Copyright	(C) 2015 mniip
License	BSD3
Maintainer	mniip <mniip@mniip.com>
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell2010

Data.Finite.Internal

Description

Synopsis

newtype Finite (n :: Nat) = Finite Integer
finite :: KnownNat n => Integer -> Finite n
getFinite :: Finite n -> Integer

Documentation

newtype Finite (n :: Nat) Source #

Finite number type. Finite n is inhabited by exactly n values. Invariants:

getFinite x < natVal x

getFinite x >= 0

Constructors

Finite Integer

Instances

KnownNat n => Bounded (Finite n) Source #	Throws an error for `Finite 0`
Instance details Defined in Data.Finite.Internal Methods minBound :: Finite n # maxBound :: Finite n #
KnownNat n => Enum (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods succ :: Finite n -> Finite n # pred :: Finite n -> Finite n # toEnum :: Int -> Finite n # fromEnum :: Finite n -> Int # enumFrom :: Finite n -> [Finite n] # enumFromThen :: Finite n -> Finite n -> [Finite n] # enumFromTo :: Finite n -> Finite n -> [Finite n] # enumFromThenTo :: Finite n -> Finite n -> Finite n -> [Finite n] #
Eq (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods (==) :: Finite n -> Finite n -> Bool # (/=) :: Finite n -> Finite n -> Bool #
KnownNat n => Integral (Finite n) Source #	Not modular arithmetic.
Instance details Defined in Data.Finite.Internal Methods quot :: Finite n -> Finite n -> Finite n # rem :: Finite n -> Finite n -> Finite n # div :: Finite n -> Finite n -> Finite n # mod :: Finite n -> Finite n -> Finite n # quotRem :: Finite n -> Finite n -> (Finite n, Finite n) # divMod :: Finite n -> Finite n -> (Finite n, Finite n) # toInteger :: Finite n -> Integer #
KnownNat n => Num (Finite n) Source #	Modular arithmetic. Only the `fromInteger` function is supposed to be useful.
Instance details Defined in Data.Finite.Internal Methods (+) :: Finite n -> Finite n -> Finite n # (-) :: Finite n -> Finite n -> Finite n # (*) :: Finite n -> Finite n -> Finite n # negate :: Finite n -> Finite n # abs :: Finite n -> Finite n # signum :: Finite n -> Finite n # fromInteger :: Integer -> Finite n #
Ord (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods compare :: Finite n -> Finite n -> Ordering # (<) :: Finite n -> Finite n -> Bool # (<=) :: Finite n -> Finite n -> Bool # (>) :: Finite n -> Finite n -> Bool # (>=) :: Finite n -> Finite n -> Bool # max :: Finite n -> Finite n -> Finite n # min :: Finite n -> Finite n -> Finite n #
KnownNat n => Read (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods readsPrec :: Int -> ReadS (Finite n) # readList :: ReadS [Finite n] # readPrec :: ReadPrec (Finite n) # readListPrec :: ReadPrec [Finite n] #
KnownNat n => Real (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods toRational :: Finite n -> Rational #
Show (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods showsPrec :: Int -> Finite n -> ShowS # show :: Finite n -> String # showList :: [Finite n] -> ShowS #
Generic (Finite n) Source #
Instance details Defined in Data.Finite.Internal Associated Types type Rep (Finite n) :: * -> * # Methods from :: Finite n -> Rep (Finite n) x # to :: Rep (Finite n) x -> Finite n #
NFData (Finite n) Source #
Instance details Defined in Data.Finite.Internal Methods rnf :: Finite n -> () #
type Rep (Finite n) Source #
Instance details Defined in Data.Finite.Internal type Rep (Finite n) = D1 (MetaData "Finite" "Data.Finite.Internal" "finite-typelits-0.1.4.2-LNt8ccQ3rb0a6MNjjNxeu" True) (C1 (MetaCons "Finite" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Integer)))

finite :: KnownNat n => Integer -> Finite n Source #

Convert an Integer into a Finite, throwing an error if the input is out of bounds.

getFinite :: Finite n -> Integer Source #

Convert a Finite into the corresponding Integer.