alg (empty) → 0.1.0.0

raw patch · 4 files changed

+124/−0 lines, 4 filesdep +basesetup-changed

Dependencies added: base

Files

• Algebra.hs +64/−0
• LICENSE +30/−0
• Setup.hs +2/−0
• alg.cabal +28/−0

@@ -0,0 +1,64 @@+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE TypeFamilies #-}++module Algebra where++import Control.Category+import Data.Functor+import Data.Functor.Const+import Data.Functor.Identity+import Data.Monoid hiding ((<>))+import Data.Proxy+import Data.Semigroup+import Prelude (Integer)+import qualified Prelude as Base++class Semigroup a => Abelian a++class Semigroup a => Idempotent a++class Monoid a => Group a where+    invert :: a -> a++instance Group () where+    invert () = ()++instance (Group a, Group b) => Group (a, b) where+    invert (a, b) = (invert a, invert b)++instance (Group a, Group b, Group c) => Group (a, b, c) where+    invert (a, b, c) = (invert a, invert b, invert c)++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)++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)++instance Group a => Group (Identity a) where invert = fmap invert++instance Group a => Group (Dual a) where invert (Dual a) = Dual (invert a)++instance Group (Proxy a) where invert Proxy = Proxy++instance Group a => Group (Const a b) where invert (Const a) = Const (invert a)++instance Group b => Group (a -> b) where invert = (.) invert++instance Group a => Group (Base.IO a) where invert = fmap invert++instance Group (Sum Integer) where invert (Sum a) = Sum (Base.negate a)++(+) :: Semigroup (Sum a) => a -> a -> a+a + b = getSum (Sum a <> Sum b)++(-) :: (Semigroup (Sum a), Group (Sum a)) => a -> a -> a+a - b = getSum (Sum a <> invert (Sum b))++(*) :: Semigroup (Product a) => a -> a -> a+a * b = getProduct (Product a <> Product b)++(/) :: (Semigroup (Product a), Group (Product a)) => a -> a -> a+a / b = getProduct (Product a <> invert (Product b))

@@ -0,0 +1,30 @@+© 2017 CE M Farkas-Dyck++All rights reserved.++Redistribution and use in source and binary forms, with or without+modification, are permitted provided that the following conditions+are met:++1. Redistributions of source code must retain the above copyright+   notice, this list of conditions and the following disclaimer.++2. 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.++3. Neither the name of the author nor the names of his contributors+   may be used to endorse or promote products derived from this software+   without specific prior written permission.++THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``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 AUTHORS 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.

@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain

@@ -0,0 +1,28 @@+name:                alg+version:             0.1.0.0+synopsis:            Algebraic structures+-- description:         +license:             BSD3+license-file:        LICENSE+author:              M Farkas-Dyck+maintainer:          strake888@gmail.com+-- copyright:           +category:            Math+build-type:          Simple+-- extra-source-files:  +cabal-version:       >=1.10++library+  exposed-modules:     Algebra+  -- other-modules:       +  other-extensions:    +  build-depends:       base >=4.9 && <5+  -- hs-source-dirs:      +  default-language:    Haskell2010+  default-extensions:  NoImplicitPrelude+                     , LambdaCase+                     , EmptyCase+                     , TypeOperators+                     , ConstraintKinds+                     , PolyKinds+  ghc-options:         -Wall