Modulenumeric-prelude-0.4.4Haskell98

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.

2 types
26 values

Packagenumeric-prelude-0.4.4
Exports28
LanguageHaskell98
LicenceBSD-3-Clause
SourcePeano.hs

datadata T

Constructors

Zero
Succ T

Instances25Bounded, Enum, Eq, Integral, Num, Ord, …

Bounded TDefined in numeric-prelude-0.4.4 · Number.Peano
Enum TDefined in numeric-prelude-0.4.4 · Number.Peano
Eq TDefined in numeric-prelude-0.4.4 · Number.Peano
Integral TDefined in numeric-prelude-0.4.4 · Number.Peano
Num TDefined in numeric-prelude-0.4.4 · Number.Peano
Ord TDefined in numeric-prelude-0.4.4 · Number.Peano
Read TDefined in numeric-prelude-0.4.4 · Number.Peano
Real TDefined in numeric-prelude-0.4.4 · Number.Peano
Show TDefined in numeric-prelude-0.4.4 · Number.Peano
Ix TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano
C TDefined in numeric-prelude-0.4.4 · Number.Peano

valueinfinity :: T

valueerr :: String -> String -> a

valueadd :: T -> T -> T

valuesub :: T -> T -> T

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

valuemul :: T -> T -> T

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

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

valueifLazy :: 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.

valueargMinFull :: (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

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

On equality the first operand is returned.

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

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

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

On equality the first operand is returned.

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

valueisAscendingFiniteList :: [T] -> Bool

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

valueisAscendingFiniteNumbers :: [T] -> Bool

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

valueglue :: 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

valueisAscending :: [T] -> Bool

datadata Valuable a

Constructors

Valuable
- costs :: T
- value :: a

Instances3Eq, Ord, Show

Eq a => Eq (Valuable a)Defined in numeric-prelude-0.4.4 · Number.Peano
Ord a => Ord (Valuable a)Defined in numeric-prelude-0.4.4 · Number.Peano
Show a => Show (Valuable a)Defined in numeric-prelude-0.4.4 · Number.Peano

valueincreaseCosts :: T -> Valuable a -> Valuable a

value(&&~) :: Valuable Bool -> Valuable Bool -> Valuable Bool

Compute (&&) with minimal costs.

valueandW :: [Valuable Bool] -> Valuable Bool

valueleW :: T -> T -> Valuable Bool

valueisAscendingW :: [T] -> Valuable Bool

valuenotImplemented :: String -> a