groups-0.4.0.0/0000755000000000000000000000000012220506530011351 5ustar0000000000000000groups-0.4.0.0/LICENSE0000644000000000000000000000301212220506530012352 0ustar0000000000000000Copyright (c) 2013, Nathan "Taneb" van Doorn All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. * Neither the name of Nathan "Taneb" van Doorn nor the names of other contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. groups-0.4.0.0/groups.cabal0000644000000000000000000000113012220506530013647 0ustar0000000000000000name: groups version: 0.4.0.0 synopsis: Haskell 98 groups description: Haskell 98 groups. A group is a monoid with invertibility. license: BSD3 license-file: LICENSE author: Nathan "Taneb" van Doorn maintainer: nvd1234@gmail.com copyright: Copyright (C) 2013 Nathan van Doorn category: Algebra, Data, Math build-type: Simple cabal-version: >=1.8 library exposed-modules: Data.Group -- other-modules: build-depends: base <5 hs-source-dirs: src groups-0.4.0.0/Setup.hs0000644000000000000000000000005612220506530013006 0ustar0000000000000000import Distribution.Simple main = defaultMain groups-0.4.0.0/src/0000755000000000000000000000000012220506530012140 5ustar0000000000000000groups-0.4.0.0/src/Data/0000755000000000000000000000000012220506530013011 5ustar0000000000000000groups-0.4.0.0/src/Data/Group.hs0000644000000000000000000000523512220506530014446 0ustar0000000000000000module Data.Group where import Data.Monoid -- |A 'Group' is a 'Monoid' plus a function, 'invert', such that: -- -- @a \<> invert a == mempty@ -- -- @invert a \<> a == mempty@ class Monoid m => Group m where invert :: m -> m -- |@'pow' a n == a \<> a \<> ... \<> a @ -- -- @ (n lots of a) @ -- -- If n is negative, the result is inverted. pow :: Integral x => m -> x -> m pow x0 n0 = case compare n0 0 of LT -> invert . f x0 $ negate n0 EQ -> mempty GT -> f x0 n0 where f x n | even n = f (x `mappend` x) (n `quot` 2) | n == 1 = x | otherwise = g (x `mappend` x) ((n - 1) `quot` 2) x g x n c | even n = g (x `mappend` x) (n `quot` 2) c | n == 1 = x `mappend` c | otherwise = g (x `mappend` x) ((n - 1) `quot` 2) (x `mappend` c) instance Group () where invert () = () pow () _ = () instance Num a => Group (Sum a) where invert = Sum . negate . getSum {-# INLINE invert #-} pow (Sum a) b = Sum (a * fromIntegral b) instance Fractional a => Group (Product a) where invert = Product . recip . getProduct {-# INLINE invert #-} pow (Product a) b = Product (a ^^ b) instance Group a => Group (Dual a) where invert = Dual . invert . getDual {-# INLINE invert #-} pow (Dual a) n = Dual (pow a n) instance Group b => Group (a -> b) where invert f = invert . f pow f n e = pow (f e) n instance (Group a, Group b) => Group (a, b) where invert (a, b) = (invert a, invert b) pow (a, b) n = (pow a n, pow b n) instance (Group a, Group b, Group c) => Group (a, b, c) where invert (a, b, c) = (invert a, invert b, invert c) pow (a, b, c) n = (pow a n, pow b n, pow c n) instance (Group a, Group b, Group c, Group d) => Group (a, b, c, d) where invert (a, b, c, d) = (invert a, invert b, invert c, invert d) pow (a, b, c, d) n = (pow a n, pow b n, pow c n, pow d n) instance (Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e) where invert (a, b, c, d, e) = (invert a, invert b, invert c, invert d, invert e) pow (a, b, c, d, e) n = (pow a n, pow b n, pow c n, pow d n, pow e n) -- |An 'Abelian' group is a 'Group' that follows the rule: -- -- @a \<> b == b \<> a@ class Group g => Abelian g instance Abelian () instance Num a => Abelian (Sum a) instance Fractional a => Abelian (Product a) instance Abelian a => Abelian (Dual a) instance Abelian b => Abelian (a -> b) instance (Abelian a, Abelian b) => Abelian (a, b) instance (Abelian a, Abelian b, Abelian c) => Abelian (a, b, c) instance (Abelian a, Abelian b, Abelian c, Abelian d) => Abelian (a, b, c, d) instance (Abelian a, Abelian b, Abelian c, Abelian d, Abelian e) => Abelian (a, b, c, d, e)