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author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-10-14 11:37:33 +0000 |
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committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-10-14 11:37:33 +0000 |
commit | 888c41d2bf95bb84fee28a8737515c9ff66aa94e (patch) | |
tree | 80c67a7a2aa22cabc94335bc14dcd33bed981417 /theories/Numbers/Integer/SpecViaZ/ZSig.v | |
parent | d7a3d9b4fbfdd0df8ab4d0475fc7afa1ed5f5bcb (diff) |
Numbers: new functions pow, even, odd + many reorganisations
- Simplification of functor names, e.g. ZFooProp instead of ZFooPropFunct
- The axiomatisations of the different fonctions are now in {N,Z}Axioms.v
apart for Z division (three separate flavours in there own files).
Content of {N,Z}AxiomsSig is extended, old version is {N,Z}AxiomsMiniSig.
- In NAxioms, the recursion field isn't that useful, since we axiomatize
other functions and not define them (apart in the toy NDefOps.v).
We leave recursion there, but in a separate NAxiomsFullSig.
- On Z, the pow function is specified to behave as Zpower : a^(-1)=0
- In BigN/BigZ, (power:t->N->t) is now pow_N, while pow is t->t->t
These pow could be more clever (we convert 2nd arg to N and use pow_N).
Default "^" is now (pow:t->t->t). BigN/BigZ ring is adapted accordingly
- In BigN, is_even is now even, its spec is changed to use Zeven_bool.
We add an odd. In BigZ, we add even and odd.
- In ZBinary (implem of ZAxioms by ZArith), we create an efficient Zpow
to implement pow. This Zpow should replace the current linear Zpower
someday.
- In NPeano (implem of NAxioms by Arith), we create pow, even, odd functions,
and we modify the div and mod functions for them to be linear, structural,
tail-recursive.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13546 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Integer/SpecViaZ/ZSig.v')
-rw-r--r-- | theories/Numbers/Integer/SpecViaZ/ZSig.v | 15 |
1 files changed, 11 insertions, 4 deletions
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSig.v b/theories/Numbers/Integer/SpecViaZ/ZSig.v index 021f4b1bf..b33ed5f8e 100644 --- a/theories/Numbers/Integer/SpecViaZ/ZSig.v +++ b/theories/Numbers/Integer/SpecViaZ/ZSig.v @@ -46,8 +46,9 @@ Module Type ZType. Parameter opp : t -> t. Parameter mul : t -> t -> t. Parameter square : t -> t. - Parameter power_pos : t -> positive -> t. - Parameter power : t -> N -> t. + Parameter pow_pos : t -> positive -> t. + Parameter pow_N : t -> N -> t. + Parameter pow : t -> t -> t. Parameter sqrt : t -> t. Parameter div_eucl : t -> t -> t * t. Parameter div : t -> t -> t. @@ -55,6 +56,8 @@ Module Type ZType. Parameter gcd : t -> t -> t. Parameter sgn : t -> t. Parameter abs : t -> t. + Parameter even : t -> bool. + Parameter odd : t -> bool. Parameter spec_compare: forall x y, compare x y = Zcompare [x] [y]. Parameter spec_eq_bool: forall x y, eq_bool x y = Zeq_bool [x] [y]. @@ -70,8 +73,9 @@ Module Type ZType. Parameter spec_opp: forall x, [opp x] = - [x]. Parameter spec_mul: forall x y, [mul x y] = [x] * [y]. Parameter spec_square: forall x, [square x] = [x] * [x]. - Parameter spec_power_pos: forall x n, [power_pos x n] = [x] ^ Zpos n. - Parameter spec_power: forall x n, [power x n] = [x] ^ Z_of_N n. + Parameter spec_pow_pos: forall x n, [pow_pos x n] = [x] ^ Zpos n. + Parameter spec_pow_N: forall x n, [pow_N x n] = [x] ^ Z_of_N n. + Parameter spec_pow: forall x n, [pow x n] = [x] ^ [n]. Parameter spec_sqrt: forall x, 0 <= [x] -> [sqrt x] ^ 2 <= [x] < ([sqrt x] + 1) ^ 2. Parameter spec_div_eucl: forall x y, @@ -81,6 +85,8 @@ Module Type ZType. Parameter spec_gcd: forall a b, [gcd a b] = Zgcd (to_Z a) (to_Z b). Parameter spec_sgn : forall x, [sgn x] = Zsgn [x]. Parameter spec_abs : forall x, [abs x] = Zabs [x]. + Parameter spec_even : forall x, even x = Zeven_bool [x]. + Parameter spec_odd : forall x, odd x = Zodd_bool [x]. End ZType. @@ -91,6 +97,7 @@ Module Type ZType_Notation (Import Z:ZType). Infix "+" := add. Infix "-" := sub. Infix "*" := mul. + Infix "^" := pow. Notation "- x" := (opp x). Infix "<=" := le. Infix "<" := lt. |