Safe Haskell	None
Language	Haskell2010

Data.Type.BinP

Contents

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

Description

Positive binary natural numbers. DataKinds stuff.

Synopsis

data SBinP (b :: BinP ) where
- SBE :: SBinP ' BE
- SB0 :: SBinPI b => SBinP (' B0 b)
- SB1 :: SBinPI b => SBinP (' B1 b)
sbinpToBinP :: forall n. SBinP n -> BinP
sbinpToNatural :: forall n. SBinP n -> Natural
class SBinPI (b :: BinP ) where
- sbinp :: SBinP b
withSBinP :: SBinP b -> ( SBinPI b => r) -> r
reify :: forall r. BinP -> ( forall b. SBinPI b => Proxy b -> r) -> r
reflect :: forall b proxy. SBinPI b => proxy b -> BinP
reflectToNum :: forall b proxy a. ( SBinPI b, Num a) => proxy b -> a
eqBinP :: forall a b. ( SBinPI a, SBinPI b) => Maybe (a :~: b)
induction :: forall b f. SBinPI b => f ' BE -> ( forall bb. SBinPI bb => f bb -> f (' B0 bb)) -> ( forall bb. SBinPI bb => f bb -> f (' B1 bb)) -> f b
type family Succ (b :: BinP ) :: BinP where ...
withSucc :: forall b r. SBinPI b => Proxy b -> ( SBinPI ( Succ b) => r) -> r
type family Plus (a :: BinP ) (b :: BinP ) :: BinP where ...
type family ToGHC (b :: BinP ) :: Nat where ...
type family FromGHC (n :: Nat ) :: BinP where ...
type family ToNat (b :: BinP ) :: Nat where ...
type BinP1 = ' BE
type BinP2 = ' B0 BinP1
type BinP3 = ' B1 BinP1
type BinP4 = ' B0 BinP2
type BinP5 = ' B1 BinP2
type BinP6 = ' B0 BinP3
type BinP7 = ' B1 BinP3
type BinP8 = ' B0 BinP4
type BinP9 = ' B1 BinP4

Singleton

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

Instances details

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

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

Cconvert SBinP to BinP .

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

Convert SBinP to Natural .

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

Implicit

class SBinPI (b :: BinP ) where Source #

Let constraint solver construct SBinP .

Methods

sbinp :: SBinP b Source #

Instances

Instances details

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 #

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

Construct SBinPI dictionary from SBinP .

reify :: forall r. BinP -> ( forall b. SBinPI b => Proxy b -> r) -> r Source #

Reify BinP .

reflect :: forall b proxy. SBinPI b => proxy b -> BinP Source #

Reflect type-level BinP to the term level.

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

Reflect type-level BinP to the term level Num .

Type equality

eqBinP :: forall a b. ( SBinPI a, SBinPI b) => Maybe (a :~: b) Source #

Induction

induction Source #

Arguments

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

Induction on BinP .

Arithmetic

Successor

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

Equations

Succ ' BE = ' B0 ' BE
Succ (' B0 n) = ' B1 n
Succ (' B1 n) = ' B0 ( Succ n)

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

Addition

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

Equations

Plus ' BE b = Succ b
Plus a ' BE = Succ a
Plus (' B0 a) (' B0 b) = ' B0 ( Plus a b)
Plus (' B1 a) (' B0 b) = ' B1 ( Plus a b)
Plus (' B0 a) (' B1 b) = ' B1 ( Plus a b)
Plus (' B1 a) (' B1 b) = ' B0 ( Succ ( Plus a b))