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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,3 @@ +#! /usr/bin/env runhaskell +> import Distribution.Simple +> main = defaultMain diff --git a/Test/Main.hs b/Test/Main.hs new file mode 100644 --- /dev/null +++ b/Test/Main.hs @@ -0,0 +1,14 @@ +module Main where + +import qualified Test.Numeric.NonNegative.Chunky as Chunky + +prefix :: String -> [(String, IO ())] -> [(String, IO ())] +prefix msg = + map (\(str,test) -> (msg ++ "." ++ str, test)) + +main :: IO () +main = + mapM_ (\(msg,io) -> putStr (msg++": ") >> io) $ + concat $ + prefix "NonNegative.Chunky" Chunky.tests : + [] diff --git a/Test/Numeric/NonNegative/Chunky.hs b/Test/Numeric/NonNegative/Chunky.hs new file mode 100644 --- /dev/null +++ b/Test/Numeric/NonNegative/Chunky.hs @@ -0,0 +1,216 @@ +{- | +Copyright : (c) Henning Thielemann 2007 + +Maintainer : haskell@henning-thielemann.de +Stability : stable +Portability : Haskell 98 +-} +module Test.Numeric.NonNegative.Chunky (tests) where + +-- import Test.Utility +import Test.QuickCheck (test, Property, (==>)) + +import qualified Numeric.NonNegative.Chunky as Chunky +import qualified Numeric.NonNegative.Class as NonNeg +import qualified Numeric.NonNegative.Wrapper as NonNegW +-- import Numeric.NonNegative.Class ((-|)) + +-- import Debug.Trace (trace) + +import qualified Prelude as P +import Prelude hiding (min, max, abs, signum, compare) + + +infixl 5 $~ + +($~) :: NonNeg.C a => + (a -> b) -> (Chunky.T a -> b) +($~) f = f . Chunky.toNumber + +infixl 4 ==~ + +(==~) :: NonNeg.C a => + Chunky.T a -> a -> Bool +(==~) xs ys = + Chunky.toNumber xs == ys + + + +add :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +add x y = x+y ==~ (+) $~ x $~ y + +sub :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +sub x y = + if x>y + then x-y ==~ (-) $~ x $~ y + else y-x ==~ (-) $~ y $~ x + +mul :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +mul x y = x*y ==~ (*) $~ x $~ y + +min :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +min x y = P.min x y ==~ P.min $~ x $~ y + +max :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +max x y = P.max x y ==~ P.max $~ x $~ y + +abs :: NonNeg.C a => Chunky.T a -> Bool +abs x = P.abs x ==~ P.abs $~ x + +signum :: NonNeg.C a => Chunky.T a -> Bool +signum x = P.signum x ==~ P.signum $~ x + +equal :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +equal x y = (x == y) == (==) $~ x $~ y + +compare :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Bool +compare x y = P.compare x y == P.compare $~ x $~ y + + +infinity :: NonNeg.C a => a -> Chunky.T a +infinity = Chunky.fromChunks . repeat . (1+) + +checkInfinity :: NonNeg.C a => a -> Chunky.T a -> Bool +checkInfinity limit x = + let y = Chunky.fromNumber limit + in P.min x y == y + +addInfiniteL :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +addInfiniteL limit x y = + checkInfinity limit (infinity x + y) + +addInfiniteR :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +addInfiniteR limit x y = + checkInfinity limit (y + infinity x) + + +mulInfiniteL :: NonNeg.C a => a -> a -> Chunky.T a -> Property +mulInfiniteL limit x y = + Chunky.isPositive y ==> + checkInfinity limit (infinity x * y) + +{- | +Without normalization the test would fail for +@y = Chunky.fromChunks [0,1]@ +-} +mulInfiniteR :: NonNeg.C a => a -> a -> Chunky.T a -> Property +mulInfiniteR limit x y = + Chunky.isPositive y ==> + checkInfinity limit (Chunky.normalize y * infinity x) + +{- +mulInfiniteL :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +mulInfiniteL limit x y = + if Chunky.isNull y + then Chunky.isNull (infinity x * y) + else checkInfinity limit (infinity x * y) + +mulInfiniteR :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +mulInfiniteR limit x y = + if Chunky.isNull y + then Chunky.isNull (y * infinity x) + else checkInfinity limit (y * infinity x) +-} + +minRecursiveL :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Property +minRecursiveL x y = + Chunky.isPositive x ==> + let z = P.min (x+z) y + in z == y + +minRecursiveR :: NonNeg.C a => Chunky.T a -> Chunky.T a -> Property +minRecursiveR x y = + Chunky.isPositive x ==> + let z = P.min y (x+z) + in z == y + +minInfiniteL :: NonNeg.C a => a -> Chunky.T a -> Bool +minInfiniteL x y = + P.min (infinity x) y == y + +minInfiniteR :: NonNeg.C a => a -> Chunky.T a -> Bool +minInfiniteR x y = + P.min y (infinity x) == y + +maxInfiniteL :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +maxInfiniteL limit x y = + checkInfinity limit (P.max (infinity x) y) + +maxInfiniteR :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +maxInfiniteR limit x y = + checkInfinity limit (P.max y (infinity x)) + +minInfiniteAssociative :: NonNeg.C a => a -> a -> Chunky.T a -> Bool +minInfiniteAssociative x y z = + P.min (P.min (infinity x) (infinity y)) z == z + +maxInfiniteAssociative :: NonNeg.C a => a -> a -> a -> Chunky.T a -> Bool +maxInfiniteAssociative limit x y z = + checkInfinity limit + (P.max (P.max (infinity x) (infinity y)) z) + +compareInfiniteL :: NonNeg.C a => a -> Chunky.T a -> Bool +compareInfiniteL x y = + P.compare (infinity x) y == GT + +compareInfiniteR :: NonNeg.C a => a -> Chunky.T a -> Bool +compareInfiniteR x y = + P.compare y (infinity x) == LT + + + + + +type Card = NonNegW.T Int + +tests :: [(String, IO ())] +tests = + ("add", + test (add :: Chunky.T Card -> Chunky.T Card -> Bool)) : + ("sub", + test (sub :: Chunky.T Card -> Chunky.T Card -> Bool)) : + ("mul", + test (mul :: Chunky.T Card -> Chunky.T Card -> Bool)) : + ("min", + test (min :: Chunky.T Card -> Chunky.T Card -> Bool)) : + ("max", + test (max :: Chunky.T Card -> Chunky.T Card -> Bool)) : + ("abs", + test (abs :: Chunky.T Card -> Bool)) : + ("signum", + test (signum :: Chunky.T Card -> Bool)) : + ("equal", + test (equal :: Chunky.T Card -> Chunky.T Card -> Bool)) : + ("compare", + test (compare :: Chunky.T Card -> Chunky.T Card -> Bool)) : + + ("addInfiniteL", + test (addInfiniteL :: Card -> Card -> Chunky.T Card -> Bool)) : + ("addInfiniteR", + test (addInfiniteR :: Card -> Card -> Chunky.T Card -> Bool)) : + ("mulInfiniteL", + test (mulInfiniteL :: Card -> Card -> Chunky.T Card -> Property)) : + ("mulInfiniteR", + test (mulInfiniteR :: Card -> Card -> Chunky.T Card -> Property)) : + ("minRecursiveL", + test (minRecursiveL :: Chunky.T Card -> Chunky.T Card -> Property)) : + ("minRecursiveR", + test (minRecursiveR :: Chunky.T Card -> Chunky.T Card -> Property)) : + ("minInfiniteL", + test (minInfiniteL :: Card -> Chunky.T Card -> Bool)) : + ("minInfiniteR", + test (minInfiniteR :: Card -> Chunky.T Card -> Bool)) : + ("maxInfiniteL", + test (maxInfiniteL :: Card -> Card -> Chunky.T Card -> Bool)) : + ("maxInfiniteR", + test (maxInfiniteR :: Card -> Card -> Chunky.T Card -> Bool)) : + ("minInfiniteAssociative", + test (minInfiniteAssociative :: Card -> Card -> Chunky.T Card -> Bool)) : + ("maxInfiniteAssociative", + test (maxInfiniteAssociative :: Card -> Card -> Card -> Chunky.T Card -> Bool)) : + + ("compareInfiniteL", + test (compareInfiniteL :: Card -> Chunky.T Card -> Bool)) : + ("compareInfiniteR", + test (compareInfiniteR :: Card -> Chunky.T Card -> Bool)) : + [] diff --git a/Test/Utility.hs b/Test/Utility.hs new file mode 100644 --- /dev/null +++ b/Test/Utility.hs @@ -0,0 +1,28 @@ +module Test.Utility where + +import Test.QuickCheck (Arbitrary(..)) + +import qualified Numeric.NonNegative.Wrapper as NonNeg +import Control.Monad (liftM) +import Data.Char (chr) + + +type TimeDiff = NonNeg.Int + +timeToDouble :: TimeDiff -> NonNeg.Double +timeToDouble = fromIntegral + +makeFracTime :: (TimeDiff, TimeDiff) -> NonNeg.Double +makeFracTime (n,d) = + timeToDouble n / (timeToDouble d + 1) + + +instance Arbitrary Char where + arbitrary = liftM (chr . (32+) . flip mod 96) arbitrary + coarbitrary = undefined + +instance Arbitrary a => Arbitrary (Maybe a) where + arbitrary = + arbitrary >>= + \b -> if b then fmap Just arbitrary else return Nothing + coarbitrary = undefined diff --git a/non-negative.cabal b/non-negative.cabal new file mode 100644 --- /dev/null +++ b/non-negative.cabal @@ -0,0 +1,34 @@ +Name: non-negative +Version: 0.0.1 +License: GPL +License-File: LICENSE +Author: Henning Thielemann +Maintainer: Henning Thielemann +Homepage: http://darcs.haskell.org/non-negative/ +Category: Math +Build-Type: Simple +Build-Depends: base>=1.0, QuickCheck +Synopsis: Non-negative numbers +Description: + Provides a class for non-negative numbers, + a wrapper which can turn any ordered numeric type into a member of that class, + and a lazy number type for non-negative numbers + (a generalization of Peano numbers). + This library is used by the 'event-list' package. +GHC-Options: -Wall +Tested-With: GHC==6.4.1 +Hs-Source-Dirs: src +Exposed-Modules: + Numeric.NonNegative.Class + Numeric.NonNegative.Wrapper + Numeric.NonNegative.Chunky +Other-Modules: + Numeric.NonNegative.Utility + +Executable: test +Hs-source-dirs: src, . +GHC-Options: -Wall +Main-Is: Test/Main.hs +Other-Modules: + Test.Utility + Test.Numeric.NonNegative.Chunky diff --git a/src/Numeric/NonNegative/Chunky.hs b/src/Numeric/NonNegative/Chunky.hs new file mode 100644 --- /dev/null +++ b/src/Numeric/NonNegative/Chunky.hs @@ -0,0 +1,152 @@ +{- | +Copyright : (c) Henning Thielemann 2007 + +Maintainer : haskell@henning-thielemann.de +Stability : stable +Portability : Haskell 98 + +A lazy number type, which is a generalization of lazy Peano numbers. +Comparisons can be made lazy and +thus computations are possible which are impossible with strict number types, +e.g. you can compute @let y = min (1+y) 2 in y@. +You can even work with infinite values. +However, depending on the granularity, +the memory consumption is higher than that for strict number types. +This number type is of interest for the merge operation of event lists, +which allows for co-recursive merges. +-} +module Numeric.NonNegative.Chunky + (T, fromChunks, fromNumber, toNumber, normalize, isNull, isPositive) where + +import qualified Numeric.NonNegative.Class as NonNeg +import Control.Monad (liftM, liftM2) + +import Test.QuickCheck (Arbitrary(..)) + +{- | +A chunky non-negative number is a list of non-negative numbers. +It represents the sum of the list elements. +It is possible to represent a finite number with infinitely many chunks +by using an infinite number of zeros. + +Note the following problems: + +Addition is commutative only for finite representations. +E.g. @let y = min (1+y) 2 in y@ is defined, +@let y = min (y+1) 2 in y@ is not. +-} +newtype T a = Cons {decons :: [a]} + + +fromChunks :: NonNeg.C a => [a] -> T a +fromChunks = Cons + +fromNumber :: NonNeg.C a => a -> T a +fromNumber = fromChunks . (:[]) + +toNumber :: NonNeg.C a => T a -> a +toNumber = sum . decons + + +instance (Show a) => Show (T a) where + showsPrec p x = + showParen (p>10) + (showString "Chunky.fromChunks " . showsPrec 10 (decons x)) + + +lift2 :: ([a] -> [a] -> [a]) -> (T a -> T a -> T a) +lift2 f (Cons x) (Cons y) = Cons $ f x y + +{- | +Remove zero chunks. +-} +normalize :: NonNeg.C a => T a -> T a +normalize = Cons . filter (>0) . decons + +isNullList :: NonNeg.C a => [a] -> Bool +isNullList = null . filter (>0) + +isNull :: NonNeg.C a => T a -> Bool +isNull = isNullList . decons + -- null . decons . normalize + +isPositive :: NonNeg.C a => T a -> Bool +isPositive = not . isNull + +check :: String -> Bool -> a -> a +check funcName b x = + if b + then x + else error ("Numeric.NonNegative.Chunky."++funcName++": negative number") + + +{- | +In @glue x y == (z,r,b)@ +@z@ represents @min x y@, +@r@ represents @max x y - min x y@, +and @x b@ or @x>y ==> not b@, for @x==y@ the value of b is arbitrary. +-} +glue :: (NonNeg.C a) => [a] -> [a] -> ([a], [a], Bool) +glue [] ys = ([], ys, True) +glue xs [] = ([], xs, False) +glue (x:xs) (y:ys) = + let (z,(zs,rs,b)) = + case compare x y of + LT -> (x, glue xs ((y-x):ys)) + GT -> (y, glue ((x-y):xs) ys) + EQ -> (x, glue xs ys) + in (z:zs,rs,b) + +equalList :: (NonNeg.C a) => [a] -> [a] -> Bool +equalList x y = + let (_,r,_) = glue x y + in isNullList r + +compareList :: (NonNeg.C a) => [a] -> [a] -> Ordering +compareList x y = + let (_,r,b) = glue x y + in if isNullList r + then EQ + else if b then LT else GT + +minList :: (NonNeg.C a) => [a] -> [a] -> [a] +minList x y = + let (z,_,_) = glue x y in z + +maxList :: (NonNeg.C a) => [a] -> [a] -> [a] +maxList x y = + let (z,r,_) = glue x y in z++r + + +instance (NonNeg.C a) => Eq (T a) where + (Cons x) == (Cons y) = equalList x y + +instance (NonNeg.C a) => Ord (T a) where + compare (Cons x) (Cons y) = compareList x y + min = lift2 minList + max = lift2 maxList + + +instance (NonNeg.C a) => NonNeg.C (T a) where + (Cons x) -| (Cons w) = + let sub _ [] = [] + sub z (y:ys) = + if z Num (T a) where + (+) = lift2 (++) + (Cons x) - (Cons y) = + let (_,d,b) = glue x y + d' = Cons d + in check "-" (not b || isNull d') d' + negate x = check "negate" (isNull x) x + fromInteger = fromNumber . fromInteger + (*) = lift2 (liftM2 (*)) + abs = id + signum = fromNumber . (\b -> if b then 1 else 0) . isPositive + + +instance (NonNeg.C a, Arbitrary a) => Arbitrary (T a) where + arbitrary = liftM Cons arbitrary + coarbitrary = undefined diff --git a/src/Numeric/NonNegative/Class.hs b/src/Numeric/NonNegative/Class.hs new file mode 100644 --- /dev/null +++ b/src/Numeric/NonNegative/Class.hs @@ -0,0 +1,35 @@ +{- | +Copyright : (c) Henning Thielemann 2007 + +Maintainer : haskell@henning-thielemann.de +Stability : stable +Portability : Haskell 98 + +A type class for non-negative numbers. +Prominent instances are 'Numeric.NonNegative.Wrapper.T' and peano numbers. +This class cannot do any checks, +but it let you show to the user what arguments your function expects. +In fact many standard functions ('take', '(!!)', ...) +should have this type class constraint. +Thus you must define class instances with care. +-} +module Numeric.NonNegative.Class (C(..)) where + + +{- | +Instances of this class must ensure non-negative values. +We cannot enforce this by types, but the type class constraint @NonNegative.C@ +avoids accidental usage of types which allow for negative numbers. +-} +class (Ord a, Num a) => C a where + {- | + @x -| y == max 0 (x-y)@ + + The default implementation is not efficient, + because it compares the values and then subtracts, again, if safe. + @max 0 (x-y)@ is more elegant and efficient + but not possible in the general case, + since @x-y@ may already yield a negative number. + -} + (-|) :: a -> a -> a + x -| y = if x >= y then x-y else 0 diff --git a/src/Numeric/NonNegative/Utility.hs b/src/Numeric/NonNegative/Utility.hs new file mode 100644 --- /dev/null +++ b/src/Numeric/NonNegative/Utility.hs @@ -0,0 +1,11 @@ +module Numeric.NonNegative.Utility where + + +mapPair :: (a -> c, b -> d) -> (a,b) -> (c,d) +mapPair ~(f,g) ~(x,y) = (f x, g y) + +mapFst :: (a -> c) -> (a,b) -> (c,b) +mapFst f ~(x,y) = (f x, y) + +mapSnd :: (b -> d) -> (a,b) -> (a,d) +mapSnd g ~(x,y) = (x, g y) diff --git a/src/Numeric/NonNegative/Wrapper.hs b/src/Numeric/NonNegative/Wrapper.hs new file mode 100644 --- /dev/null +++ b/src/Numeric/NonNegative/Wrapper.hs @@ -0,0 +1,185 @@ +{- | +Copyright : (c) Henning Thielemann 2007 + +Maintainer : haskell@henning-thielemann.de +Stability : stable +Portability : Haskell 98 + +A type for non-negative numbers. +It performs a run-time check at construction time (i.e. at run-time) +and is a member of the non-negative number type class +'Numeric.NonNegative.Class.C'. +-} +module Numeric.NonNegative.Wrapper + (T, fromNumber, fromNumberMsg, fromNumberClip, fromNumberUnsafe, toNumber, + Int, Integer, Float, Double, Ratio, Rational) where + +import qualified Numeric.NonNegative.Class as NonNeg + +import Test.QuickCheck (Arbitrary(..)) +import Numeric.NonNegative.Utility(mapPair, mapSnd) +import Control.Monad (liftM) + +import qualified Data.Ratio as R +import qualified Prelude as P +import Prelude hiding (Int, Integer, Float, Double, Rational) + + +newtype T a = Cons {unwrap :: a} + deriving (Eq, Ord) + +instance Show a => Show (T a) where + showsPrec p (Cons a) = showsPrec p a + + +{- | +Convert a number to a non-negative number. +If a negative number is given, an error is raised. +-} +fromNumber :: (Ord a, Num a) => + a + -> T a +fromNumber = fromNumberMsg "fromNumber" + +fromNumberMsg :: (Ord a, Num a) => + String {- ^ name of the calling function to be used in the error message -} + -> a + -> T a +fromNumberMsg funcName x = + if x>=0 + then Cons x + else error (funcName++": negative number") + +fromNumberWrap :: (Ord a, Num a) => + String + -> a + -> T a +fromNumberWrap funcName = + fromNumberMsg ("NonNegative.Wrapper."++funcName) + +{- | +Convert a number to a non-negative number. +A negative number will be replaced by zero. +Use this function with care since it may hide bugs. +-} +fromNumberClip :: (Ord a, Num a) => + a + -> T a +fromNumberClip = Cons . max 0 + +{- | +Wrap a number into a non-negative number without doing checks. +This routine exists entirely for efficiency reasons +and must be used only in cases where you are absolutely sure, +that the input number is non-negative. +-} +fromNumberUnsafe :: + a + -> T a +fromNumberUnsafe = Cons + +{- +export only this in order to disable direct access to the record field +by record update syntax +-} +toNumber :: T a -> a +toNumber = unwrap + + +{- | +Results are not checked for positivity. +-} +lift :: (a -> a) -> (T a -> T a) +lift f = Cons . f . toNumber + +liftWrap :: (Ord a, Num a) => String -> (a -> a) -> (T a -> T a) +liftWrap msg f = fromNumberWrap msg . f . toNumber + + +{- | +Results are not checked for positivity. +-} +lift2 :: (a -> a -> a) -> (T a -> T a -> T a) +lift2 f (Cons x) (Cons y) = Cons $ f x y + + + +instance (Ord a, Num a) => NonNeg.C (T a) where + (Cons x) -| (Cons y) = fromNumberClip (x-y) + +instance (Ord a, Num a) => Num (T a) where + (+) = lift2 (+) + (Cons x) - (Cons y) = fromNumberWrap "-" (x-y) + negate = liftWrap "negate" negate + fromInteger x = fromNumberWrap "fromInteger" (fromInteger x) + (*) = lift2 (*) + abs = lift abs + signum = lift signum + +instance Real a => Real (T a) where + toRational = toRational . toNumber + +{- required for Integral instance -} +instance (Ord a, Num a, Enum a) => Enum (T a) where + toEnum = fromNumberWrap "toEnum" . toEnum + fromEnum = fromEnum . toNumber + +instance (Ord a, Num a, Bounded a) => Bounded (T a) where + minBound = fromNumberClip minBound + maxBound = fromNumberWrap "maxBound" maxBound + +instance Integral a => Integral (T a) where + toInteger = toInteger . toNumber + quot = lift2 quot + rem = lift2 rem + quotRem (Cons x) (Cons y) = + mapPair (Cons, Cons) (quotRem x y) + div = lift2 div + mod = lift2 mod + divMod (Cons x) (Cons y) = + mapPair (Cons, Cons) (divMod x y) + +instance (Ord a, Fractional a) => Fractional (T a) where + fromRational = fromNumberWrap "fromRational" . fromRational + (/) = lift2 (/) + + +instance (RealFrac a) => RealFrac (T a) where + properFraction = mapSnd fromNumberUnsafe . properFraction . toNumber + truncate = truncate . toNumber + round = round . toNumber + ceiling = ceiling . toNumber + floor = floor . toNumber + +instance (Ord a, Floating a) => Floating (T a) where + pi = fromNumber pi + exp = lift exp + sqrt = lift sqrt + log = liftWrap "log" log + (**) = lift2 (**) + logBase (Cons x) = liftWrap "logBase" (logBase x) + sin = liftWrap "sin" sin + tan = liftWrap "tan" tan + cos = liftWrap "cos" cos + asin = liftWrap "asin" asin + atan = liftWrap "atan" atan + acos = liftWrap "acos" acos + sinh = liftWrap "sinh" sinh + tanh = liftWrap "tanh" tanh + cosh = liftWrap "cosh" cosh + asinh = liftWrap "asinh" asinh + atanh = liftWrap "atanh" atanh + acosh = liftWrap "acosh" acosh + + +instance (Num a, Arbitrary a) => Arbitrary (T a) where + arbitrary = liftM (Cons . abs) arbitrary + coarbitrary = undefined + + +type Int = T P.Int +type Integer = T P.Integer +type Ratio a = T (R.Ratio a) +type Rational = T P.Rational +type Float = T P.Float +type Double = T P.Double