basement-0.0.3: Foundation scrap box of array & string

LicenseBSD-style
MaintainerHaskell Foundation
Safe HaskellNone
LanguageHaskell2010

Basement.Bounded

Description

Types to represent ℤ/nℤ.

ℤ/nℤ is a finite field and is defined as the set of natural number: {0, 1, ..., n − 1}.

Synopsis

Documentation

data Zn64 n Source #

A type level bounded natural backed by a Word64

Instances

Eq (Zn64 n) Source # 

Methods

(==) :: Zn64 n -> Zn64 n -> Bool #

(/=) :: Zn64 n -> Zn64 n -> Bool #

Ord (Zn64 n) Source # 

Methods

compare :: Zn64 n -> Zn64 n -> Ordering #

(<) :: Zn64 n -> Zn64 n -> Bool #

(<=) :: Zn64 n -> Zn64 n -> Bool #

(>) :: Zn64 n -> Zn64 n -> Bool #

(>=) :: Zn64 n -> Zn64 n -> Bool #

max :: Zn64 n -> Zn64 n -> Zn64 n #

min :: Zn64 n -> Zn64 n -> Zn64 n #

Show (Zn64 n) Source # 

Methods

showsPrec :: Int -> Zn64 n -> ShowS #

show :: Zn64 n -> String #

showList :: [Zn64 n] -> ShowS #

From (Zn64 n) Word256 Source # 

Methods

from :: Zn64 n -> Word256 Source #

From (Zn64 n) Word128 Source # 

Methods

from :: Zn64 n -> Word128 Source #

From (Zn64 n) Word64 Source # 

Methods

from :: Zn64 n -> Word64 Source #

(KnownNat n, NatWithinBound Word32 n) => From (Zn64 n) Word32 Source # 

Methods

from :: Zn64 n -> Word32 Source #

(KnownNat n, NatWithinBound Word16 n) => From (Zn64 n) Word16 Source # 

Methods

from :: Zn64 n -> Word16 Source #

(KnownNat n, NatWithinBound Word8 n) => From (Zn64 n) Word8 Source # 

Methods

from :: Zn64 n -> Word8 Source #

(KnownNat n, NatWithinBound Word64 n) => From (Zn n) (Zn64 n) Source # 

Methods

from :: Zn n -> Zn64 n Source #

KnownNat n => From (Zn64 n) (Zn n) Source # 

Methods

from :: Zn64 n -> Zn n Source #

data Zn n Source #

A type level bounded natural

Instances

Eq (Zn n) Source # 

Methods

(==) :: Zn n -> Zn n -> Bool #

(/=) :: Zn n -> Zn n -> Bool #

Ord (Zn n) Source # 

Methods

compare :: Zn n -> Zn n -> Ordering #

(<) :: Zn n -> Zn n -> Bool #

(<=) :: Zn n -> Zn n -> Bool #

(>) :: Zn n -> Zn n -> Bool #

(>=) :: Zn n -> Zn n -> Bool #

max :: Zn n -> Zn n -> Zn n #

min :: Zn n -> Zn n -> Zn n #

Show (Zn n) Source # 

Methods

showsPrec :: Int -> Zn n -> ShowS #

show :: Zn n -> String #

showList :: [Zn n] -> ShowS #

(KnownNat n, NatWithinBound Word256 n) => From (Zn n) Word256 Source # 

Methods

from :: Zn n -> Word256 Source #

(KnownNat n, NatWithinBound Word128 n) => From (Zn n) Word128 Source # 

Methods

from :: Zn n -> Word128 Source #

(KnownNat n, NatWithinBound Word64 n) => From (Zn n) Word64 Source # 

Methods

from :: Zn n -> Word64 Source #

(KnownNat n, NatWithinBound Word32 n) => From (Zn n) Word32 Source # 

Methods

from :: Zn n -> Word32 Source #

(KnownNat n, NatWithinBound Word16 n) => From (Zn n) Word16 Source # 

Methods

from :: Zn n -> Word16 Source #

(KnownNat n, NatWithinBound Word8 n) => From (Zn n) Word8 Source # 

Methods

from :: Zn n -> Word8 Source #

(KnownNat n, NatWithinBound Word64 n) => From (Zn n) (Zn64 n) Source # 

Methods

from :: Zn n -> Zn64 n Source #

KnownNat n => From (Zn64 n) (Zn n) Source # 

Methods

from :: Zn64 n -> Zn n Source #

zn64 :: forall n. (KnownNat n, NatWithinBound Word64 n) => Word64 -> Zn64 n Source #

Create an element of ℤ/nℤ from a Word64

If the value is greater than n, then the value is normalized by using the integer modulus n

zn :: forall n. KnownNat n => Natural -> Zn n Source #

Create an element of ℤ/nℤ from a Natural.

If the value is greater than n, then the value is normalized by using the integer modulus n

zn64Nat :: forall m n. (KnownNat m, KnownNat n, NatWithinBound Word64 m, NatWithinBound Word64 n, CmpNat m n ~ LT) => Proxy m -> Zn64 n Source #

Create an element of ℤ/nℤ from a type level Nat

znNat :: forall m n. (KnownNat m, KnownNat n, CmpNat m n ~ LT) => Proxy m -> Zn n Source #

Create an element of ℤ/nℤ from a type level Nat