groups 0.4.1.0 → 0.5

raw patch · 2 files changed

+115/−15 lines, 2 filesdep ~basePVP ok

version bump matches the API change (PVP)

Dependency ranges changed: base

API changes (from Hackage documentation)

Files

• groups.cabal +13/−8
• src/Data/Group.hs +102/−7

@@ -1,19 +1,24 @@+cabal-version:       2.4 name:                groups-version:             0.4.1.0-synopsis:            Haskell 98 groups-description:         -  Haskell 98 groups. A group is a monoid with invertibility.-license:             BSD3+version:             0.5+synopsis:            Groups+description:+  A group is a monoid with invertibility.+license:             BSD-3-Clause 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 +source-repository head+  type:     git+  location: https://github.com/Taneb/groups.git+ library   exposed-modules:     Data.Group-  -- other-modules:       -  build-depends:       base <5+  -- other-modules:+  build-depends:       base >= 4.6 && < 5   hs-source-dirs:      src+  default-language:    Haskell2010

@@ -1,14 +1,34 @@+{-# LANGUAGE CPP           #-}+#if MIN_VERSION_base(4,12,0)+{-# LANGUAGE TypeOperators #-}+#endif+ module Data.Group where  import Data.Monoid+#if MIN_VERSION_base(4,7,0)+import Data.Proxy+#endif+#if MIN_VERSION_base(4,9,0)+import Data.Functor.Const+import Data.Functor.Identity+#endif+#if MIN_VERSION_base(4,12,0)+import GHC.Generics+#endif --- |A 'Group' is a 'Monoid' plus a function, 'invert', such that: +-- |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++  -- | Group subtraction: @x ~~ y == x \<> invert y@+  (~~) :: m -> m -> m+  x ~~ y = x `mappend` invert y+   -- |@'pow' a n == a \<> a \<> ... \<> a @   --   -- @ (n lots of a) @@@ -20,7 +40,7 @@     EQ -> mempty     GT -> f x0 n0     where-      f x n +      f x n         | even n = f (x `mappend` x) (n `quot` 2)         | n == 1 = x         | otherwise = g (x `mappend` x) (n `quot` 2) x@@ -28,16 +48,18 @@         | even n = g (x `mappend` x) (n `quot` 2) c         | n == 1 = x `mappend` c         | otherwise = g (x `mappend` x) (n `quot` 2) (x `mappend` c)-  ++infixl 7 ~~+ instance Group () where   invert () = ()-  pow () _ = ()+  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 #-}@@ -55,7 +77,7 @@ 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)@@ -68,8 +90,9 @@   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 @@ -90,3 +113,75 @@ 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)+++-- | A 'Group' G is 'Cyclic' if there exists an element x of G such that for all y in G, there exists an n, such that+--+-- @y = pow x n@+class Group a => Cyclic a where+  generator :: a++generated :: Cyclic a => [a]+generated =+  iterate (mappend generator) mempty++instance Cyclic () where+  generator = ()++#if MIN_VERSION_base(4,7,0)+-- | Trivial group, Functor style.+instance Group (Proxy x) where+  invert _ = Proxy+  _ ~~ _ = Proxy+  pow _ _ = Proxy++instance Abelian (Proxy x)++instance Cyclic (Proxy x) where+  generator = Proxy+#endif++-- 'Const' has existed for a long time, but the Monoid instance+-- arrives in base-4.9.0.0. Similarly, 'Identity' was defined in+-- base-4.8.0.0 but doesn't get the Monoid instance until base-4.9.0.0+#if MIN_VERSION_base(4,9,0)+-- | 'Const' lifts groups into a functor.+instance Group a => Group (Const a x) where+  invert (Const a) = Const (invert a)+  Const a ~~ Const b = Const (a ~~ b)++-- | 'Identity' lifts groups pointwise (at only one point).+instance Group a => Group (Identity a) where+  invert (Identity a) = Identity (invert a)+  Identity a ~~ Identity b = Identity (a ~~ b)++instance Abelian a => Abelian (Const a x)++instance Abelian a => Abelian (Identity a)++instance Cyclic a => Cyclic (Const a x) where+  generator = Const generator++instance Cyclic a => Cyclic (Identity a) where+  generator = Identity generator+#endif++-- (:*:) and (:.:) exist since base-4.6.0.0 but the Monoid instances+-- arrive in base-4.12.0.0.+#if MIN_VERSION_base(4,12,0)+-- | Product of groups, Functor style.+instance (Group (f a), Group (g a)) => Group ((f :*: g) a) where+  invert (a :*: b) = invert a :*: invert b+  (a :*: b) ~~ (c :*: d) = (a ~~ c) :*: (b ~~ d)++-- See https://gitlab.haskell.org/ghc/ghc/issues/11135#note_111802 for the reason Compose is not also provided.+-- Base does not define Monoid (Compose f g a) so this is the best we can+-- really do for functor composition.+instance Group (f (g a)) => Group ((f :.: g) a) where+  invert (Comp1 xs) = Comp1 (invert xs)+  Comp1 xs ~~ Comp1 ys = Comp1 (xs ~~ ys)++instance (Abelian (f a), Abelian (g a)) => Abelian ((f :*: g) a)++instance Abelian (f (g a)) => Abelian ((f :.: g) a)+#endif