Copyright	© Anders Kaseorg 2013
License	BSD-style
Maintainer	Anders Kaseorg <andersk@mit.edu>
Stability	experimental
Portability	Non-portable (GHC extensions)
Safe Haskell	None
Language	Haskell98

Data.Nimber

Description

The finite nimbers, Nimber, are a quadratically closed field of characteristic 2 introduced in combinatorial game theory.

>>> 257 + 258 :: Nimber
*3
>>> sqrt 123456789 :: Nimber
*98433322
>>> 123456789/sqrt 123456789 :: Nimber
*98433322

This implementation was inspired by Patrick Hurst’s slow Haskell implementation that this replaced (with his permission), and by Michel Van den Bergh’s Python implementation at https://web.archive.org/web/20101124110959/http://alpha.uhasselt.be/Research/Algebra/Members/nimbers/nimbers.py.

Synopsis

data Nimber
fromNimber :: Nimber -> Integer
data NimberException
- = NegativeNimber
- | Innimerable String

Documentation

data Nimber Source #

The type of finite nimbers.

Instances

Enum Nimber Source #
Instance details Defined in Data.Nimber Methods succ :: Nimber -> Nimber # pred :: Nimber -> Nimber # toEnum :: Int -> Nimber # fromEnum :: Nimber -> Int # enumFrom :: Nimber -> [Nimber] # enumFromThen :: Nimber -> Nimber -> [Nimber] # enumFromTo :: Nimber -> Nimber -> [Nimber] # enumFromThenTo :: Nimber -> Nimber -> Nimber -> [Nimber] #
Eq Nimber Source #
Instance details Defined in Data.Nimber Methods (==) :: Nimber -> Nimber -> Bool # (/=) :: Nimber -> Nimber -> Bool #
Floating Nimber Source #	This partial `Floating` instance only supports `sqrt`. All other operations will throw the `Innimerable` exception.
Instance details Defined in Data.Nimber Methods pi :: Nimber # exp :: Nimber -> Nimber # log :: Nimber -> Nimber # sqrt :: Nimber -> Nimber # (**) :: Nimber -> Nimber -> Nimber # logBase :: Nimber -> Nimber -> Nimber # sin :: Nimber -> Nimber # cos :: Nimber -> Nimber # tan :: Nimber -> Nimber # asin :: Nimber -> Nimber # acos :: Nimber -> Nimber # atan :: Nimber -> Nimber # sinh :: Nimber -> Nimber # cosh :: Nimber -> Nimber # tanh :: Nimber -> Nimber # asinh :: Nimber -> Nimber # acosh :: Nimber -> Nimber # atanh :: Nimber -> Nimber # log1p :: Nimber -> Nimber # expm1 :: Nimber -> Nimber # log1pexp :: Nimber -> Nimber # log1mexp :: Nimber -> Nimber #
Fractional Nimber Source #	Note: Although nimbers support division, the `fromRational` operation makes little sense because `Rational`s are reduced according to ordinary multiplication instead of nimber multiplication.
Instance details Defined in Data.Nimber Methods (/) :: Nimber -> Nimber -> Nimber # recip :: Nimber -> Nimber # fromRational :: Rational -> Nimber #
Num Nimber Source #
Instance details Defined in Data.Nimber Methods (+) :: Nimber -> Nimber -> Nimber # (-) :: Nimber -> Nimber -> Nimber # (*) :: Nimber -> Nimber -> Nimber # negate :: Nimber -> Nimber # abs :: Nimber -> Nimber # signum :: Nimber -> Nimber # fromInteger :: Integer -> Nimber #
Ord Nimber Source #
Instance details Defined in Data.Nimber Methods compare :: Nimber -> Nimber -> Ordering # (<) :: Nimber -> Nimber -> Bool # (<=) :: Nimber -> Nimber -> Bool # (>) :: Nimber -> Nimber -> Bool # (>=) :: Nimber -> Nimber -> Bool # max :: Nimber -> Nimber -> Nimber # min :: Nimber -> Nimber -> Nimber #
Read Nimber Source #
Instance details Defined in Data.Nimber Methods readsPrec :: Int -> ReadS Nimber # readList :: ReadS [Nimber] # readPrec :: ReadPrec Nimber # readListPrec :: ReadPrec [Nimber] #
Show Nimber Source #
Instance details Defined in Data.Nimber Methods showsPrec :: Int -> Nimber -> ShowS # show :: Nimber -> String # showList :: [Nimber] -> ShowS #

fromNimber :: Nimber -> Integer Source #

Convert a Nimber to the corresponding natural number.

data NimberException Source #

The type of exceptions thrown by impossible Nimber operations.

Constructors

NegativeNimber	A negative integer was converted to a nimber.
Innimerable String	A transcendental function was called on nimbers.

Instances

Eq NimberException Source #
Instance details Defined in Data.Nimber Methods (==) :: NimberException -> NimberException -> Bool # (/=) :: NimberException -> NimberException -> Bool #
Ord NimberException Source #
Instance details Defined in Data.Nimber Methods compare :: NimberException -> NimberException -> Ordering # (<) :: NimberException -> NimberException -> Bool # (<=) :: NimberException -> NimberException -> Bool # (>) :: NimberException -> NimberException -> Bool # (>=) :: NimberException -> NimberException -> Bool # max :: NimberException -> NimberException -> NimberException # min :: NimberException -> NimberException -> NimberException #
Show NimberException Source #
Instance details Defined in Data.Nimber Methods showsPrec :: Int -> NimberException -> ShowS # show :: NimberException -> String # showList :: [NimberException] -> ShowS #
Exception NimberException Source #
Instance details Defined in Data.Nimber Methods toException :: NimberException -> SomeException # fromException :: SomeException -> Maybe NimberException # displayException :: NimberException -> String #