ZkFold.Symbolic.Data.Ord

Documentation

class Monoid ordering => IsOrdering ordering where

Methods

lt :: ordering

eq :: ordering

gt :: ordering

Instances

IsOrdering Ordering

Defined in ZkFold.Symbolic.Data.Ord

Methods

lt :: Ordering

eq :: Ordering

gt :: Ordering

Symbolic c => IsOrdering (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

lt :: Ordering c

eq :: Ordering c

gt :: Ordering c

data Ordering c

Instances

Symbolic c => Monoid (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

mempty :: Ordering c

mappend :: Ordering c -> Ordering c -> Ordering c

mconcat :: [Ordering c] -> Ordering c

Symbolic c => Semigroup (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

(<>) :: Ordering c -> Ordering c -> Ordering c

sconcat :: NonEmpty (Ordering c) -> Ordering c

stimes :: Integral b => b -> Ordering c -> Ordering c

Generic (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type Rep (Ordering c) :: Type -> Type

Methods

from :: Ordering c -> Rep (Ordering c) x

to :: Rep (Ordering c) x -> Ordering c

Show (c Par1) => Show (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

showsPrec :: Int -> Ordering c -> ShowS

show :: Ordering c -> String

showList :: [Ordering c] -> ShowS

NFData (c Par1) => NFData (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

rnf :: Ordering c -> ()

Symbolic c => SymbolicData (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type Context (Ordering c) :: (Type -> Type) -> Type

type Support (Ordering c)

type Layout (Ordering c) :: Type -> Type

type Payload (Ordering c) :: Type -> Type

Methods

arithmetize :: Ordering c -> Support (Ordering c) -> Context (Ordering c) (Layout (Ordering c))

payload :: Ordering c -> Support (Ordering c) -> Payload (Ordering c) (WitnessField (Context (Ordering c)))

restore :: Context (Ordering c) ~ c0 => (Support (Ordering c) -> (c0 (Layout (Ordering c)), Payload (Ordering c) (WitnessField c0))) -> Ordering c

Symbolic c => Eq (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type BooleanOf (Ordering c)

Methods

(==) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(/=) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

Symbolic c => IsOrdering (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

lt :: Ordering c

eq :: Ordering c

gt :: Ordering c

Symbolic c => Ord (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf (Ordering c)

Methods

ordering :: Ordering c -> Ordering c -> Ordering c -> OrderingOf (Ordering c) -> Ordering c

compare :: Ordering c -> Ordering c -> OrderingOf (Ordering c)

(<) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(<=) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(>) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(>=) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

max :: Ordering c -> Ordering c -> Ordering c

min :: Ordering c -> Ordering c -> Ordering c

Symbolic c => Conditional (Bool c) (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Methods

bool :: Ordering c -> Ordering c -> Bool c -> Ordering c

type Rep (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type Rep (Ordering c) = D1 ('MetaData "Ordering" "ZkFold.Symbolic.Data.Ord" "symbolic-base-0.1.0.0-inplace" 'True) (C1 ('MetaCons "Ordering" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (c Par1))))

type Context (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type Context (Ordering c) = GContext (Rep (Ordering c))

type Layout (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type Layout (Ordering c) = GLayout (Rep (Ordering c))

type Payload (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type Payload (Ordering c) = GPayload (Rep (Ordering c))

type Support (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type Support (Ordering c) = GSupport (Rep (Ordering c))

type BooleanOf (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type BooleanOf (Ordering c) = BooleanOf (c Par1)

type OrderingOf (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

type OrderingOf (Ordering c) = OrderingOf (c Par1)

class (Eq a, IsOrdering (OrderingOf a)) => Ord a where

Minimal complete definition

Nothing

Associated Types

type OrderingOf a

type OrderingOf a = GOrderingOf (Rep a)

Methods

ordering :: a -> a -> a -> OrderingOf a -> a

default ordering :: (Generic a, GOrd (Rep a), OrderingOf a ~ GOrderingOf (Rep a)) => a -> a -> a -> OrderingOf a -> a

compare :: a -> a -> OrderingOf a

default compare :: (Generic a, GOrd (Rep a), OrderingOf a ~ GOrderingOf (Rep a)) => a -> a -> OrderingOf a

(<) :: a -> a -> BooleanOf a infix 4

default (<) :: (Ord (BooleanOf a), OrderingOf (BooleanOf a) ~ OrderingOf a) => a -> a -> BooleanOf a

(<=) :: a -> a -> BooleanOf a infix 4

default (<=) :: (Ord (BooleanOf a), OrderingOf (BooleanOf a) ~ OrderingOf a) => a -> a -> BooleanOf a

(>) :: a -> a -> BooleanOf a infix 4

default (>) :: (Ord (BooleanOf a), OrderingOf (BooleanOf a) ~ OrderingOf a) => a -> a -> BooleanOf a

(>=) :: a -> a -> BooleanOf a infix 4

default (>=) :: (Ord (BooleanOf a), OrderingOf (BooleanOf a) ~ OrderingOf a) => a -> a -> BooleanOf a

max :: a -> a -> a

min :: a -> a -> a

Instances

Ord String

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf String

Methods

ordering :: String -> String -> String -> OrderingOf String -> String

compare :: String -> String -> OrderingOf String

(<) :: String -> String -> BooleanOf String

(<=) :: String -> String -> BooleanOf String

(>) :: String -> String -> BooleanOf String

(>=) :: String -> String -> BooleanOf String

max :: String -> String -> String

min :: String -> String -> String

Ord Natural

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf Natural

Methods

ordering :: Natural -> Natural -> Natural -> OrderingOf Natural -> Natural

compare :: Natural -> Natural -> OrderingOf Natural

(<) :: Natural -> Natural -> BooleanOf Natural

(<=) :: Natural -> Natural -> BooleanOf Natural

(>) :: Natural -> Natural -> BooleanOf Natural

(>=) :: Natural -> Natural -> BooleanOf Natural

max :: Natural -> Natural -> Natural

min :: Natural -> Natural -> Natural

Ord Bool

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf Bool

Methods

ordering :: Bool -> Bool -> Bool -> OrderingOf Bool -> Bool

compare :: Bool -> Bool -> OrderingOf Bool

(<) :: Bool -> Bool -> BooleanOf Bool

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

(>) :: Bool -> Bool -> BooleanOf Bool

(>=) :: Bool -> Bool -> BooleanOf Bool

max :: Bool -> Bool -> Bool

min :: Bool -> Bool -> Bool

KnownNat n => Ord (Zp n)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf (Zp n)

Methods

ordering :: Zp n -> Zp n -> Zp n -> OrderingOf (Zp n) -> Zp n

compare :: Zp n -> Zp n -> OrderingOf (Zp n)

(<) :: Zp n -> Zp n -> BooleanOf (Zp n)

(<=) :: Zp n -> Zp n -> BooleanOf (Zp n)

(>) :: Zp n -> Zp n -> BooleanOf (Zp n)

(>=) :: Zp n -> Zp n -> BooleanOf (Zp n)

max :: Zp n -> Zp n -> Zp n

min :: Zp n -> Zp n -> Zp n

Symbolic c => Ord (Bool c)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf (Bool c)

Methods

ordering :: Bool c -> Bool c -> Bool c -> OrderingOf (Bool c) -> Bool c

compare :: Bool c -> Bool c -> OrderingOf (Bool c)

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

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

(>) :: Bool c -> Bool c -> BooleanOf (Bool c)

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

max :: Bool c -> Bool c -> Bool c

min :: Bool c -> Bool c -> Bool c

Symbolic c => Ord (FieldElement c)

Defined in ZkFold.Symbolic.Data.FieldElement

Associated Types

type OrderingOf (FieldElement c)

Methods

ordering :: FieldElement c -> FieldElement c -> FieldElement c -> OrderingOf (FieldElement c) -> FieldElement c

compare :: FieldElement c -> FieldElement c -> OrderingOf (FieldElement c)

(<) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c)

(<=) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c)

(>) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c)

(>=) :: FieldElement c -> FieldElement c -> BooleanOf (FieldElement c)

max :: FieldElement c -> FieldElement c -> FieldElement c

min :: FieldElement c -> FieldElement c -> FieldElement c

Symbolic c => Ord (Ordering c)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf (Ordering c)

Methods

ordering :: Ordering c -> Ordering c -> Ordering c -> OrderingOf (Ordering c) -> Ordering c

compare :: Ordering c -> Ordering c -> OrderingOf (Ordering c)

(<) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(<=) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(>) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

(>=) :: Ordering c -> Ordering c -> BooleanOf (Ordering c)

max :: Ordering c -> Ordering c -> Ordering c

min :: Ordering c -> Ordering c -> Ordering c

(Symbolic c, LayoutFunctor f) => Ord (c f)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type OrderingOf (c f)

Methods

ordering :: c f -> c f -> c f -> OrderingOf (c f) -> c f

compare :: c f -> c f -> OrderingOf (c f)

(<) :: c f -> c f -> BooleanOf (c f)

(<=) :: c f -> c f -> BooleanOf (c f)

(>) :: c f -> c f -> BooleanOf (c f)

(>=) :: c f -> c f -> BooleanOf (c f)

max :: c f -> c f -> c f

min :: c f -> c f -> c f

(Symbolic c, KnownNat n, KnownRegisterSize r, KnownRegisters c n r, regSize ~ GetRegisterSize (BaseField c) n r, KnownNat (Ceil regSize OrdWord)) => Ord (UInt n r c)

Defined in ZkFold.Symbolic.Data.UInt

Associated Types

type OrderingOf (UInt n r c)

Methods

ordering :: UInt n r c -> UInt n r c -> UInt n r c -> OrderingOf (UInt n r c) -> UInt n r c

compare :: UInt n r c -> UInt n r c -> OrderingOf (UInt n r c)

(<) :: UInt n r c -> UInt n r c -> BooleanOf (UInt n r c)

(<=) :: UInt n r c -> UInt n r c -> BooleanOf (UInt n r c)

(>) :: UInt n r c -> UInt n r c -> BooleanOf (UInt n r c)

(>=) :: UInt n r c -> UInt n r c -> BooleanOf (UInt n r c)

max :: UInt n r c -> UInt n r c -> UInt n r c

min :: UInt n r c -> UInt n r c -> UInt n r c

class (GEq u, IsOrdering (GOrderingOf u)) => GOrd u where

Associated Types

type GOrderingOf u

Methods

gordering :: u x -> u x -> u x -> GOrderingOf u -> u x

gcompare :: u x -> u x -> GOrderingOf u

Instances

Ord x => GOrd (Rec0 x :: k -> Type)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type GOrderingOf (Rec0 x)

Methods

gordering :: forall (x0 :: k0). Rec0 x x0 -> Rec0 x x0 -> Rec0 x x0 -> GOrderingOf (Rec0 x) -> Rec0 x x0

gcompare :: forall (x0 :: k0). Rec0 x x0 -> Rec0 x x0 -> GOrderingOf (Rec0 x)

(GOrd u, GOrd v, GBooleanOf u ~ GBooleanOf v, GOrderingOf u ~ GOrderingOf v) => GOrd (u :*: v :: k -> Type)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type GOrderingOf (u :*: v)

Methods

gordering :: forall (x :: k0). (u :*: v) x -> (u :*: v) x -> (u :*: v) x -> GOrderingOf (u :*: v) -> (u :*: v) x

gcompare :: forall (x :: k0). (u :*: v) x -> (u :*: v) x -> GOrderingOf (u :*: v)

GOrd v => GOrd (M1 i c v :: k -> Type)

Defined in ZkFold.Symbolic.Data.Ord

Associated Types

type GOrderingOf (M1 i c v)

Methods

gordering :: forall (x :: k0). M1 i c v x -> M1 i c v x -> M1 i c v x -> GOrderingOf (M1 i c v) -> M1 i c v x

gcompare :: forall (x :: k0). M1 i c v x -> M1 i c v x -> GOrderingOf (M1 i c v)