diff options
| author | letouzey | 2010-11-02 15:10:43 +0000 |
|---|---|---|
| committer | letouzey | 2010-11-02 15:10:43 +0000 |
| commit | d6ebd62341fd6bbe2b7d4e5309d8e13f786a9462 (patch) | |
| tree | 575ec66b8028a599f94d293ae32260b09e7874ef /theories/Numbers/Integer/Abstract | |
| parent | 1dccdb6b2c792969c5e09faebc2f761e46192ec4 (diff) | |
Numbers : log2. Abstraction, properties and implementations.
Btw, we finally declare the original Zpower as the power on Z.
We should switch to a more efficient one someday, but in the
meantime BigN is proved with respect to the old one.
TODO: reform Zlogarithm with respect to Zlog_def
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13606 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Integer/Abstract')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZAxioms.v | 8 | ||||
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZProperties.v | 2 |
2 files changed, 5 insertions, 5 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZAxioms.v b/theories/Numbers/Integer/Abstract/ZAxioms.v index 6e6cd7f0fc..47286c729e 100644 --- a/theories/Numbers/Integer/Abstract/ZAxioms.v +++ b/theories/Numbers/Integer/Abstract/ZAxioms.v @@ -9,7 +9,7 @@ (************************************************************************) Require Export NZAxioms. -Require Import NZPow NZSqrt. +Require Import NZPow NZSqrt NZLog. (** We obtain integers by postulating that successor of predecessor is identity. *) @@ -70,16 +70,16 @@ Module Type Parity (Import Z : ZAxiomsMiniSig'). Axiom odd_spec : forall n, odd n = true <-> Odd n. End Parity. -(** For the power and sqrt functions, the NZ axiomatizations are enough. *) +(** For pow sqrt log2, the NZ axiomatizations are enough. *) (** Let's group everything *) Module Type ZAxiomsSig := ZAxiomsMiniSig <+ HasCompare <+ HasAbs <+ HasSgn <+ Parity - <+ NZPow.NZPow <+ NZSqrt.NZSqrt. + <+ NZPow.NZPow <+ NZSqrt.NZSqrt <+ NZLog.NZLog2. Module Type ZAxiomsSig' := ZAxiomsMiniSig' <+ HasCompare <+ HasAbs <+ HasSgn <+ Parity - <+ NZPow.NZPow' <+ NZSqrt.NZSqrt'. + <+ NZPow.NZPow' <+ NZSqrt.NZSqrt' <+ NZLog.NZLog2. (** Division is left apart, since many different flavours are available *) diff --git a/theories/Numbers/Integer/Abstract/ZProperties.v b/theories/Numbers/Integer/Abstract/ZProperties.v index 8b34e5b2db..d2e9626737 100644 --- a/theories/Numbers/Integer/Abstract/ZProperties.v +++ b/theories/Numbers/Integer/Abstract/ZProperties.v @@ -12,4 +12,4 @@ Require Export ZAxioms ZMaxMin ZSgnAbs ZParity ZPow. Module Type ZProp (Z:ZAxiomsSig) := ZMaxMinProp Z <+ ZSgnAbsProp Z <+ ZParityProp Z <+ ZPowProp Z - <+ NZSqrt.NZSqrtProp Z Z. + <+ NZSqrt.NZSqrtProp Z Z <+ NZLog.NZLog2Prop Z Z Z. |