module Algebra.Core(
Handle,stdin,stdout,stderr,
Bytes,readBytes,writeBytes,readHBytes,writeHBytes,
Chunk,readChunk,writeChunk,readHChunk,writeHChunk,
readString,writeString,readHString,writeHString,
Void,(:*:),(:+:),
Semigroup(..),Monoid(..),Disjonctive(..),Semiring(..),Ring(..),Invertible(..),
SubSemi(..),
Unit(..),
Endo(..),StrictEndo(..),
Dual(..),Product(..),
OrdList(..),Interleave(..),Accum(..),Max(..),Min(..),Id(..),
Deductive(..),Category(..),(<<<),(>>>),(+++),
Choice(..),Split(..),
Constraint,c'listOf,c'list,c'int,c'char,c'string,c'float,c'_,
const,(&),($^),is,fix,
first,second,
ifThenElse,bool,extreme,guard,fail,unit,when,unless,
tailSafe,headDef,fromMaybe,
rmod,inside,swap,
comparing,inOrder,insertOrd,invertOrd,
Assoc(..),assoc,
Range(..),
amb,unamb,
module Prelude,IsString(..)
) where
import Prelude hiding (
readFile,writeFile,
Functor(..),Monad(..),
sequence,mapM,mapM_,sequence_,(=<<),
map,(++),foldl,foldr,foldr1,concat,filter,length,sum,lookup,
(+),(*),(.),id,const,(),(/),recip,
or,any,and,all,elem,span,break,splitAt,take,drop,takeWhile,dropWhile,
until,negate,zipWith,zipWith3,
minimum,maximum,product)
import Control.Concurrent (killThread,newEmptyMVar,forkIO,putMVar,takeMVar)
import Control.Exception (evaluate)
import System.IO.Unsafe (unsafePerformIO)
import System.IO (stdin,stdout,stderr)
import qualified Prelude as P
import Data.Tree
import qualified Data.ByteString.Lazy as BSL
import qualified Data.ByteString as BSS
import GHC.IO.Handle (Handle,hGetContents,hPutStr)
import Data.Ord (comparing)
import GHC.Exts (IsString(..))
type Constraint a = a -> a
c'listOf :: Constraint a -> Constraint [a]
c'listOf _ = c'_
c'list :: Constraint [a]
c'list = c'listOf c'_
c'int :: Constraint Int
c'int = c'_
c'char :: Constraint Char
c'char = c'_
c'string :: Constraint String
c'string = c'_
c'float :: Constraint Float
c'float = c'_
c'couple :: Constraint a -> Constraint b -> Constraint (a,b)
c'couple _ _ = c'_
c'_ :: Constraint a
c'_ = id
type Chunk = BSS.ByteString
type Bytes = BSL.ByteString
readBytes :: String -> IO Bytes
readBytes = BSL.readFile
readChunk :: String -> IO Chunk
readChunk = BSS.readFile
readString :: String -> IO String
readString = P.readFile
writeBytes :: String -> Bytes -> IO ()
writeBytes = BSL.writeFile
writeChunk :: String -> Chunk -> IO ()
writeChunk = BSS.writeFile
writeString :: String -> String -> IO ()
writeString = P.writeFile
readHBytes :: Handle -> IO Bytes
readHBytes = BSL.hGetContents
readHChunk :: Handle -> IO Chunk
readHChunk = BSS.hGetContents
readHString :: Handle -> IO String
readHString = hGetContents
writeHBytes :: Handle -> Bytes -> IO ()
writeHBytes = BSL.hPut
writeHChunk :: Handle -> Chunk -> IO ()
writeHChunk = BSS.hPut
writeHString :: Handle -> String -> IO ()
writeHString = hPutStr
data Void
type a:*:b = (a,b)
type a:+:b = Either a b
class Semigroup m where
(+) :: m -> m -> m
default (+) :: Num m => m -> m -> m
(+) = (P.+)
infixr 6 +
instance Semigroup Void where _+_ = undefined
instance Semigroup () where _+_ = ()
instance Semigroup Bool where (+) = (||)
instance Semigroup Int
instance Semigroup Integer
instance Semigroup Rational
instance Semigroup Float
instance Semigroup Double
instance Semigroup Bytes where (+) = BSL.append
instance Semigroup Chunk where (+) = BSS.append
instance Semigroup [a] where
(+) (x:t) = \l -> x:(t+l)
(+) [] = \l -> l
instance (Semigroup a,Semigroup b) => Semigroup (a:*:b) where ~(a,b) + ~(c,d) = (a+c,b+d)
instance (Semigroup a,Semigroup b,Semigroup c) => Semigroup (a,b,c) where
~(a,b,c) + ~(a',b',c') = (a+a',b+b',c+c')
instance SubSemi b a => Semigroup (a:+:b) where
Left a+Left b = Left (a+b)
a+b = Right (from a+from b)
where from = cast <|> id
instance Semigroup (Maybe a) where
Nothing + b = b ; a + _ = a
class Semigroup m => Monoid m where
zero :: m
default zero :: Num m => m
zero = 0
instance Monoid Void where zero = undefined
instance Monoid () where zero = ()
instance Monoid Int ; instance Monoid Integer
instance Monoid Rational
instance Monoid Float ; instance Monoid Double
instance Monoid Bytes where zero = BSL.empty
instance Monoid Chunk where zero = BSS.empty
instance Monoid [a] where zero = []
instance (Monoid a,Monoid b) => Monoid (a:*:b) where zero = (zero,zero)
instance (Monoid a,Monoid b,Monoid c) => Monoid (a,b,c) where
zero = (zero,zero,zero)
instance (SubSemi b a,Monoid a) => Monoid (a:+:b) where zero = Left zero
instance Monoid Bool where zero = False
instance Monoid (Maybe a) where zero = Nothing
class (Semigroup a,Semigroup b) => SubSemi a b where
cast :: b -> a
instance Monoid a => SubSemi a () where cast _ = zero
instance Monoid a => SubSemi a Void where cast _ = zero
instance Semigroup a => SubSemi a a where cast = id
class Monoid m => Disjonctive m where
negate :: m -> m
negate = (zero )
() :: m -> m -> m
ab = a+negate b
instance Disjonctive Int where
negate = P.negate ; () = (P.-)
instance Disjonctive Integer where
negate = P.negate ; () = (P.-)
instance Disjonctive Rational where
negate = P.negate ; () = (P.-)
instance Disjonctive Float where
negate = P.negate ; () = (P.-)
instance Disjonctive Double where
negate = P.negate ; () = (P.-)
instance Disjonctive Bool where
negate = not
a b = not (a==b)
instance (Disjonctive a,Disjonctive b) => Disjonctive (a:*:b) where
negate (a,b) = (negate a,negate b)
(a,b)(c,d) = (ac,bd)
class Monoid m => Semiring m where
(*) :: m -> m -> m
default (*) :: Num m => m -> m -> m
(*) = (P.*)
class Semiring m => Ring m where
one :: m
default one :: Num m => m
one = 1
infixl 7 *
instance Semiring Bool where (*) = (&&)
instance Ring Bool where one = True
instance Semiring Int ; instance Ring Int
instance Semiring Rational ; instance Ring Rational
instance Semiring Integer ; instance Ring Integer
instance Semiring Float ; instance Ring Float
instance Semiring Double ; instance Ring Double
instance Monoid a => Semiring [a] where
(a:as) * (b:bs) = a+b:as*bs
_ * _ = zero
instance Monoid a => Ring [a] where
one = zero:one
instance (Semiring a,Semiring b) => Semiring (a:*:b) where
~(a,b) * ~(c,d) = (a*c,b*d)
instance (Ring a,Ring b) => Ring (a:*:b) where
one = (one,one)
class (Ring m,Disjonctive m) => Invertible m where
recip :: m -> m
recip = (one /)
(/) :: m -> m -> m
a / b = a * recip b
instance Invertible Rational where
recip = P.recip ; (/) = (P./)
instance Invertible Float where
recip = P.recip ; (/) = (P./)
instance Invertible Double where
recip = P.recip ; (/) = (P./)
class Unit f where
pure :: a -> f a
instance Unit (Either a) where pure = Right
instance Unit Maybe where pure = Just
instance Monoid w => Unit ((,) w) where pure a = (zero,a)
instance Unit ((->) b) where pure = P.const
instance Unit [] where pure a = [a]
instance Unit Tree where pure a = Node a []
instance Unit IO where pure = P.return
class Deductive k where
(.) :: k b c -> k a b -> k a c
class Deductive k => Category k where
id :: k a a
instance Deductive (->) where
(.) = (P..)
instance Category (->) where
id = P.id
(<<<) :: Category k => k b c -> k a b -> k a c
(<<<) = (.)
(>>>) :: Category k => k a b -> k b c -> k a c
(>>>) = flip (<<<)
infixr 1 >>>,<<<
infixr 9 .
class Category k => Choice k where
(<|>) :: k a c -> k b c -> k (a:+:b) c
infixr 1 <|>
instance Choice (->) where
(f <|> _) (Left a) = f a
(_ <|> g) (Right b) = g b
class Category k => Split k where
(<#>) :: k a c -> k b d -> k (a,b) (c,d)
infixr 2 <#>
instance Split (->) where f <#> g = \ ~(a,b) -> (f a,g b)
newtype Product a = Product { getProduct :: a }
deriving (Eq,Ord,Show)
instance Ring a => Semigroup (Product a) where
Product a+Product b = Product (a*b)
instance Ring a => Monoid (Product a) where
zero = Product one
newtype Endo k a = Endo { runEndo :: k a a }
instance Category k => Semigroup (Endo k a) where Endo f+Endo g = Endo (g . f)
instance Category k => Monoid (Endo k a) where zero = Endo id
newtype StrictEndo a = StrictEndo { runStrictEndo :: a -> a }
instance Semigroup (StrictEndo a) where
StrictEndo f + StrictEndo g = StrictEndo h
where h a = let fa = f a in fa `seq` g fa
newtype Accum a = Accum { getAccum :: Maybe a }
instance Monoid a => Semigroup (Accum a) where
Accum Nothing + Accum Nothing = Accum Nothing
Accum a + Accum b = Accum (Just (from a+from b))
where from = maybe zero id
instance Monoid a => Monoid (Accum a) where zero = Accum Nothing
instance Unit Accum where pure = Accum . pure
newtype Id a = Id { getId :: a }
instance Show a => Show (Id a) where
show (Id a) = "Id "+show a
instance Unit Id where pure = Id
instance Semigroup (Id a) where a + _ = a
newtype Max a = Max { getMax :: a }
deriving (Eq,Ord,Bounded,Show)
instance Ord a => Semigroup (Max a) where a + b = max a b
instance (Ord a,Bounded a) => Monoid (Max a) where zero = minBound
instance (Ord a,Bounded a) => Semiring (Max a) where a * b = min a b
instance (Ord a,Bounded a) => Ring (Max a) where one = maxBound
newtype Min a = Min { getMin :: a }
deriving (Eq,Show)
instance Ord a => Ord (Min a) where
compare (Min a) (Min b) = compare b a
instance Bounded a => Bounded (Min a) where
minBound = Min maxBound
maxBound = Min minBound
instance Ord a => Semigroup (Min a) where a + b = max a b
instance (Ord a,Bounded a) => Monoid (Min a) where zero = minBound
instance (Ord a,Bounded a) => Semiring (Min a) where a * b = min a b
instance (Ord a,Bounded a) => Ring (Min a) where one = maxBound
newtype Dual m = Dual { getDual :: m }
instance Semigroup m => Semigroup (Dual m) where Dual a+Dual b = Dual (b+a)
deriving instance Monoid m => Monoid (Dual m)
instance Semiring m => Semiring (Dual m) where Dual a * Dual b = Dual (b*a)
instance Ring m => Ring (Dual m) where one = Dual one
newtype OrdList a = OrdList { getOrdList :: [a] }
deriving (Eq,Ord,Show)
instance Ord a => Semigroup (OrdList a) where
OrdList oa + OrdList ob = OrdList (oa ++ ob)
where (x:xt) ++ (y:yt) = a : c : cs
where (a,_,z) = inOrder x y
~(c:cs) = if z then xt ++ (y:yt) else (x:xt) ++ yt
a ++ b = a + b
deriving instance Ord a => Monoid (OrdList a)
deriving instance Unit OrdList
data Assoc k a = Assoc k a
deriving Show
instance Ord k => Eq (Assoc k a) where
a == b = compare a b == EQ
instance Ord k => Ord (Assoc k a) where
compare (Assoc k _) (Assoc k' _) = compare k k'
assoc :: a -> Assoc a a
assoc a = Assoc a a
inOrder :: Ord t => t -> t -> (t,t,Bool)
inOrder a b = (x,y,z)
where ~(x,y) | z = (a,b)
| otherwise = (b,a)
z = a<=b
insertOrd :: Ord t => t -> [t] -> [t]
insertOrd e [] = [e]
insertOrd e (x:xs) = a:y:ys
where (a,_,z) = inOrder e x
~(y:ys) = if z then x:xs else insertOrd e xs
newtype Range a = Range (a,a)
instance Unit Range where pure a = Range (a,a)
instance Ord a => Ord (Range a) where
compare (Range (a,b)) (Range (a',b'))
| b<a' = LT
| b'<a = GT
| otherwise = EQ
instance Ord a => Eq (Range a) where
a == b = compare a b == EQ
extreme :: Bounded a => Bool -> a
extreme b = if b then maxBound else minBound
newtype Interleave a = Interleave { interleave :: [a] }
instance Semigroup (Interleave a) where
Interleave ia + Interleave ib = Interleave (inter ia ib)
where inter (a:as) bs = a:inter bs as
inter [] bs = bs
deriving instance Monoid (Interleave a)
(&) :: a -> (a -> b) -> b
(&) = flip ($)
infixl 0 &
is :: a -> (a -> Bool) -> Bool
is = (&)
infixr 1 +++
(+++) :: Split k => (a -> k c c) -> (b -> k d d) -> (a:+:b) -> k (c,d) (c,d)
f +++ g = first.f <|> second.g
second :: Split k => k a b -> k (c,a) (c,b)
second a = id <#> a
first :: Split k => k a b -> k (a,c) (b,c)
first a = a <#> id
guard :: (Unit m,Monoid (m ())) => Bool -> m ()
guard p = if p then unit else zero
ifThenElse :: Bool -> a -> a -> a
ifThenElse b th el = if b then th else el
bool :: a -> a -> Bool -> a
bool th el b = ifThenElse b th el
tailSafe :: [a] -> [a]
tailSafe [] = [] ; tailSafe (_:t) = t
headDef :: a -> [a] -> a
headDef d [] = d ; headDef _ (x:_) = x
fail :: String -> a
fail = error
const :: Unit m => a -> m a
const = pure
fix :: (a -> a) -> a
fix f = y where y = f y
unit :: Unit m => m ()
unit = pure ()
when :: Unit m => Bool -> m () -> m ()
when p m = if p then m else unit
unless :: Unit m => Bool -> m () -> m ()
unless p m = if p then unit else m
invertOrd :: Ordering -> Ordering
invertOrd GT = LT ; invertOrd LT = GT ; invertOrd EQ = EQ
inside :: Ord t => t -> t -> (t -> Bool)
inside x y = \z -> x<=z && z<=y
rmod :: (RealFloat m,Invertible m) => m -> m -> m
a`rmod`b = b * r
where (_n,r) = c'couple c'int c'_ $ properFraction (a/b)
infixl 7 `rmod`
swap :: (a,b) -> (b,a)
swap (a,b) = (b,a)
fromMaybe :: a -> Maybe a -> a
fromMaybe a = maybe a id
($^) :: (a -> b -> c) -> b -> a -> c
($^) = flip
amb :: IO a -> IO a -> IO a
ma `amb` mb = do
res <- newEmptyMVar
ta <- forkIO $ ma P.>>= putMVar res . Left
tb <- forkIO $ mb P.>>= putMVar res . Right
takeMVar res P.>>= \c -> case c of
Left a -> P.fmap (const a) (killThread tb)
Right a -> P.fmap (const a) (killThread ta)
unamb :: a -> a -> a
unamb a b = unsafePerformIO (evaluate a `amb` evaluate b)