Safe Haskell	None
Language	Haskell2010

Data.Type.Bin

Contents

Singleton
Implicit
Type equality
Induction
Arithmetic
Conversions
- To GHC Nat
- To fin Nat
Aliases

Description

Binary natural numbers. DataKinds stuff.

Synopsis

data SBin (b :: Bin) where
- SBZ :: SBin BZ
- SBP :: SBinPI b => SBin (BP b)
data SBinP (b :: BinP) where
- SBE :: SBinP BE
- SB0 :: SBinPI b => SBinP (B0 b)
- SB1 :: SBinPI b => SBinP (B1 b)
sbinToBin :: forall n. SBin n -> Bin
sbinpToBinP :: forall n. SBinP n -> BinP
sbinToNatural :: forall n. SBin n -> Natural
sbinpToNatural :: forall n. SBinP n -> Natural
class SBinI (b :: Bin) where
- sbin :: SBin b
class SBinPI (b :: BinP) where
- sbinp :: SBinP b
withSBin :: SBin b -> (SBinI b => r) -> r
withSBinP :: SBinP b -> (SBinPI b => r) -> r
reify :: forall r. Bin -> (forall b. SBinI b => Proxy b -> r) -> r
reflect :: forall b proxy. SBinI b => proxy b -> Bin
reflectToNum :: forall b proxy a. (SBinI b, Num a) => proxy b -> a
eqBin :: forall a b. (SBinI a, SBinI b) => Maybe (a :~: b)
induction :: forall b f. SBinI b => f BZ -> f (BP BE) -> (forall bb. SBinPI bb => f (BP bb) -> f (BP (B0 bb))) -> (forall bb. SBinPI bb => f (BP bb) -> f (BP (B1 bb))) -> f b
type Succ b = BP (Succ' b)
type family Succ' (b :: Bin) :: BinP where ...
type Succ'' b = BP (Succ b)
withSucc :: forall b r. SBinI b => Proxy b -> (SBinPI (Succ' b) => r) -> r
type family Pred (b :: BinP) :: Bin where ...
type family Plus (a :: Bin) (b :: Bin) :: Bin where ...
type family Mult2 (b :: Bin) :: Bin where ...
type family Mult2Plus1 (b :: Bin) :: BinP where ...
type family ToGHC (b :: Bin) :: Nat where ...
type family FromGHC (n :: Nat) :: Bin where ...
type family ToNat (b :: Bin) :: Nat where ...
type family FromNat (n :: Nat) :: Bin where ...
type Bin0 = BZ
type Bin1 = BP BinP1
type Bin2 = BP BinP2
type Bin3 = BP BinP3
type Bin4 = BP BinP4
type Bin5 = BP BinP5
type Bin6 = BP BinP6
type Bin7 = BP BinP7
type Bin8 = BP BinP8
type Bin9 = BP BinP9

Singleton

data SBin (b :: Bin) where Source #

Singleton of Bin.

Constructors

SBZ :: SBin BZ
SBP :: SBinPI b => SBin (BP b)

Instances

TestEquality SBin Source #
Instance details Defined in Data.Type.Bin Methods testEquality :: SBin a -> SBin b -> Maybe (a :~: b) #

data SBinP (b :: BinP) where Source #

Singleton of BinP.

Constructors

SBE :: SBinP BE
SB0 :: SBinPI b => SBinP (B0 b)
SB1 :: SBinPI b => SBinP (B1 b)

Instances

TestEquality SBinP Source #
Instance details Defined in Data.Type.BinP Methods testEquality :: SBinP a -> SBinP b -> Maybe (a :~: b) #

sbinToBin :: forall n. SBin n -> Bin Source #

Convert SBin to Bin.

sbinpToBinP :: forall n. SBinP n -> BinP Source #

Cconvert SBinP to BinP.

sbinToNatural :: forall n. SBin n -> Natural Source #

Convert SBin to Natural.

>>> sbinToNatural (sbin :: SBin Bin9)
9

sbinpToNatural :: forall n. SBinP n -> Natural Source #

Convert SBinP to Natural.

>>> sbinpToNatural (sbinp :: SBinP BinP8)
8

Implicit

class SBinI (b :: Bin) where Source #

Let constraint solver construct SBin.

Methods

sbin :: SBin b Source #

Instances

SBinI BZ Source #
Instance details Defined in Data.Type.Bin Methods sbin :: SBin BZ Source #
SBinPI b => SBinI (BP b) Source #
Instance details Defined in Data.Type.Bin Methods sbin :: SBin (BP b) Source #

class SBinPI (b :: BinP) where Source #

Let constraint solver construct SBinP.

Methods

sbinp :: SBinP b Source #

Instances

SBinPI BE Source #
Instance details Defined in Data.Type.BinP Methods sbinp :: SBinP BE Source #
SBinPI b => SBinPI (B0 b) Source #
Instance details Defined in Data.Type.BinP Methods sbinp :: SBinP (B0 b) Source #
SBinPI b => SBinPI (B1 b) Source #
Instance details Defined in Data.Type.BinP Methods sbinp :: SBinP (B1 b) Source #

withSBin :: SBin b -> (SBinI b => r) -> r Source #

Construct SBinI dictionary from SBin.

withSBinP :: SBinP b -> (SBinPI b => r) -> r Source #

Construct SBinPI dictionary from SBinP.

reify :: forall r. Bin -> (forall b. SBinI b => Proxy b -> r) -> r Source #

Reify Bin

>>> reify bin3 reflect
3

reflect :: forall b proxy. SBinI b => proxy b -> Bin Source #

Reflect type-level Bin to the term level.

reflectToNum :: forall b proxy a. (SBinI b, Num a) => proxy b -> a Source #

Reflect type-level Bin to the term level Num.

Type equality

eqBin :: forall a b. (SBinI a, SBinI b) => Maybe (a :~: b) Source #

Induction

induction Source #

Arguments

:: SBinI b
=> f BZ	\(P(0)\)
-> f (BP BE)	\(P(1)\)
-> (forall bb. SBinPI bb => f (BP bb) -> f (BP (B0 bb)))	\(\forall b. P(b) \to P(2b)\)
-> (forall bb. SBinPI bb => f (BP bb) -> f (BP (B1 bb)))	\(\forall b. P(b) \to P(2b + 1)\)
-> f b

Induction on Bin.

Arithmetic

Successor

type Succ b = BP (Succ' b) Source #

Successor type family.

>>> :kind! Succ Bin5
Succ Bin5 :: Bin
= 'BP ('B0 ('B1 'BE))

Succ   :: Bin -> Bin
Succ'  :: Bin -> BinP
Succ'' :: BinP -> Bin

type family Succ' (b :: Bin) :: BinP where ... Source #

Equations

Succ' BZ = BE
Succ' (BP b) = Succ b

type Succ'' b = BP (Succ b) Source #

withSucc :: forall b r. SBinI b => Proxy b -> (SBinPI (Succ' b) => r) -> r Source #

Predecessor

type family Pred (b :: BinP) :: Bin where ... Source #

Predecessor type family..

>>> :kind! Pred BP.BinP1
Pred BP.BinP1 :: Bin
= 'BZ

>>> :kind! Pred BP.BinP5
Pred BP.BinP5 :: Bin
= 'BP ('B0 ('B0 BP.BinP1))

>>> :kind! Pred BP.BinP8
Pred BP.BinP8 :: Bin
= 'BP ('B1 ('B1 'BE))

>>> :kind! Pred BP.BinP6
Pred BP.BinP6 :: Bin
= 'BP ('B1 ('B0 'BE))

Equations

Pred BE = BZ
Pred (B1 n) = BP (B0 n)
Pred (B0 n) = BP (Pred' n)

Addition

type family Plus (a :: Bin) (b :: Bin) :: Bin where ... Source #

Addition.

>>> :kind! Plus Bin7 Bin7
Plus Bin7 Bin7 :: Bin
= 'BP ('B0 ('B1 ('B1 'BE)))

>>> :kind! Mult2 Bin7
Mult2 Bin7 :: Bin
= 'BP ('B0 ('B1 BinP3))

Equations

Plus BZ b = b
Plus a BZ = a
Plus (BP a) (BP b) = BP (Plus a b)

Extras

type family Mult2 (b :: Bin) :: Bin where ... Source #

Multiply by two.

>>> :kind! Mult2 Bin0
Mult2 Bin0 :: Bin
= 'BZ

>>> :kind! Mult2 Bin7
Mult2 Bin7 :: Bin
= 'BP ('B0 ('B1 BinP3))

Equations

Mult2 BZ = BZ
Mult2 (BP n) = BP (B0 n)

type family Mult2Plus1 (b :: Bin) :: BinP where ... Source #

Multiply by two and add one.

>>> :kind! Mult2Plus1 Bin0
Mult2Plus1 Bin0 :: BinP
= 'BE

>>> :kind! Mult2Plus1 Bin5
Mult2Plus1 Bin5 :: BinP
= 'B1 ('B1 BinP2)

Equations

Mult2Plus1 BZ = BE
Mult2Plus1 (BP n) = B1 n

Conversions

To GHC Nat

type family ToGHC (b :: Bin) :: Nat where ... Source #

Convert to GHC Nat.

>>> :kind! ToGHC Bin5
ToGHC Bin5 :: GHC.Nat
= 5

Equations

ToGHC BZ = 0
ToGHC (BP n) = ToGHC n

type family FromGHC (n :: Nat) :: Bin where ... Source #

Convert from GHC Nat.

>>> :kind! FromGHC 7
FromGHC 7 :: Bin
= 'BP ('B1 ('B1 'BE))

Equations

FromGHC n = FromGHC' (GhcDivMod2 n)

To fin Nat

type family ToNat (b :: Bin) :: Nat where ... Source #

Convert to fin Nat.

>>> :kind! ToNat Bin5
ToNat Bin5 :: Nat
= 'S ('S ('S ('S ('S 'Z))))

Equations

ToNat BZ = Z
ToNat (BP n) = ToNat n

type family FromNat (n :: Nat) :: Bin where ... Source #

Convert from fin Nat.

>>> :kind! FromNat N.Nat5
FromNat N.Nat5 :: Bin
= 'BP ('B1 ('B0 'BE))

Equations

FromNat n = FromNat' (DivMod2 n)

Aliases

type Bin0 = BZ Source #

type Bin1 = BP BinP1 Source #

type Bin2 = BP BinP2 Source #

type Bin3 = BP BinP3 Source #

type Bin4 = BP BinP4 Source #

type Bin5 = BP BinP5 Source #

type Bin6 = BP BinP6 Source #

type Bin7 = BP BinP7 Source #

type Bin8 = BP BinP8 Source #

type Bin9 = BP BinP9 Source #