Voting.Protocol.FFC

Finite Field Cryptography (FFC) is a method of implementing discrete logarithm cryptography using finite field mathematics.

Documentation

class ToNatural a where

Methods

nat :: a -> Natural

Instances

ToNatural Natural

Defined in Voting.Protocol.FFC

Methods

nat :: Natural -> Natural

ToNatural (E c)

Defined in Voting.Protocol.FFC

Methods

nat :: E c -> Natural

ToNatural (G c)

Defined in Voting.Protocol.FFC

Methods

nat :: G c -> Natural

ToNatural (F c)

Defined in Voting.Protocol.FFC

Methods

nat :: F c -> Natural

class FromNatural a where

Methods

fromNatural :: Natural -> a

Instances

Reifies c FFC => FromNatural (E c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> E c

Reifies c FFC => FromNatural (G c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> G c

Reifies c FFC => FromNatural (F c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> F c

newtype E c

An exponent of a (necessarily cyclic) subgroup of a Finite Prime Field. The value is always in [0..groupOrder-1].

Constructors

E

Fields

• unE :: Natural

Instances

Reifies c FFC => Enum (E c)

Defined in Voting.Protocol.FFC

Methods

succ :: E c -> E c

pred :: E c -> E c

toEnum :: Int -> E c

fromEnum :: E c -> Int

enumFrom :: E c -> [E c]

enumFromThen :: E c -> E c -> [E c]

enumFromTo :: E c -> E c -> [E c]

enumFromThenTo :: E c -> E c -> E c -> [E c]

Eq (E c)

Defined in Voting.Protocol.FFC

Methods

(==) :: E c -> E c -> Bool

(/=) :: E c -> E c -> Bool

Ord (E c)

Defined in Voting.Protocol.FFC

Methods

compare :: E c -> E c -> Ordering

(<) :: E c -> E c -> Bool

(<=) :: E c -> E c -> Bool

(>) :: E c -> E c -> Bool

(>=) :: E c -> E c -> Bool

max :: E c -> E c -> E c

min :: E c -> E c -> E c

Show (E c)

Defined in Voting.Protocol.FFC

Methods

showsPrec :: Int -> E c -> ShowS

show :: E c -> String

showList :: [E c] -> ShowS

ToJSON (E c)

Defined in Voting.Protocol.FFC

Methods

toJSON :: E c -> Value

toEncoding :: E c -> Encoding

toJSONList :: [E c] -> Value

toEncodingList :: [E c] -> Encoding

Reifies c FFC => FromJSON (E c)

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser (E c)

parseJSONList :: Value -> Parser [E c]

NFData (E c)

Defined in Voting.Protocol.FFC

Methods

rnf :: E c -> ()

Reifies c FFC => Random (E c)

Defined in Voting.Protocol.FFC

Methods

randomR :: RandomGen g => (E c, E c) -> g -> (E c, g)

random :: RandomGen g => g -> (E c, g)

randomRs :: RandomGen g => (E c, E c) -> g -> [E c]

randoms :: RandomGen g => g -> [E c]

randomRIO :: (E c, E c) -> IO (E c)

randomIO :: IO (E c)

ToNatural (E c)

Defined in Voting.Protocol.FFC

Methods

nat :: E c -> Natural

Reifies c FFC => FromNatural (E c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> E c

Reifies c FFC => Multiplicative (E c)

Defined in Voting.Protocol.FFC

Methods

one :: E c

(*) :: E c -> E c -> E c

Reifies c FFC => Negable (E c)

Defined in Voting.Protocol.FFC

Methods

neg :: E c -> E c

(-) :: E c -> E c -> E c

Reifies c FFC => Additive (E c)

Defined in Voting.Protocol.FFC

Methods

zero :: E c

(+) :: E c -> E c -> E c

sum :: Foldable f => f (E c) -> E c

newtype G c

The type of the elements of a Multiplicative subgroup of a Finite Prime Field.

Constructors

G

Fields

• unG :: F c

Instances

Eq (G c)

Defined in Voting.Protocol.FFC

Methods

(==) :: G c -> G c -> Bool

(/=) :: G c -> G c -> Bool

Ord (G c)

Defined in Voting.Protocol.FFC

Methods

compare :: G c -> G c -> Ordering

(<) :: G c -> G c -> Bool

(<=) :: G c -> G c -> Bool

(>) :: G c -> G c -> Bool

(>=) :: G c -> G c -> Bool

max :: G c -> G c -> G c

min :: G c -> G c -> G c

Show (G c)

Defined in Voting.Protocol.FFC

Methods

showsPrec :: Int -> G c -> ShowS

show :: G c -> String

showList :: [G c] -> ShowS

ToJSON (G c)

Defined in Voting.Protocol.FFC

Methods

toJSON :: G c -> Value

toEncoding :: G c -> Encoding

toJSONList :: [G c] -> Value

toEncodingList :: [G c] -> Encoding

Reifies c FFC => FromJSON (G c)

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser (G c)

parseJSONList :: Value -> Parser [G c]

NFData (G c)

Defined in Voting.Protocol.FFC

Methods

rnf :: G c -> ()

ToNatural (G c)

Defined in Voting.Protocol.FFC

Methods

nat :: G c -> Natural

Reifies c FFC => FromNatural (G c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> G c

Reifies c FFC => Invertible (G c)

Defined in Voting.Protocol.FFC

Methods

inv :: G c -> G c

(/) :: G c -> G c -> G c

Reifies c FFC => Multiplicative (G c)

Defined in Voting.Protocol.FFC

Methods

one :: G c

(*) :: G c -> G c -> G c

class Multiplicative a => Invertible a where

Minimal complete definition

inv

Methods

inv :: a -> a

(/) :: a -> a -> a infixl 7

Instances

Reifies c FFC => Invertible (G c)

Defined in Voting.Protocol.FFC

Methods

inv :: G c -> G c

(/) :: G c -> G c -> G c

class Multiplicative a where

Methods

one :: a

(*) :: a -> a -> a infixl 7

Instances

Multiplicative Int

Defined in Voting.Protocol.FFC

Methods

one :: Int

(*) :: Int -> Int -> Int

Multiplicative Integer

Defined in Voting.Protocol.FFC

Methods

one :: Integer

(*) :: Integer -> Integer -> Integer

Multiplicative Natural

Defined in Voting.Protocol.FFC

Methods

one :: Natural

(*) :: Natural -> Natural -> Natural

Reifies c FFC => Multiplicative (E c)

Defined in Voting.Protocol.FFC

Methods

one :: E c

(*) :: E c -> E c -> E c

Reifies c FFC => Multiplicative (G c)

Defined in Voting.Protocol.FFC

Methods

one :: G c

(*) :: G c -> G c -> G c

Reifies c FFC => Multiplicative (F c)

Defined in Voting.Protocol.FFC

Methods

one :: F c

(*) :: F c -> F c -> F c

class Additive a => Negable a where

Minimal complete definition

neg

Methods

neg :: a -> a

(-) :: a -> a -> a infixl 6

Instances

Negable Int

Defined in Voting.Protocol.FFC

Methods

neg :: Int -> Int

(-) :: Int -> Int -> Int

Negable Integer

Defined in Voting.Protocol.FFC

Methods

neg :: Integer -> Integer

(-) :: Integer -> Integer -> Integer

Reifies c FFC => Negable (E c)

Defined in Voting.Protocol.FFC

Methods

neg :: E c -> E c

(-) :: E c -> E c -> E c

Reifies c FFC => Negable (F c)

Defined in Voting.Protocol.FFC

Methods

neg :: F c -> F c

(-) :: F c -> F c -> F c

class Additive a where

Minimal complete definition

zero, (+)

Methods

zero :: a

(+) :: a -> a -> a infixl 6

sum :: Foldable f => f a -> a

Instances

Additive Int

Defined in Voting.Protocol.FFC

Methods

zero :: Int

(+) :: Int -> Int -> Int

sum :: Foldable f => f Int -> Int

Additive Integer

Defined in Voting.Protocol.FFC

Methods

zero :: Integer

(+) :: Integer -> Integer -> Integer

sum :: Foldable f => f Integer -> Integer

Additive Natural

Defined in Voting.Protocol.FFC

Methods

zero :: Natural

(+) :: Natural -> Natural -> Natural

sum :: Foldable f => f Natural -> Natural

Reifies c FFC => Additive (E c)

Defined in Voting.Protocol.FFC

Methods

zero :: E c

(+) :: E c -> E c -> E c

sum :: Foldable f => f (E c) -> E c

Reifies c FFC => Additive (F c)

Defined in Voting.Protocol.FFC

Methods

zero :: F c

(+) :: F c -> F c -> F c

sum :: Foldable f => f (F c) -> F c

Reifies c FFC => Additive (Encryption c)

Additive homomorphism. Using the fact that: groupGen ^x * groupGen ^y == groupGen ^(x+y).

Defined in Voting.Protocol.Election

Methods

zero :: Encryption c

(+) :: Encryption c -> Encryption c -> Encryption c

sum :: Foldable f => f (Encryption c) -> Encryption c

newtype F c

The type of the elements of a Finite Prime Field.

A field must satisfy the following properties:

• (f, (+), zero) forms an abelian group, called the Additive group of f.
• (NonNull f, (*), one) forms an abelian group, called the Multiplicative group of f.
• (*) is associative: (a*b)*c == a*(b*c) and a*(b*c) == (a*b)*c.
• (*) and (+) are both commutative: a*b == b*a and a+b == b+a
• (*) and (+) are both left and right distributive: a*(b+c) == (a*b) + (a*c) and (a+b)*c == (a*c) + (b*c)

The Natural is always within [0..fieldCharac-1].

Constructors

F

Fields

• unF :: Natural

Instances

Eq (F c)

Defined in Voting.Protocol.FFC

Methods

(==) :: F c -> F c -> Bool

(/=) :: F c -> F c -> Bool

Ord (F c)

Defined in Voting.Protocol.FFC

Methods

compare :: F c -> F c -> Ordering

(<) :: F c -> F c -> Bool

(<=) :: F c -> F c -> Bool

(>) :: F c -> F c -> Bool

(>=) :: F c -> F c -> Bool

max :: F c -> F c -> F c

min :: F c -> F c -> F c

Show (F c)

Defined in Voting.Protocol.FFC

Methods

showsPrec :: Int -> F c -> ShowS

show :: F c -> String

showList :: [F c] -> ShowS

ToJSON (F c)

Defined in Voting.Protocol.FFC

Methods

toJSON :: F c -> Value

toEncoding :: F c -> Encoding

toJSONList :: [F c] -> Value

toEncodingList :: [F c] -> Encoding

Reifies c FFC => FromJSON (F c)

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser (F c)

parseJSONList :: Value -> Parser [F c]

NFData (F c)

Defined in Voting.Protocol.FFC

Methods

rnf :: F c -> ()

Reifies c FFC => Random (F c)

Defined in Voting.Protocol.FFC

Methods

randomR :: RandomGen g => (F c, F c) -> g -> (F c, g)

random :: RandomGen g => g -> (F c, g)

randomRs :: RandomGen g => (F c, F c) -> g -> [F c]

randoms :: RandomGen g => g -> [F c]

randomRIO :: (F c, F c) -> IO (F c)

randomIO :: IO (F c)

ToNatural (F c)

Defined in Voting.Protocol.FFC

Methods

nat :: F c -> Natural

Reifies c FFC => FromNatural (F c)

Defined in Voting.Protocol.FFC

Methods

fromNatural :: Natural -> F c

Reifies c FFC => Multiplicative (F c)

Defined in Voting.Protocol.FFC

Methods

one :: F c

(*) :: F c -> F c -> F c

Reifies c FFC => Negable (F c)

Defined in Voting.Protocol.FFC

Methods

neg :: F c -> F c

(-) :: F c -> F c -> F c

Reifies c FFC => Additive (F c)

Defined in Voting.Protocol.FFC

Methods

zero :: F c

(+) :: F c -> F c -> F c

sum :: Foldable f => f (F c) -> F c

data FFC

Mutiplicative Sub-Group of a Finite Prime Field.

NOTE: an FFC term-value is brought into the context of many functions through a type-variable c whose Reifies constraint enables to reflect that FFC at the term-level (a surprising technique but a very useful one). Doing like this is simpler than working in a Monad (like a Reader), and enables that FFC term to be used simply in instances' methods not supporting an inner Monad, like parseJSON, randomR, fromEnum or arbitrary. Aside from that, the sharing of FFC amongst several types is encoded at the type-level by including c as a phantom type of F, G and E.

Constructors

FFC

Fields

• ffc_name :: Text
• ffc_fieldCharac :: !Natural

  The prime number characteristic of a Finite Prime Field.

  ElGamal's hardness to decrypt requires a large prime number to form the Multiplicative subgroup.

• ffc_groupGen :: !Natural

  A generator of the Multiplicative subgroup of the Finite Prime Field.

  NOTE: since ffc_fieldCharac is prime, the Multiplicative subgroup is cyclic, and there are phi(fieldCharac-1) many choices for the generator of the group, where phi is the Euler totient function.

• ffc_groupOrder :: !Natural

  The order of the subgroup.

  WARNING: ffc_groupOrder MUST be a prime number dividing (ffc_fieldCharac-1) to ensure that ElGamal is secure in terms of the DDH assumption.

Instances

Eq FFC

Defined in Voting.Protocol.FFC

Methods

(==) :: FFC -> FFC -> Bool

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

Show FFC

Defined in Voting.Protocol.FFC

Methods

showsPrec :: Int -> FFC -> ShowS

show :: FFC -> String

showList :: [FFC] -> ShowS

Generic FFC

Defined in Voting.Protocol.FFC

Associated Types

type Rep FFC :: Type -> Type

Methods

from :: FFC -> Rep FFC x

to :: Rep FFC x -> FFC

ToJSON FFC

Defined in Voting.Protocol.FFC

Methods

toJSON :: FFC -> Value

toEncoding :: FFC -> Encoding

toJSONList :: [FFC] -> Value

toEncodingList :: [FFC] -> Encoding

FromJSON FFC

Defined in Voting.Protocol.FFC

Methods

parseJSON :: Value -> Parser FFC

parseJSONList :: Value -> Parser [FFC]

NFData FFC

Defined in Voting.Protocol.FFC

Methods

rnf :: FFC -> ()

type Rep FFC

Defined in Voting.Protocol.FFC

type Rep FFC = D1 (MetaData "FFC" "Voting.Protocol.FFC" "hjugement-protocol-0.0.0.20190519-C0jAKryjQbCA8A0oOhdfpH" False) (C1 (MetaCons "FFC" PrefixI True) ((S1 (MetaSel (Just "ffc_name") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Text) :*: S1 (MetaSel (Just "ffc_fieldCharac") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Natural)) :*: (S1 (MetaSel (Just "ffc_groupGen") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Natural) :*: S1 (MetaSel (Just "ffc_groupOrder") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Natural))))

fieldCharac :: forall c. Reifies c FFC => Natural

groupGen :: forall c. Reifies c FFC => G c

groupOrder :: forall c. Reifies c FFC => Natural

weakFFC :: FFC

Weak parameters for debugging purposes only.

beleniosFFC :: FFC

Parameters used in Belenios. A 2048-bit fieldCharac of a Finite Prime Field, with a 256-bit groupOrder for a Multiplicative subgroup generated by groupGen.

groupGenInverses :: forall c. Reifies c FFC => [G c]

groupGenInverses returns the infinite list of inverse powers of groupGen: [groupGen ^ neg i | i <- [0..]], but by computing each value from the previous one.

Used by intervalDisjunctions.

groupGenPowers :: forall c. Reifies c FFC => [G c]

hash :: Reifies c FFC => ByteString -> [G c] -> E c

(hash bs gs) returns as a number in E the SHA256 of the given ByteString bs prefixing the decimal representation of given subgroup elements gs, with a comma (",") intercalated between them.

NOTE: to avoid any collision when the hash function is used in different contexts, a message gs is actually prefixed by a bs indicating the context.

Used by proveEncryption and verifyEncryption, where the bs usually contains the statement to be proven, and the gs contains the commitments.

(^) :: Reifies c FFC => G c -> E c -> G c infixr 8

(b ^ e) returns the modular exponentiation of base b by exponent e.

randomR :: Monad m => RandomGen r => Random i => Negable i => Multiplicative i => i -> StateT r m i

(randomR i) returns a random integer in [0..i-1].

random :: Monad m => RandomGen r => Random i => Negable i => Multiplicative i => StateT r m i

(random) returns a random integer in the range determined by its type.

bytesNat :: ToNatural n => n -> ByteString

(bytesNat x) returns the serialization of x.

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

Enum Natural

Since: base-4.8.0.0

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

Defined in GHC.Natural

Methods

(==) :: Natural -> Natural -> Bool

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

Integral Natural

Since: base-4.8.0.0

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

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

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

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

Defined in GHC.Real

Methods

toRational :: Natural -> Rational

Show Natural

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Lift Natural

Defined in Language.Haskell.TH.Syntax

Methods

lift :: Natural -> Q Exp

Hashable Natural

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Natural -> Int

hash :: Natural -> Int

ToJSON Natural

Defined in Data.Aeson.Types.ToJSON

Methods

toJSON :: Natural -> Value

toEncoding :: Natural -> Encoding

toJSONList :: [Natural] -> Value

toEncodingList :: [Natural] -> Encoding

ToJSONKey Natural

Defined in Data.Aeson.Types.ToJSON

Methods

toJSONKey :: ToJSONKeyFunction Natural

toJSONKeyList :: ToJSONKeyFunction [Natural]

FromJSON Natural

Defined in Data.Aeson.Types.FromJSON

Methods

parseJSON :: Value -> Parser Natural

parseJSONList :: Value -> Parser [Natural]

FromJSONKey Natural

Defined in Data.Aeson.Types.FromJSON

Methods

fromJSONKey :: FromJSONKeyFunction Natural

fromJSONKeyList :: FromJSONKeyFunction [Natural]

Bits Natural

Since: base-4.8.0

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

Subtractive Natural

Defined in Basement.Numerical.Subtractive

Associated Types

type Difference Natural :: Type

Methods

(-) :: Natural -> Natural -> Difference Natural

NFData Natural

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Natural -> ()

Random Natural

Defined in Voting.Protocol.FFC

Methods

randomR :: RandomGen g => (Natural, Natural) -> g -> (Natural, g)

random :: RandomGen g => g -> (Natural, g)

randomRs :: RandomGen g => (Natural, Natural) -> g -> [Natural]

randoms :: RandomGen g => g -> [Natural]

randomRIO :: (Natural, Natural) -> IO Natural

randomIO :: IO Natural

ToNatural Natural

Defined in Voting.Protocol.FFC

Methods

nat :: Natural -> Natural

Multiplicative Natural

Defined in Voting.Protocol.FFC

Methods

one :: Natural

(*) :: Natural -> Natural -> Natural

Additive Natural

Defined in Voting.Protocol.FFC

Methods

zero :: Natural

(+) :: Natural -> Natural -> Natural

sum :: Foldable f => f Natural -> Natural

type Difference Natural

Defined in Basement.Numerical.Subtractive

type Difference Natural = Maybe Natural

class RandomGen g

The class RandomGen provides a common interface to random number generators.

Minimal complete definition

next, split

Instances

RandomGen StdGen

Defined in System.Random

Methods

next :: StdGen -> (Int, StdGen)

genRange :: StdGen -> (Int, Int)

split :: StdGen -> (StdGen, StdGen)

class Reifies (s :: k) a | s -> a where

Methods

reflect :: proxy s -> a

Recover a value inside a reify context, given a proxy for its reified type.

Instances

KnownNat n => Reifies (n :: Nat) Integer

Defined in Data.Reflection

Methods

reflect :: proxy n -> Integer

KnownSymbol n => Reifies (n :: Symbol) String

Defined in Data.Reflection

Methods

reflect :: proxy n -> String

Reifies Z Int

Defined in Data.Reflection

Methods

reflect :: proxy Z -> Int

Reifies n Int => Reifies (D n :: Type) Int

Defined in Data.Reflection

Methods

reflect :: proxy (D n) -> Int

Reifies n Int => Reifies (SD n :: Type) Int

Defined in Data.Reflection

Methods

reflect :: proxy (SD n) -> Int

Reifies n Int => Reifies (PD n :: Type) Int

Defined in Data.Reflection

Methods

reflect :: proxy (PD n) -> Int

(B b0, B b1, B b2, B b3, B b4, B b5, B b6, B b7, w0 ~ W b0 b1 b2 b3, w1 ~ W b4 b5 b6 b7) => Reifies (Stable w0 w1 a :: Type) a

Defined in Data.Reflection

Methods

reflect :: proxy (Stable w0 w1 a) -> a

reify :: a -> (forall s. Reifies s a => Proxy s -> r) -> r

Reify a value at the type level, to be recovered with reflect.

data Proxy (t :: k) :: forall k. k -> Type

Proxy is a type that holds no data, but has a phantom parameter of arbitrary type (or even kind). Its use is to provide type information, even though there is no value available of that type (or it may be too costly to create one).

Historically, Proxy :: Proxy a is a safer alternative to the 'undefined :: a' idiom.

>>> Proxy :: Proxy (Void, Int -> Int)
Proxy

Proxy can even hold types of higher kinds,

>>> Proxy :: Proxy Either
Proxy

>>> Proxy :: Proxy Functor
Proxy

>>> Proxy :: Proxy complicatedStructure
Proxy

Constructors

Proxy

Instances

Generic1 (Proxy :: k -> Type)

Defined in GHC.Generics

Associated Types

type Rep1 Proxy :: k -> Type

Methods

from1 :: Proxy a -> Rep1 Proxy a

to1 :: Rep1 Proxy a -> Proxy a

Monad (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b

(>>) :: Proxy a -> Proxy b -> Proxy b

return :: a -> Proxy a

fail :: String -> Proxy a

Functor (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

fmap :: (a -> b) -> Proxy a -> Proxy b

(<$) :: a -> Proxy b -> Proxy a

Applicative (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

pure :: a -> Proxy a

(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b

liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c

(*>) :: Proxy a -> Proxy b -> Proxy b

(<*) :: Proxy a -> Proxy b -> Proxy a

Foldable (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m

foldMap :: Monoid m => (a -> m) -> Proxy a -> m

foldr :: (a -> b -> b) -> b -> Proxy a -> b

foldr' :: (a -> b -> b) -> b -> Proxy a -> b

foldl :: (b -> a -> b) -> b -> Proxy a -> b

foldl' :: (b -> a -> b) -> b -> Proxy a -> b

foldr1 :: (a -> a -> a) -> Proxy a -> a

foldl1 :: (a -> a -> a) -> Proxy a -> a

toList :: Proxy a -> [a]

null :: Proxy a -> Bool

length :: Proxy a -> Int

elem :: Eq a => a -> Proxy a -> Bool

maximum :: Ord a => Proxy a -> a

minimum :: Ord a => Proxy a -> a

sum :: Num a => Proxy a -> a

product :: Num a => Proxy a -> a

Traversable (Proxy :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b)

sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a)

mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b)

sequence :: Monad m => Proxy (m a) -> m (Proxy a)

ToJSON1 (Proxy :: Type -> Type)

Defined in Data.Aeson.Types.ToJSON

Methods

liftToJSON :: (a -> Value) -> ([a] -> Value) -> Proxy a -> Value

liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [Proxy a] -> Value

liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> Proxy a -> Encoding

liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [Proxy a] -> Encoding

FromJSON1 (Proxy :: Type -> Type)

Defined in Data.Aeson.Types.FromJSON

Methods

liftParseJSON :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser (Proxy a)

liftParseJSONList :: (Value -> Parser a) -> (Value -> Parser [a]) -> Value -> Parser [Proxy a]

Alternative (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

empty :: Proxy a

(<|>) :: Proxy a -> Proxy a -> Proxy a

some :: Proxy a -> Proxy [a]

many :: Proxy a -> Proxy [a]

MonadPlus (Proxy :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

mzero :: Proxy a

mplus :: Proxy a -> Proxy a -> Proxy a

NFData1 (Proxy :: Type -> Type)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Proxy a -> ()

Hashable1 (Proxy :: Type -> Type)

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Proxy a -> Int

Bounded (Proxy t)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

minBound :: Proxy t

maxBound :: Proxy t

Enum (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

succ :: Proxy s -> Proxy s

pred :: Proxy s -> Proxy s

toEnum :: Int -> Proxy s

fromEnum :: Proxy s -> Int

enumFrom :: Proxy s -> [Proxy s]

enumFromThen :: Proxy s -> Proxy s -> [Proxy s]

enumFromTo :: Proxy s -> Proxy s -> [Proxy s]

enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s]

Eq (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

(==) :: Proxy s -> Proxy s -> Bool

(/=) :: Proxy s -> Proxy s -> Bool

Ord (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

compare :: Proxy s -> Proxy s -> Ordering

(<) :: Proxy s -> Proxy s -> Bool

(<=) :: Proxy s -> Proxy s -> Bool

(>) :: Proxy s -> Proxy s -> Bool

(>=) :: Proxy s -> Proxy s -> Bool

max :: Proxy s -> Proxy s -> Proxy s

min :: Proxy s -> Proxy s -> Proxy s

Read (Proxy t)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

readsPrec :: Int -> ReadS (Proxy t)

readList :: ReadS [Proxy t]

readPrec :: ReadPrec (Proxy t)

readListPrec :: ReadPrec [Proxy t]

Show (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

showsPrec :: Int -> Proxy s -> ShowS

show :: Proxy s -> String

showList :: [Proxy s] -> ShowS

Ix (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

range :: (Proxy s, Proxy s) -> [Proxy s]

index :: (Proxy s, Proxy s) -> Proxy s -> Int

unsafeIndex :: (Proxy s, Proxy s) -> Proxy s -> Int

inRange :: (Proxy s, Proxy s) -> Proxy s -> Bool

rangeSize :: (Proxy s, Proxy s) -> Int

unsafeRangeSize :: (Proxy s, Proxy s) -> Int

Generic (Proxy t)

Defined in GHC.Generics

Associated Types

type Rep (Proxy t) :: Type -> Type

Methods

from :: Proxy t -> Rep (Proxy t) x

to :: Rep (Proxy t) x -> Proxy t

Semigroup (Proxy s)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s

sconcat :: NonEmpty (Proxy s) -> Proxy s

stimes :: Integral b => b -> Proxy s -> Proxy s

Monoid (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

mempty :: Proxy s

mappend :: Proxy s -> Proxy s -> Proxy s

mconcat :: [Proxy s] -> Proxy s

Hashable (Proxy a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Proxy a -> Int

hash :: Proxy a -> Int

ToJSON (Proxy a)

Defined in Data.Aeson.Types.ToJSON

Methods

toJSON :: Proxy a -> Value

toEncoding :: Proxy a -> Encoding

toJSONList :: [Proxy a] -> Value

toEncodingList :: [Proxy a] -> Encoding

FromJSON (Proxy a)

Defined in Data.Aeson.Types.FromJSON

Methods

parseJSON :: Value -> Parser (Proxy a)

parseJSONList :: Value -> Parser [Proxy a]

NFData (Proxy a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Proxy a -> ()

type Rep1 (Proxy :: k -> Type)

Since: base-4.6.0.0

Defined in GHC.Generics

type Rep1 (Proxy :: k -> Type) = D1 (MetaData "Proxy" "Data.Proxy" "base" False) (C1 (MetaCons "Proxy" PrefixI False) (U1 :: k -> Type))

type Rep (Proxy t)

Since: base-4.6.0.0

Defined in GHC.Generics

type Rep (Proxy t) = D1 (MetaData "Proxy" "Data.Proxy" "base" False) (C1 (MetaCons "Proxy" PrefixI False) (U1 :: Type -> Type))

Orphan instances

Random Natural

Methods

randomR :: RandomGen g => (Natural, Natural) -> g -> (Natural, g)

random :: RandomGen g => g -> (Natural, g)

randomRs :: RandomGen g => (Natural, Natural) -> g -> [Natural]

randoms :: RandomGen g => g -> [Natural]

randomRIO :: (Natural, Natural) -> IO Natural

randomIO :: IO Natural