Copyright | (c) Henning Thielemann 2007-2012 |
---|---|

Maintainer | numericprelude@henning-thielemann.de |

Stability | provisional |

Portability | portable |

Safe Haskell | None |

Language | Haskell98 |

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.

## Synopsis

- data T
- 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
- argMinFull :: (T, a) -> (T, a) -> (T, a)
- argMin :: (T, a) -> (T, a) -> a
- argMinimum :: [(T, a)] -> a
- argMaxFull :: (T, a) -> (T, a) -> (T, a)
- argMax :: (T, a) -> (T, a) -> a
- argMaximum :: [(T, a)] -> a
- isAscendingFiniteList :: [T] -> Bool
- isAscendingFiniteNumbers :: [T] -> Bool
- toListMaybe :: a -> T -> [Maybe a]
- glue :: T -> T -> (T, (Bool, T))
- isAscending :: [T] -> Bool
- data Valuable a = Valuable {}
- increaseCosts :: T -> Valuable a -> Valuable a
- (&&~) :: Valuable Bool -> Valuable Bool -> Valuable Bool
- andW :: [Valuable Bool] -> Valuable Bool
- leW :: T -> T -> Valuable Bool
- isAscendingW :: [T] -> Valuable Bool
- notImplemented :: String -> a

# Documentation

#### Instances

Bounded T Source # | |

Enum T Source # | |

Eq T Source # | |

Integral T Source # | |

Num T Source # | |

Ord T Source # | |

Read T Source # | |

Real T Source # | |

Defined in Number.Peano toRational :: T -> Rational # | |

Show T Source # | |

Ix T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

C T Source # | |

Defined in Number.Peano toRational :: T -> Rational Source # | |

C T Source # | |

C T Source # | |

ifLazy :: Bool -> T -> T -> T Source #

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) Source #

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

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

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

isAscendingFiniteList :: [T] -> Bool Source #

`x0 <= x1 && x1 <= x2 ... `

for possibly infinite numbers in finite lists.

isAscendingFiniteNumbers :: [T] -> Bool Source #

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

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

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 Source #

#### Instances

Eq a => Eq (Valuable a) Source # | |

Ord a => Ord (Valuable a) Source # | |

Show a => Show (Valuable a) Source # | |

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

Compute `(&&)`

with minimal costs.

notImplemented :: String -> a Source #