset Template Check` to the failure/ dir, but comment it
for now
Template test-suite test explanation
Overlays for PR 9918
Overlay for paramcoq
Add overlay for fiat_parsers (-no-template-check)
Add overlay for fiat_crypto_legacy
Update fiat-crypto legacy overlay
Now it points at the version that I plan on merging; I am hoping that doing this will guard against mistakes by adding an extra check that the target tested by Coq's CI on this branch works with the change I made.
Remove overlay that should no longer be necessary
The setting in the compat file should handle it
Remove now-merged fiat-crypto-legacy overlay
Update `Print Assumptions` to reflect the typing flag for template checking
Fix About and Print Assumptions for template poly, giving info on which
variables are actually polymorphic
Fix pretty printing to print global universe levels properly
Fix printing of template polymorphic universes
Fix pretty printing for template polymorphism on no universe
Fix interaction of template check and universes(template) flag
Fix indTyping to really check if there is any point in polymorphism: the
conclusion sort should be parameterized over at least one local universe
Indtyping fixes for template polymorphic Props
Allow explicit template polymorphism again
Adapt to new indTyping interface
Handle the case of template-polymorphic on no universes
correctly (morally Type0m univ represented as Prop).
Fix check of meaningfullness of template polymorphism in the kernel.
It is now done w.r.t the min_univ, the minimal universe inferred for the
inductive/record type, independently of the user-written annotation
which must only be larger than min_univ. This preserves compatibility
with UniMath and template-polymorphism as it has been implemented up-to
now.
Comment on identity non-template-polymorphism
Remove incorrect universes(template) attributes from ssr
simpl_fun can be meaningfully template-poly, as well as
pred_key (although the use is debatable: it could just
as well be in Prop).
Move `fun_of_simpl` coercion declaration out of section to respect
uniform inheritance
Remove incorrect uses of #[universes(template)] from the stdlib
Extraction of micromega changes due to moving an ind decl out of a section
Remove incorrect uses of #[universes(template)] from plugins
Fix test-suite files, removing incorrect #[universes(template)] attributes
Remove incorrect #[universes(template)] attributes in test-suite
Fix test-suite
Remove overlays as they have been merged upstream.
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#10551).
Reviewed-by: maximedenes
Reviewed-by: proux01
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Reviewed-by: Zimmi48
Reviewed-by: maximedenes
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implementations.
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This lemma is lsl_add_distr (about “<<” rather than “>>”).
See lemmas bit_add_or and lor_lsr for related properties.
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Most of these files were introduced after #6543 but used older headers
copied from somewhere else.
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sometimes, to use "intros [= ...]" rather than things like "intros H;
injection H as [= ...]".
Co-Authored-By: Théo Zimmermann <theo.zimmermann@univ-paris-diderot.fr>
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There are three implementations of this primitive:
* one in OCaml on 63 bits integer in kernel/uint63_amd64.ml
* one in OCaml on Int64 in kernel/uint63_x86.ml
* one in C on unsigned 64 bit integers in kernel/byterun/coq_uint63_native.h
Its specification is the axiom `diveucl_21_spec` in
theories/Numbers/Cyclic/Int63/Int63.v
* comment the implementations with loop invariants to enable an easy
pen&paper proof of correctness (note to reviewers: the one in
uint63_amd64.ml might be the easiest to read)
* make sure the three implementations are equivalent
* fix the specification in Int63.v
(only the lowest part of the result is actually returned)
* make a little optimisation in div21 enabled by the proof of correctness
(cmp is computed at the end of the first loop rather than at the beginning,
potentially saving one loop iteration while remaining correct)
* update the proofs in Int63.v and Cyclic63.v to take into account the
new specifiation of div21
* add a test
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This work makes it possible to take advantage of a compact
representation for integers in the entire system, as opposed to only
in some reduction machines. It is useful for heavily computational
applications, where even constructing terms is not possible without such
a representation.
Concretely, it replaces part of the retroknowledge machinery with
a primitive construction for integers in terms, and introduces a kind of
FFI which maps constants to operators (on integers). Properties of these
operators are expressed as explicit axioms, whereas they were hidden in
the retroknowledge-based approach.
This has been presented at the Coq workshop and some Coq Working Groups,
and has been used by various groups for STM trace checking,
computational analysis, etc.
Contributions by Guillaume Bertholon and Pierre Roux <Pierre.Roux@onera.fr>
Co-authored-by: Benjamin Grégoire <Benjamin.Gregoire@inria.fr>
Co-authored-by: Vincent Laporte <Vincent.Laporte@fondation-inria.fr>
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Previously, hints added without a specified database where implicitly
put in the "core" database, which was discouraged by the user manual
(because of the lack of modularity of this approach).
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The compilation to bytecode of the elimination schemes for int31 must
happen after the int31 type is registered to the retroknowledge.
Otherwise, the “decompint” instruction is not emitted.
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Removing in passing two Local which are no-ops in practice.
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Because that's the sane thing to do.
This will inevitably cause issues for projects which do not `Import
Coq.Strings.Ascii` before trying to use ascii notations.
We also move the syntax plugin for `int31` notations from `Cyclic31` to
`Int31`, so that users (like CompCert) who merely `Require Import
Coq.Numbers.Cyclic.Int31.Int31` get the `int31` numeral syntax. Since
`Cyclic31` `Export`s `Int31`, this should not cause any additional
incompatibilities.
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