constructive-algebra (empty) → 0.0.0

raw patch · 4 files changed

+197/−0 lines, 4 filesdep +QuickCheckdep +basesetup-changed

Dependencies added: QuickCheck, base

Files

LICENSE +30/−0
Setup.hs +3/−0
constructive-algebra.cabal +54/−0
src/Algebra/Structures/Ring.hs +110/−0

+ LICENSE view

@@ -0,0 +1,30 @@+Copyright Anders Mörtberg 2010++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 Anders Mörtberg 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.

+ Setup.hs view

@@ -0,0 +1,3 @@+#!/usr/bin/env runhaskell+import Distribution.Simple+main = defaultMain

+ constructive-algebra.cabal view

@@ -0,0 +1,54 @@+-- constructive-algebra.cabal auto-generated by cabal init. For+-- additional options, see+-- http://www.haskell.org/cabal/release/cabal-latest/doc/users-guide/authors.html#pkg-descr.++Name:                constructive-algebra++-- The package version. See the Haskell package versioning policy+-- (http://www.haskell.org/haskellwiki/Package_versioning_policy) for+-- standards guiding when and how versions should be incremented.+Version:             0.0.0++Synopsis:            A library for constructive algebra.+Description:         A library for constructive algebra.++License:             BSD3+License-file:        LICENSE++Author:              Anders Mortberg, Bassel Mannaa++Maintainer:          mortberg@student.chalmers.se++-- A copyright notice.+-- Copyright:           ++-- Stability of the pakcage (experimental, provisional, stable...)+Stability:           Experimental++Category:            Math, Algebra++Build-type:          Simple++-- Extra files to be distributed with the package, such as examples or+-- a README.+-- Extra-source-files:  ++-- Constraint on the version of Cabal needed to build this package.+Cabal-version:       >=1.2+++Library+  -- Modules exported by the library.+  Exposed-modules:     Algebra.Structures.Ring+  +  -- Packages needed in order to build this package.+  Build-depends:       base >= 3 && <= 4, QuickCheck >= 2 +  +  -- Modules not exported by this package.+  -- Other-modules:       +  +  -- Extra tools (e.g. alex, hsc2hs, ...) needed to build the source.+  -- Build-tools:         +  +  -- Source directories+  hs-source-dirs: src, .

+ src/Algebra/Structures/Ring.hs view

@@ -0,0 +1,110 @@+-- | The representation of the ring structure.+module Algebra.Structures.Ring +  ( Ring(..)+  , propRing+  , (<->), (<^>)+  , sumRing, productRing+  ) where++import Test.QuickCheck+++infixl 8 <^>+infixl 7 <*>+infixl 6 <+>+infixl 6 <->+++-------------------------------------------------------------------------------+-- | Definition of rings++class Ring a where+  -- | Addition+  (<+>) :: a -> a -> a++  -- | Multiplication+  (<*>) :: a -> a -> a+  +  -- | Compute additive inverse+  neg   :: a -> a++  -- | The additive identity+  zero  :: a++  -- | The multiplicative identity+  one   :: a+++-------------------------------------------------------------------------------+-- Properties++-- Addition satisfy the same properties as a commutative group+propAddAssoc :: (Ring a, Eq a) => a -> a -> a -> (Bool,String)+propAddAssoc a b c = ((a <+> b) <+> c == a <+> (b <+> c), "propAddAssoc")++-- Zero is the additive identity+propAddIdentity :: (Ring a, Eq a) => a -> (Bool,String)+propAddIdentity a = (a <+> zero == a && zero <+> a == a, "propAddIdentity")++-- Negation is the additive inverse+propAddInv :: (Ring a, Eq a) => a -> (Bool,String)+propAddInv a = (neg a <+> a == zero && a <+> neg a == zero, "propAddInv")++-- Addition is commutative+propAddComm :: (Ring a, Eq a) => a -> a -> (Bool,String)+propAddComm x y = (x <+> y == y <+> x, "propAddComm")++-- Multiplication is associative+propMulAssoc :: (Ring a, Eq a) => a -> a -> a -> (Bool,String)+propMulAssoc a b c = ((a <*> b) <*> c == a <*> (b <*> c), "propMulAssoc")++-- Multiplication is right-distributive over addition+propRightDist :: (Ring a, Eq a) => a -> a -> a -> (Bool,String)+propRightDist a b c = +  ((a <+> b) <*> c == (a <*> c) <+> (b <*> c), "propRightDist")++-- Multiplication is left-ditributive over addition+propLeftDist :: (Ring a, Eq a) => a -> a -> a -> (Bool,String)+propLeftDist a b c = + (a <*> (b <+> c) == (a <*> b) <+> (a <*> c), "propLeftDist")++-- One is multiplicative identity+propMulIdentity :: (Ring a, Eq a) => a -> (Bool,String)+propMulIdentity a = (one <*> a == a && a <*> one == a, "propMulIdentity")++-- | Specification of rings.+-- Test that the arguments satisfy the ring axioms.+propRing :: (Ring a, Eq a) => a -> a -> a -> Property+propRing a b c = whenFail (print errorMsg) cond+  where+  (cond,errorMsg) = +    propAddAssoc a b c &&& propAddIdentity a  &&& propAddInv a        &&&+    propAddComm a b    &&& propMulAssoc a b c &&& propRightDist a b c &&&+    propLeftDist a b c &&& propMulIdentity a++  (False,x) &&& _         = (False,x)+  _         &&& (False,x) = (False,x)+  _         &&& _         = (True,"")+++-------------------------------------------------------------------------------+-- Operations++-- | Subtraction+(<->) :: Ring a => a -> a -> a+a <-> b = a <+> neg b++-- | Summation+sumRing :: Ring a => [a] -> a+sumRing = foldr (<+>) zero++-- | Product+productRing :: Ring a => [a] -> a+productRing = foldr (<*>) one++-- | Exponentiation+(<^>) :: Ring a => a -> Integer -> a+x <^> 0 = one+x <^> y = if y < 0 +             then error "<^>: Input should be positive"+             else x <*> x <^> (y-1)