Data.BinP

Positive binary natural numbers, BinP.

This module is designed to be imported qualified.

Documentation

data BinP

Non-zero binary natural numbers.

We could have called this type Bin1, but that's used as type alias for promoted BP BE in Data.Type.Bin.

Constructors

BE

one

B0 BinP

mult2

B1 BinP

mult2 plus 1

Instances

Arbitrary BinP

Defined in Data.BinP

Methods

arbitrary :: Gen BinP

shrink :: BinP -> [BinP]

CoArbitrary BinP

Defined in Data.BinP

Methods

coarbitrary :: BinP -> Gen b -> Gen b

Function BinP

Defined in Data.BinP

Methods

function :: (BinP -> b) -> BinP :-> b

Data BinP

Defined in Data.BinP

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> BinP -> c BinP

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c BinP

toConstr :: BinP -> Constr

dataTypeOf :: BinP -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c BinP)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c BinP)

gmapT :: (forall b. Data b => b -> b) -> BinP -> BinP

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> BinP -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> BinP -> r

gmapQ :: (forall d. Data d => d -> u) -> BinP -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> BinP -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> BinP -> m BinP

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> BinP -> m BinP

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> BinP -> m BinP

Bits BinP

NOTE: .&., xor, shiftR and rotateR are __NOT_ implemented. They may make number zero.

Defined in Data.BinP

Methods

(.&.) :: BinP -> BinP -> BinP

(.|.) :: BinP -> BinP -> BinP

xor :: BinP -> BinP -> BinP

complement :: BinP -> BinP

shift :: BinP -> Int -> BinP

rotate :: BinP -> Int -> BinP

zeroBits :: BinP

bit :: Int -> BinP

setBit :: BinP -> Int -> BinP

clearBit :: BinP -> Int -> BinP

complementBit :: BinP -> Int -> BinP

testBit :: BinP -> Int -> Bool

bitSizeMaybe :: BinP -> Maybe Int

bitSize :: BinP -> Int

isSigned :: BinP -> Bool

shiftL :: BinP -> Int -> BinP

unsafeShiftL :: BinP -> Int -> BinP

shiftR :: BinP -> Int -> BinP

unsafeShiftR :: BinP -> Int -> BinP

rotateL :: BinP -> Int -> BinP

rotateR :: BinP -> Int -> BinP

popCount :: BinP -> Int

Enum BinP

Defined in Data.BinP

Methods

succ :: BinP -> BinP

pred :: BinP -> BinP

toEnum :: Int -> BinP

fromEnum :: BinP -> Int

enumFrom :: BinP -> [BinP]

enumFromThen :: BinP -> BinP -> [BinP]

enumFromTo :: BinP -> BinP -> [BinP]

enumFromThenTo :: BinP -> BinP -> BinP -> [BinP]

Num BinP

Defined in Data.BinP

Methods

(+) :: BinP -> BinP -> BinP

(-) :: BinP -> BinP -> BinP

(*) :: BinP -> BinP -> BinP

negate :: BinP -> BinP

abs :: BinP -> BinP

signum :: BinP -> BinP

fromInteger :: Integer -> BinP

Integral BinP

Defined in Data.BinP

Methods

quot :: BinP -> BinP -> BinP

rem :: BinP -> BinP -> BinP

div :: BinP -> BinP -> BinP

mod :: BinP -> BinP -> BinP

quotRem :: BinP -> BinP -> (BinP, BinP)

divMod :: BinP -> BinP -> (BinP, BinP)

toInteger :: BinP -> Integer

Real BinP

Defined in Data.BinP

Methods

toRational :: BinP -> Rational

Show BinP

Defined in Data.BinP

Methods

showsPrec :: Int -> BinP -> ShowS

show :: BinP -> String

showList :: [BinP] -> ShowS

NFData BinP

Defined in Data.BinP

Methods

rnf :: BinP -> ()

Eq BinP

Defined in Data.BinP

Methods

(==) :: BinP -> BinP -> Bool

(/=) :: BinP -> BinP -> Bool

Ord BinP

>>> sort [ 1 .. 9 :: BinP ]
[1,2,3,4,5,6,7,8,9]

>>> sort $ reverse [ 1 .. 9 :: BinP ]
[1,2,3,4,5,6,7,8,9]

>>> sort $ [ 1 .. 9 ] ++ [ 1 .. 9 :: BinP ]
[1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9]

Defined in Data.BinP

Methods

compare :: BinP -> BinP -> Ordering

(<) :: BinP -> BinP -> Bool

(<=) :: BinP -> BinP -> Bool

(>) :: BinP -> BinP -> Bool

(>=) :: BinP -> BinP -> Bool

max :: BinP -> BinP -> BinP

min :: BinP -> BinP -> BinP

Hashable BinP

Defined in Data.BinP

Methods

hashWithSalt :: Int -> BinP -> Int

hash :: BinP -> Int

TestEquality SBinP

Defined in Data.Type.BinP

Methods

testEquality :: forall (a :: k) (b :: k). SBinP a -> SBinP b -> Maybe (a :~: b)

EqP PosP

Since: 0.1.3

Defined in Data.BinP.PosP

Methods

eqp :: forall (a :: k) (b :: k). PosP a -> PosP b -> Bool

EqP SBinP

Since: 0.1.3

Defined in Data.Type.BinP

Methods

eqp :: forall (a :: k) (b :: k). SBinP a -> SBinP b -> Bool

GNFData SBinP

Since: 0.1.2

Defined in Data.Type.BinP

Methods

grnf :: forall (a :: k). SBinP a -> ()

GEq SBinP

Since: 0.1.2

Defined in Data.Type.BinP

Methods

geq :: forall (a :: k) (b :: k). SBinP a -> SBinP b -> Maybe (a :~: b)

GShow PosP

Since: 0.1.3

Defined in Data.BinP.PosP

Methods

gshowsPrec :: forall (a :: k). Int -> PosP a -> ShowS

GShow SBinP

Since: 0.1.2

Defined in Data.Type.BinP

Methods

gshowsPrec :: forall (a :: k). Int -> SBinP a -> ShowS

OrdP PosP

Since: 0.1.3

Defined in Data.BinP.PosP

Methods

comparep :: forall (a :: k) (b :: k). PosP a -> PosP b -> Ordering

SNatI n => GShow (PosP' n :: BinP -> Type)

Since: 0.1.3

Defined in Data.BinP.PosP

Methods

gshowsPrec :: forall (a :: k). Int -> PosP' n a -> ShowS

Conversions

cata

Arguments

:: a

\(1\)

-> (a -> a)

\(2x\)

-> (a -> a)

\(2x + 1\)

-> BinP

-> a

Fold BinP.

toNatural :: BinP -> Natural

toNatural for BinP.

fromNatural :: Natural -> BinP

fromNatural for BinP.

Throws when given 0.

toNat :: BinP -> Nat

Convert from BinP to Nat.

Showing

explicitShow :: BinP -> String

show displaying a structure of BinP.

>>> explicitShow 11
"B1 (B1 (B0 BE))"

explicitShowsPrec :: Int -> BinP -> ShowS

showsPrec displaying a structure of BinP.

Extras

predMaybe :: BinP -> Maybe BinP

Aliases

binP1 :: BinP

binP2 :: BinP

binP3 :: BinP

binP4 :: BinP

binP5 :: BinP

binP6 :: BinP

binP7 :: BinP

binP8 :: BinP

binP9 :: BinP