Number.Peano

Lazy Peano numbers represent natural numbers inclusive infinity. Since they are lazily evaluated, they are optimally for use as number type of genericLength et.al.

Documentation

data T

Constructors

Zero

Succ T

Instances

Bounded T

Defined in Number.Peano

Methods

minBound :: T

maxBound :: T

Enum T

Defined in Number.Peano

Methods

succ :: T -> T

pred :: T -> T

toEnum :: Int -> T

fromEnum :: T -> Int

enumFrom :: T -> [T]

enumFromThen :: T -> T -> [T]

enumFromTo :: T -> T -> [T]

enumFromThenTo :: T -> T -> T -> [T]

Eq T

Defined in Number.Peano

Methods

(==) :: T -> T -> Bool

(/=) :: T -> T -> Bool

Integral T

Defined in Number.Peano

Methods

quot :: T -> T -> T

rem :: T -> T -> T

div :: T -> T -> T

mod :: T -> T -> T

quotRem :: T -> T -> (T, T)

divMod :: T -> T -> (T, T)

toInteger :: T -> Integer

Num T

Defined in Number.Peano

Methods

(+) :: T -> T -> T

(-) :: T -> T -> T

(*) :: T -> T -> T

negate :: T -> T

abs :: T -> T

signum :: T -> T

fromInteger :: Integer -> T

Ord T

Defined in Number.Peano

Methods

compare :: T -> T -> Ordering

(<) :: T -> T -> Bool

(<=) :: T -> T -> Bool

(>) :: T -> T -> Bool

(>=) :: T -> T -> Bool

max :: T -> T -> T

min :: T -> T -> T

Read T

Defined in Number.Peano

Methods

readsPrec :: Int -> ReadS T

readList :: ReadS [T]

readPrec :: ReadPrec T

readListPrec :: ReadPrec [T]

Real T

Defined in Number.Peano

Methods

toRational :: T -> Rational

Show T

Defined in Number.Peano

Methods

showsPrec :: Int -> T -> ShowS

show :: T -> String

showList :: [T] -> ShowS

Ix T

Defined in Number.Peano

Methods

range :: (T, T) -> [T]

index :: (T, T) -> T -> Int

unsafeIndex :: (T, T) -> T -> Int

inRange :: (T, T) -> T -> Bool

rangeSize :: (T, T) -> Int

unsafeRangeSize :: (T, T) -> Int

C T

Defined in Number.Peano

Methods

compare :: T -> T -> Ordering

C T

Defined in Number.Peano

Methods

zero :: T

(+) :: T -> T -> T

(-) :: T -> T -> T

negate :: T -> T

C T

Defined in Number.Peano

Methods

isZero :: T -> Bool

C T

Defined in Number.Peano

Methods

(*) :: T -> T -> T

one :: T

fromInteger :: Integer -> T

(^) :: T -> Integer -> T

C T

Defined in Number.Peano

Methods

idt :: T

(<*>) :: T -> T -> T

cumulate :: [T] -> T

C T

Defined in Number.Peano

Methods

split :: T -> T -> (T, (Bool, T))

C T

Defined in Number.Peano

Methods

div :: T -> T -> T

mod :: T -> T -> T

divMod :: T -> T -> (T, T)

C T

Defined in Number.Peano

Methods

isUnit :: T -> Bool

stdAssociate :: T -> T

stdUnit :: T -> T

stdUnitInv :: T -> T

C T

Defined in Number.Peano

Methods

extendedGCD :: T -> T -> (T, (T, T))

gcd :: T -> T -> T

lcm :: T -> T -> T

C T

Defined in Number.Peano

Methods

abs :: T -> T

signum :: T -> T

C T

Defined in Number.Peano

Methods

toRational :: T -> Rational

C T

Defined in Number.Peano

Methods

quot :: T -> T -> T

rem :: T -> T -> T

quotRem :: T -> T -> (T, T)

C T

Defined in Number.Peano

Methods

toInteger :: T -> Integer

infinity :: T

err :: String -> String -> a

add :: T -> T -> T

sub :: T -> T -> T

subNeg :: T -> T -> (Bool, T)

mul :: T -> T -> T

fromPosEnum :: (C a, Enum a) => a -> T

toPosEnum :: (C a, Enum a) => T -> a

ifLazy :: Bool -> T -> T -> T

If all values are completely defined, then it holds

if b then x else y == ifLazy b x y

However if b is undefined, then it is at least known that the result is larger than min x y.

argMinFull :: (T, a) -> (T, a) -> (T, a)

cf. To how to find the shortest list in a list of lists efficiently, this means, also in the presence of infinite lists. http://www.haskell.org/pipermail/haskell-cafe/2006-October/018753.html

argMin :: (T, a) -> (T, a) -> a

On equality the first operand is returned.

argMinimum :: [(T, a)] -> a

argMaxFull :: (T, a) -> (T, a) -> (T, a)

argMax :: (T, a) -> (T, a) -> a

On equality the first operand is returned.

argMaximum :: [(T, a)] -> a

isAscendingFiniteList :: [T] -> Bool

x0 <= x1 && x1 <= x2 ... for possibly infinite numbers in finite lists.

isAscendingFiniteNumbers :: [T] -> Bool

toListMaybe :: a -> T -> [Maybe a]

glue :: T -> T -> (T, (Bool, T))

In glue x y == (z,(b,r)) z represents min x y, r represents max x y - min x y, and x<=y == b.

Cf. Numeric.NonNegative.Chunky

isAscending :: [T] -> Bool

data Valuable a

Constructors

Valuable

Fields

• costs :: T
• value :: a

Instances

Eq a => Eq (Valuable a)

Defined in Number.Peano

Methods

(==) :: Valuable a -> Valuable a -> Bool

(/=) :: Valuable a -> Valuable a -> Bool

Ord a => Ord (Valuable a)

Defined in Number.Peano

Methods

compare :: Valuable a -> Valuable a -> Ordering

(<) :: Valuable a -> Valuable a -> Bool

(<=) :: Valuable a -> Valuable a -> Bool

(>) :: Valuable a -> Valuable a -> Bool

(>=) :: Valuable a -> Valuable a -> Bool

max :: Valuable a -> Valuable a -> Valuable a

min :: Valuable a -> Valuable a -> Valuable a

Show a => Show (Valuable a)

Defined in Number.Peano

Methods

showsPrec :: Int -> Valuable a -> ShowS

show :: Valuable a -> String

showList :: [Valuable a] -> ShowS

increaseCosts :: T -> Valuable a -> Valuable a

(&&~) :: Valuable Bool -> Valuable Bool -> Valuable Bool infixr 3

Compute (&&) with minimal costs.

andW :: [Valuable Bool] -> Valuable Bool

leW :: T -> T -> Valuable Bool

isAscendingW :: [T] -> Valuable Bool

notImplemented :: String -> a