data-tensor (empty) → 0.1.0.0

raw patch · 4 files changed

+117/−0 lines, 4 filesdep +basesetup-changed

Dependencies added: base

Files

• LICENSE +20/−0
• Setup.hs +2/−0
• data-tensor.cabal +23/−0
• src/Data/Tensor.hs +72/−0

@@ -0,0 +1,20 @@+Copyright (c) 2015 Tobias Dammers++Permission is hereby granted, free of charge, to any person obtaining+a copy of this software and associated documentation files (the+"Software"), to deal in the Software without restriction, including+without limitation the rights to use, copy, modify, merge, publish,+distribute, sublicense, and/or sell copies of the Software, and to+permit persons to whom the Software is furnished to do so, subject to+the following conditions:++The above copyright notice and this permission notice shall be included+in all copies or substantial portions of the Software.++THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.+IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY+CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,+TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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

@@ -0,0 +1,23 @@+name:                data-tensor+version:             0.1.0.0+synopsis:            Tensor and Group typeclasses+description:         Typeclasses for Groups (Monoids with an 'invert'+                     operation) and Tensors.+homepage:            https://bitbucket.org/tdammers/data-tensor+license:             MIT+license-file:        LICENSE+author:              Tobias Dammers+maintainer:          tdammers@gmail.com+copyright:           2015+category:            Data+build-type:          Simple+-- extra-source-files:+cabal-version:       >=1.10++library+  exposed-modules:     Data.Tensor+  -- other-modules:+  -- other-extensions:+  build-depends:       base >=4.5 && <5.0+  hs-source-dirs:      src+  default-language:    Haskell2010

@@ -0,0 +1,72 @@+{-#LANGUAGE MultiParamTypeClasses #-}+{-#LANGUAGE FlexibleInstances #-}+-- | Typeclasses for Group and Tensor, extending 'Monoid'.+module Data.Tensor+( module Data.Monoid+, Group (..)+, Tensor (..)+)+where++import Data.Monoid++-- | A group is a monoid with an invert operation.+-- Intuition: '><' is to '<>' what subtraction is to addition; 'invert' turns a+-- value into its complement (see Laws below), and corresponds with unary minus+-- in addition.+--+-- Laws:+--+-- > a >< b == a <> (invert b)+-- > a >< mempty == a+-- > a >< a == mempty+-- > a <> (invert a) == mempty+-- > invert mempty == mempty+--+class Monoid a => Group a where+    -- | Dual to '<>'.+    (><) :: a -> a -> a+    a >< b = a <> invert b+    -- | \"Negation\": convert an operand into its dual.+    invert :: a -> a+    invert x = mempty >< x++infixl 6 ><++instance Num a => Group (Sum a) where+    invert = Sum . negate . getSum++-- | Tensor allows us to define a relationship between two types, the second+-- one forming a Group.+-- The intuition is that the first type models something like a+-- "location", and the second (the group) models the relative distance between+-- two locations. Examples of Tensors include date/time values (point in time)+-- and timespans; positions in a vector space and displacement vectors;+-- pitches and intervals in music.+--+-- Tensor provides three operations: '?<>' (\"tensor addition\"), adding a+-- \"distance\" to a \"location\"; '?><' (\"tensor subtraction\"), undoing the effect+-- of adding a \"distance\" to a \"location\", and '>?<', getting the \"distance\"+-- between two \"locations\".+--+-- Laws:+--+-- > a ?<> (b >?< a) == b+-- > a ?<> (x <> y) == a ?<> x ?<> y+-- > a ?>< b == a ?<> (invert b)+-- > a ?<> (x >< y) == a ?<> x ?>< y+class Group b => Tensor a b where+    (?<>) :: a -> b -> a+    (?><) :: a -> b -> a+    (>?<) :: a -> a -> b+    a ?>< b = a ?<> invert b++infixl 6 ?<>+infixl 6 ?><+infixl 6 >?<++-- | All groups trivially form tensors with themselves+instance Group a => Tensor a a where+    (?<>) = (<>)+    (?><) = (><)+    (>?<) = (><)