Copyright	(c) 2023 GYELD GMBH
License	Apache 2.0
Maintainer	[email protected]
Stability	develop
Safe Haskell	None
Language	Haskell2010

GeniusYield.Types

Description

Synopsis

Documentation

data Natural #

Type representing arbitrary-precision non-negative integers.

>>> 2^100 :: Natural
1267650600228229401496703205376

Operations whose result would be negative throw (Underflow :: ArithException),

>>> -1 :: Natural
*** Exception: arithmetic underflow

Since: base-4.8.0.0

Instances

Instances details

Enum Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Enum Methods succ ∷ Natural → Natural # pred ∷ Natural → Natural # toEnum ∷ Int → Natural # fromEnum ∷ Natural → Int # enumFrom ∷ Natural → [Natural] # enumFromThen ∷ Natural → Natural → [Natural] # enumFromTo ∷ Natural → Natural → [Natural] # enumFromThenTo ∷ Natural → Natural → Natural → [Natural] #
Eq Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods (==) ∷ Natural → Natural → Bool # (/=) ∷ Natural → Natural → Bool #
Integral Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot ∷ Natural → Natural → Natural # rem ∷ Natural → Natural → Natural # div ∷ Natural → Natural → Natural # mod ∷ Natural → Natural → Natural # quotRem ∷ Natural → Natural → (Natural, Natural) # divMod ∷ Natural → Natural → (Natural, Natural) # toInteger ∷ Natural → Integer #
Num Natural	Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Num Methods (+) ∷ Natural → Natural → Natural # (-) ∷ Natural → Natural → Natural # (*) ∷ Natural → Natural → Natural # negate ∷ Natural → Natural # abs ∷ Natural → Natural # signum ∷ Natural → Natural # fromInteger ∷ Integer → Natural #
Ord Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Natural Methods compare ∷ Natural → Natural → Ordering # (<) ∷ Natural → Natural → Bool # (<=) ∷ Natural → Natural → Bool # (>) ∷ Natural → Natural → Bool # (>=) ∷ Natural → Natural → Bool # max ∷ Natural → Natural → Natural # min ∷ Natural → Natural → Natural #
Read Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec ∷ Int → ReadS Natural # readList ∷ ReadS [Natural] # readPrec ∷ ReadPrec Natural # readListPrec ∷ ReadPrec [Natural] #
Real Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational ∷ Natural → Rational #
Show Natural	Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec ∷ Int → Natural → ShowS # show ∷ Natural → String # showList ∷ [Natural] → ShowS #
PrintfArg Natural	Since: base-4.8.0.0
Instance details Defined in Text.Printf Methods formatArg ∷ Natural → FieldFormatter # parseFormat ∷ Natural → ModifierParser #
Bits Natural	Since: base-4.8.0
Instance details Defined in Data.Bits Methods (.&.) ∷ Natural → Natural → Natural # (.\|.) ∷ Natural → Natural → Natural # xor ∷ Natural → Natural → Natural # complement ∷ Natural → Natural # shift ∷ Natural → Int → Natural # rotate ∷ Natural → Int → Natural # zeroBits ∷ Natural # bit ∷ Int → Natural # setBit ∷ Natural → Int → Natural # clearBit ∷ Natural → Int → Natural # complementBit ∷ Natural → Int → Natural # testBit ∷ Natural → Int → Bool # bitSizeMaybe ∷ Natural → Maybe Int # bitSize ∷ Natural → Int # isSigned ∷ Natural → Bool # shiftL ∷ Natural → Int → Natural # unsafeShiftL ∷ Natural → Int → Natural # shiftR ∷ Natural → Int → Natural # unsafeShiftR ∷ Natural → Int → Natural # rotateL ∷ Natural → Int → Natural # rotateR ∷ Natural → Int → Natural # popCount ∷ Natural → Int #
FromJSON Natural
Instance details Defined in Data.Aeson.Types.FromJSON Methods parseJSON ∷ Value → Parser Natural # parseJSONList ∷ Value → Parser [Natural] #
ToJSON Natural
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON ∷ Natural → Value # toEncoding ∷ Natural → Encoding # toJSONList ∷ [Natural] → Value # toEncodingList ∷ [Natural] → Encoding #
FromCBOR Natural
Instance details Defined in Cardano.Binary.FromCBOR Methods fromCBOR ∷ Decoder s Natural label ∷ Proxy Natural → Text
ToCBOR Natural
Instance details Defined in Cardano.Binary.ToCBOR Methods toCBOR ∷ Natural → Encoding encodedSizeExpr ∷ (∀ t. ToCBOR t ⇒ Proxy t → Size) → Proxy Natural → Size encodedListSizeExpr ∷ (∀ t. ToCBOR t ⇒ Proxy t → Size) → Proxy [Natural] → Size
NoThunks Natural
Instance details Defined in NoThunks.Class Methods noThunks ∷ Context → Natural → IO (Maybe ThunkInfo) wNoThunks ∷ Context → Natural → IO (Maybe ThunkInfo) showTypeOf ∷ Proxy Natural → String
Serialise Natural
Instance details Defined in Codec.Serialise.Class Methods encode ∷ Natural → Encoding decode ∷ Decoder s Natural encodeList ∷ [Natural] → Encoding decodeList ∷ Decoder s [Natural]
ToJSONKey Natural
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSONKey ∷ ToJSONKeyFunction Natural toJSONKeyList ∷ ToJSONKeyFunction [Natural]
FromJSONKey Natural
Instance details Defined in Data.Aeson.Types.FromJSON Methods fromJSONKey ∷ FromJSONKeyFunction Natural fromJSONKeyList ∷ FromJSONKeyFunction [Natural]
ToField Natural
Instance details Defined in Data.Csv.Conversion Methods toField ∷ Natural → Field
Pretty Natural
Instance details Defined in Prettyprinter.Internal Methods pretty ∷ Natural → Doc ann prettyList ∷ [Natural] → Doc ann
Corecursive Natural
Instance details Defined in Data.Functor.Foldable Methods embed ∷ Base Natural Natural → Natural ana ∷ (a → Base Natural a) → a → Natural apo ∷ (a → Base Natural (Either Natural a)) → a → Natural postpro ∷ Recursive Natural ⇒ (∀ b. Base Natural b → Base Natural b) → (a → Base Natural a) → a → Natural gpostpro ∷ (Recursive Natural, Monad m) ⇒ (∀ b. m (Base Natural b) → Base Natural (m b)) → (∀ c. Base Natural c → Base Natural c) → (a → Base Natural (m a)) → a → Natural
Recursive Natural
Instance details Defined in Data.Functor.Foldable Methods project ∷ Natural → Base Natural Natural cata ∷ (Base Natural a → a) → Natural → a para ∷ (Base Natural (Natural, a) → a) → Natural → a gpara ∷ (Corecursive Natural, Comonad w) ⇒ (∀ b. Base Natural (w b) → w (Base Natural b)) → (Base Natural (EnvT Natural w a) → a) → Natural → a prepro ∷ Corecursive Natural ⇒ (∀ b. Base Natural b → Base Natural b) → (Base Natural a → a) → Natural → a gprepro ∷ (Corecursive Natural, Comonad w) ⇒ (∀ b. Base Natural (w b) → w (Base Natural b)) → (∀ c. Base Natural c → Base Natural c) → (Base Natural (w a) → a) → Natural → a
Hashable Natural
Instance details Defined in Data.Hashable.Class Methods hashWithSalt ∷ Int → Natural → Int hash ∷ Natural → Int
FromHttpApiData Natural
Instance details Defined in Web.Internal.HttpApiData Methods parseUrlPiece ∷ Text → Either Text Natural parseHeader ∷ ByteString → Either Text Natural parseQueryParam ∷ Text → Either Text Natural
ToHttpApiData Natural
Instance details Defined in Web.Internal.HttpApiData Methods toUrlPiece ∷ Natural → Text toEncodedUrlPiece ∷ Natural → Builder toHeader ∷ Natural → ByteString toQueryParam ∷ Natural → Text
Subtractive Natural
Instance details Defined in Basement.Numerical.Subtractive Associated Types type Difference Natural Methods (-) ∷ Natural → Natural → Difference Natural
FromField Natural
Instance details Defined in Data.Csv.Conversion Methods parseField ∷ Field → Parser Natural
UniformRange Natural
Instance details Defined in System.Random.Internal Methods uniformRM ∷ StatefulGen g m ⇒ (Natural, Natural) → g → m Natural
Pretty Natural
Instance details Defined in Text.PrettyPrint.Annotated.WL Methods pretty ∷ Natural → Doc b prettyList ∷ [Natural] → Doc b
FromFormKey Natural
Instance details Defined in Web.Internal.FormUrlEncoded Methods parseFormKey ∷ Text → Either Text Natural
ToFormKey Natural
Instance details Defined in Web.Internal.FormUrlEncoded Methods toFormKey ∷ Natural → Text
ToParamSchema Natural
Instance details Defined in Data.Swagger.Internal.ParamSchema Methods toParamSchema ∷ ∀ (t ∷ SwaggerKind Type). Proxy Natural → ParamSchema t
ToSchema Natural
Instance details Defined in Data.Swagger.Internal.Schema Methods declareNamedSchema ∷ Proxy Natural → Declare (Definitions Schema) NamedSchema
FromText Natural
Instance details Defined in Data.Text.Class Methods fromText ∷ Text → Either TextDecodingError Natural
ToText Natural
Instance details Defined in Data.Text.Class Methods toText ∷ Natural → Text
Lift Natural
Instance details Defined in Language.Haskell.TH.Syntax Methods lift ∷ Natural → Q Exp # liftTyped ∷ Natural → Q (TExp Natural) #
PrettyDefaultBy config Natural ⇒ PrettyBy config Natural
Instance details Defined in Text.PrettyBy.Internal Methods prettyBy ∷ config → Natural → Doc ann prettyListBy ∷ config → [Natural] → Doc ann
DefaultPrettyBy config Natural
Instance details Defined in Text.PrettyBy.Internal Methods defaultPrettyBy ∷ config → Natural → Doc ann defaultPrettyListBy ∷ config → [Natural] → Doc ann
Buildable (Range Natural)
Instance details Defined in Cardano.Binary.ToCBOR Methods build ∷ Range Natural → Builder
type Base Natural
Instance details Defined in Data.Functor.Foldable type Base Natural = Maybe
type Difference Natural
Instance details Defined in Basement.Numerical.Subtractive type Difference Natural = Maybe Natural
type IntBaseType Natural
Instance details Defined in Data.IntCast type IntBaseType Natural = 'BigWordTag