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author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-18 18:02:20 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-18 18:02:20 +0000 |
commit | 59726c5343613379d38a9409af044d85cca130ed (patch) | |
tree | 185cef19334e67de344b6417a07c11ad61ed0c46 /plugins/micromega/RMicromega.v | |
parent | 16cf970765096f55a03efad96100add581ce0edb (diff) |
Some more revision of {P,N,Z}Arith + bitwise ops in Ndigits
Initial plan was only to add shiftl/shiftr/land/... to N and
other number type, this is only partly done, but this work has
diverged into a big reorganisation and improvement session
of PArith,NArith,ZArith.
Bool/Bool: add lemmas orb_diag (a||a = a) and andb_diag (a&&a = a)
PArith/BinPos:
- added a power function Ppow
- iterator iter_pos moved from Zmisc to here + some lemmas
- added Psize_pos, which is 1+log2, used to define Nlog2/Zlog2
- more lemmas on Pcompare and succ/+/* and order, allow
to simplify a lot some old proofs elsewhere.
- new/revised results on Pminus (including some direct proof of
stuff from Pnat)
PArith/Pnat:
- more direct proofs (limit the need of stuff about Pmult_nat).
- provide nicer names for some lemmas (eg. Pplus_plus instead of
nat_of_P_plus_morphism), compatibility notations provided.
- kill some too-specific lemmas unused in stdlib + contribs
NArith/BinNat:
- N_of_nat, nat_of_N moved from Nnat to here.
- a lemma relating Npred and Nminus
- revised definitions and specification proofs of Npow and Nlog2
NArith/Nnat:
- shorter proofs.
- stuff about Z_of_N is moved to Znat. This way, NArith is
entirely independent from ZArith.
NArith/Ndigits:
- added bitwise operations Nand Nor Ndiff Nshiftl Nshiftr
- revised proofs about Nxor, still using functional bit stream
- use the same approach to prove properties of Nand Nor Ndiff
ZArith/BinInt: huge simplification of Zplus_assoc + cosmetic stuff
ZArith/Zcompare: nicer proofs of ugly things like Zcompare_Zplus_compat
ZArith/Znat: some nicer proofs and names, received stuff about Z_of_N
ZArith/Zmisc: almost empty new, only contain stuff about badly-named
iter. Should be reformed more someday.
ZArith/Zlog_def: Zlog2 is now based on Psize_pos, this factorizes
proofs and avoid slowdown due to adding 1 in Z instead of in positive
Zarith/Zpow_def: Zpower_opt is renamed more modestly Zpower_alt
as long as I dont't know why it's slower on powers of two.
Elsewhere: propagate new names + some nicer proofs
NB: Impact on compatibility is probably non-zero, but should be
really moderate. We'll see on contribs, but a few Require here
and there might be necessary.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13651 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'plugins/micromega/RMicromega.v')
-rw-r--r-- | plugins/micromega/RMicromega.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/plugins/micromega/RMicromega.v b/plugins/micromega/RMicromega.v index 2b6ef8c5d..3f29a4fcf 100644 --- a/plugins/micromega/RMicromega.v +++ b/plugins/micromega/RMicromega.v @@ -67,7 +67,7 @@ Lemma RZSORaddon : SORaddon R0 R1 Rplus Rmult Rminus Ropp (@eq R) Rle (* ring elements *) 0%Z 1%Z Zplus Zmult Zminus Zopp (* coefficients *) Zeq_bool Zle_bool - IZR Nnat.nat_of_N pow. + IZR nat_of_N pow. Proof. constructor. constructor ; intros ; try reflexivity. @@ -94,7 +94,7 @@ Definition INZ (n:N) : R := | Npos p => IZR (Zpos p) end. -Definition Reval_expr := eval_pexpr Rplus Rmult Rminus Ropp IZR Nnat.nat_of_N pow. +Definition Reval_expr := eval_pexpr Rplus Rmult Rminus Ropp IZR nat_of_N pow. Definition Reval_op2 (o:Op2) : R -> R -> Prop := @@ -112,7 +112,7 @@ Definition Reval_formula (e: PolEnv R) (ff : Formula Z) := let (lhs,o,rhs) := ff in Reval_op2 o (Reval_expr e lhs) (Reval_expr e rhs). Definition Reval_formula' := - eval_formula Rplus Rmult Rminus Ropp (@eq R) Rle Rlt IZR Nnat.nat_of_N pow. + eval_formula Rplus Rmult Rminus Ropp (@eq R) Rle Rlt IZR nat_of_N pow. Lemma Reval_formula_compat : forall env f, Reval_formula env f <-> Reval_formula' env f. Proof. |