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We deprecate unspecified locality as was done for Hint.
Close #13724
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As before, add a `bitwise as` tactic notation.
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All that really needed to be done was add an explicit intro before
nzinduct, but all the issues in this file could be fixed by moving n m p
before the colon, and I couldn't stop my self.
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Add headers to a few files which were missing them.
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Removing in passing two Local which are no-ops in practice.
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as pointed out by @jashug
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- The earlier proof-of-concept file NPeano (which instantiates
the "Numbers" framework for nat) becomes now the entry point
in the Arith lib, and gets renamed PeanoNat. It still provides
an inner module "Nat" which sums up everything about type nat
(functions, predicates and properties of them).
This inner module Nat is usable as soon as you Require Import Arith,
or just Arith_base, or simply PeanoNat.
- Definitions of operations over type nat are now grouped in a new
file Init/Nat.v. This file is meant to be used without "Import",
hence providing for instance Nat.add or Nat.sqrt as soon as coqtop
starts (but no proofs about them).
- The definitions that used to be in Init/Peano.v (pred, plus, minus, mult)
are now compatibility notations (for Nat.pred, Nat.add, Nat.sub, Nat.mul
where here Nat is Init/Nat.v).
- This Coq.Init.Nat module (with only pure definitions) is Include'd
in the aforementioned Coq.Arith.PeanoNat.Nat. You might see Init.Nat
sometimes instead of just Nat (for instance when doing "Print plus").
Normally it should be ok to just ignore these "Init" since
Init.Nat is included in the full PeanoNat.Nat. I'm investigating if
it's possible to get rid of these "Init" prefixes.
- Concerning predicates, orders le and lt are still defined in Init/Peano.v,
with their notations "<=" and "<". Properties in PeanoNat.Nat directly
refer to these predicates in Peano. For instantation reasons, PeanoNat.Nat
also contains a Nat.le and Nat.lt (defined via "Definition le := Peano.le",
we cannot yet include an Inductive to implement a Parameter), but these
aliased predicates won't probably be very convenient to use.
- Technical remark: I've split the previous property functor NProp in
two parts (NBasicProp and NExtraProp), it helps a lot for building
PeanoNat.Nat incrementally. Roughly speaking, we have the following schema:
Module Nat.
Include Coq.Init.Nat. (* definition of operations : add ... sqrt ... *)
... (** proofs of specifications for basic ops such as + * - *)
Include NBasicProp. (** generic properties of these basic ops *)
... (** proofs of specifications for advanced ops (pow sqrt log2...)
that may rely on proofs for + * - *)
Include NExtraProp. (** all remaining properties *)
End Nat.
- All other files in directory Arith are now taking advantage of PeanoNat :
they are now filled with compatibility notations (when earlier lemmas
have exact counterpart in the Nat module) or lemmas with one-line proofs
based on the Nat module. All hints for database "arith" remain declared
in these old-style file (such as Plus.v, Lt.v, etc). All the old-style
files are still Require'd (or not) by Arith.v, just as before.
- Compatibility should be almost complete. For instance in the stdlib,
the only adaptations were due to .ml code referring to some Coq constant
name such as Coq.Init.Peano.pred, which doesn't live well with the
new compatibility notations.
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15715 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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This adds two experimental features to the typeclass implementation:
- Path cuts: a way to specify through regular expressions on instance names
search pathes that should be avoided (e.g. [proper_flip proper_flip]).
Regular expression matching is implemented through naïve derivatives.
- Forward hints for subclasses: e.g. [Equivalence -> Reflexive] is no
longer applied backwards, but introducing a specific [Equivalence] in the
environment register a [Reflexive] hint as well. Currently not
backwards-compatible, the next patch will allow to specify direction
of subclasses hints.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14671 85f007b7-540e-0410-9357-904b9bb8a0f7
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Instead of hard-coding in search.ml some substrings such
as "_admitted" or "_subproof" we don't want to see in results
of SearchAbout and co, we now have a user command:
Add Search Blacklist "foo".
Remove Search Blacklist "foo". (* the opposite *)
Print Table Search Blacklist. (* the current state *)
In Prelude.v, three substrings are blacklisted originally:
- "_admitted" for internal lemmas due to admit.
- "_subproof" for internal lemmas due to abstract.
- "Private_" for hiding auxiliary modules not meant for
global usage.
Note that substrings are searched in the fully qualified names
of the available lemmas (e.g. "Coq.Init.Peano.plus").
This commit also adds the prefix "Private_" to some internal modules
in Numbers, Z, N, etc.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14408 85f007b7-540e-0410-9357-904b9bb8a0f7
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- Zpow_def, Zpower, Zpow_facts shortened thanks to stuff in BinInt.Z
- The alternative Zpower_alt is now in a separate file Zpow_alt.v,
not loaded by default.
- Some more injection lemmas in Znat (pow, div, mod, quot, rem)
- Btw, added a "square" function in Z, N, Pos, ... (instead of
Zpow_facts.Zsquare).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14253 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14244 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14238 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14237 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14230 85f007b7-540e-0410-9357-904b9bb8a0f7
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Start of a uniform treatment of compare, eqb, leb, ltb:
- We now ensure that they are provided by N,Z,BigZ,BigN,Nat and Pos
- Some generic properties are derived in OrdersFacts.BoolOrderFacts
In BinPos, more work about sub_mask with nice implications
on compare (e.g. simplier proof of lt_trans).
In BinNat/BinPos, for uniformity, compare_antisym is now
(y ?= x) = CompOpp (x ?=y) instead of the symmetrical result.
In BigN / BigZ, eq_bool is now eqb
In BinIntDef, gtb and geb are kept for the moment, but
a comment advise to rather use ltb and leb. Z.div now uses
Z.ltb and Z.leb.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14227 85f007b7-540e-0410-9357-904b9bb8a0f7
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Initial patch by Robbert Krebbers.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13900 85f007b7-540e-0410-9357-904b9bb8a0f7
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We now specify testbit by some initial and recursive equations.
The previous spec (via a complex split of the number in
low and high parts) is now a derived property in {N,Z}Bits.v
This way, proofs of implementations are quite simplier.
Note that these new specs doesn't imply anymore that testbit is a
morphism, we have to add this as a extra spec (but this lead
to trivial proofs when implementing).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13792 85f007b7-540e-0410-9357-904b9bb8a0f7
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For example, if we know that [f] is a morphism for [E1==>E2==>E],
then the goal [E (f x y) (f x' y')] will be transformed by [f_equiv]
into the subgoals [E1 x x'] and [E2 y y'].
This way, we can remove most of the explicit use of the morphism
instances in Numbers (lemmas foo_wd for each operator foo).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13763 85f007b7-540e-0410-9357-904b9bb8a0f7
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- a ltac solve_proper which generalizes solve_predicate_wd and co
- using le_elim is nicer that (apply le_lteq; destruct ...)
- "apply ->" can now be "apply" most of the time.
Benefit: NumPrelude is now almost empty
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13762 85f007b7-540e-0410-9357-904b9bb8a0f7
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git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13721 85f007b7-540e-0410-9357-904b9bb8a0f7
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See NatInt/NZBits.v for the common axiomatization of bitwise functions
over naturals / integers. Some specs aren't pretty, but easier to
prove, see alternate statements in property functors {N,Z}Bits.
Negative numbers are considered via the two's complement convention.
We provide implementations for N (in Ndigits.v), for nat (quite dummy,
just for completeness), for Z (new file Zdigits_def), for BigN
(for the moment partly by converting to N, to be improved soon)
and for BigZ.
NOTA: For BigN.shiftl and BigN.shiftr, the two arguments are now in
the reversed order (for consistency with the rest of the world):
for instance BigN.shiftl 1 10 is 2^10.
NOTA2: Zeven.Zdiv2 is _not_ doing (Zdiv _ 2), but rather (Zquot _ 2)
on negative numbers. For the moment I've kept it intact, and have
just added a Zdiv2' which is truly equivalent to (Zdiv _ 2).
To reorganize someday ?
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13689 85f007b7-540e-0410-9357-904b9bb8a0f7
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Some more results about sqrt. Similar results for sqrt_up.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13649 85f007b7-540e-0410-9357-904b9bb8a0f7
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as log2
Some more results about log2. Similar results for log2_up.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13648 85f007b7-540e-0410-9357-904b9bb8a0f7
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No infix notation "rem" for Zrem (that will probably become Z.rem in
a close future). This way, we avoid conflict with people already using
rem for their own need. Same for BigZ. We still use infix rem, but
only in the abstract layer of Numbers, in a way that doesn't inpact
the rest of Coq. Btw, the axiomatized function is now named rem
instead of remainder.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13640 85f007b7-540e-0410-9357-904b9bb8a0f7
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