type AsHaskell PPositive	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type AsHaskell PPositive = AsHaskell (DeriveNewtypePLiftable PPositive Positive)
type PlutusRepr PPositive
Instance details Defined in Plutarch.Internal.Numeric type PlutusRepr PPositive = PlutusRepr (DeriveNewtypePLiftable PPositive Positive)

Methods

haskToRepr :: AsHaskell PPositive -> PlutusRepr PPositive Source #

reprToHask :: PlutusRepr PPositive -> Either LiftError (AsHaskell PPositive) Source #

reprToPlut :: forall (s :: S). PlutusRepr PPositive -> PLifted s PPositive Source #

plutToRepr :: (forall (s :: S). PLifted s PPositive) -> Either LiftError (PlutusRepr PPositive) Source #

PAdditiveSemigroup PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

pscalePositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

PMultiplicativeMonoid PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PPositive Source #

ppowNatural :: forall (s :: S). Term s PPositive -> Term s PNatural -> Term s PPositive Source #

PMultiplicativeSemigroup PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

ppowPositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

POrd PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#<=) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PBool Source #

(#<) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PBool Source #

pmax :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

pmin :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #

PValidateData PPositive Source #

Checks that we have a positive I.

Since: 1.13.0

Instance details

Defined in Plutarch.Internal.Parse

Methods

pwithValidated :: forall (s :: S). Term s PData -> forall (r :: S -> Type). Term s r -> Term s r Source #

PlutusType PPositive Source #

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type PInner PPositive	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type PInner PPositive = PInner (DeriveNewtypePlutusType PPositive)

Methods

pcon' :: forall (s :: S). PPositive s -> Term s (PInner PPositive) Source #

pmatch' :: forall (s :: S) (b :: S -> Type). Term s (PInner PPositive) -> (PPositive s -> Term s b) -> Term s b Source #

PShow PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Show

Methods

pshow' :: forall (s :: S). Bool -> Term s PPositive -> Term s PString Source #

PTryFrom PInteger PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.TryFrom

Associated Types

type PTryFromExcess PInteger PPositive
Instance details Defined in Plutarch.Internal.TryFrom type PTryFromExcess PInteger PPositive = Const () :: S -> Type

Methods

ptryFrom' :: forall (s :: S) (r :: S -> Type). Term s PInteger -> ((Term s PPositive, Reduce (PTryFromExcess PInteger PPositive s)) -> Term s r) -> Term s r Source #

PTryFrom PData (PAsData PPositive) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.TryFrom

Associated Types

type PTryFromExcess PData (PAsData PPositive)
Instance details Defined in Plutarch.Internal.TryFrom type PTryFromExcess PData (PAsData PPositive) = PTryFromExcess PData (PInner (PAsData PPositive))

Methods

ptryFrom' :: forall (s :: S) (r :: S -> Type). Term s PData -> ((Term s (PAsData PPositive), Reduce (PTryFromExcess PData (PAsData PPositive) s)) -> Term s r) -> Term s r Source #

Generic (PPositive s) Source #

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Rep (PPositive s)	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type Rep (PPositive s) = D1 ('MetaData "PPositive" "Plutarch.Internal.Numeric" "plutarch-1.14.0-6fw3gqGsL7f3TFINWPu1lG" 'True) (C1 ('MetaCons "PPositive" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Term s PNatural))))

Methods

from :: PPositive s -> Rep (PPositive s) x Source #

to :: Rep (PPositive s) x -> PPositive s Source #

Generic (PPositive s) Source #

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Code (PPositive s)	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type Code (PPositive s) = GCode (PPositive s)

Methods

from :: PPositive s -> Rep (PPositive s)

to :: Rep (PPositive s) -> PPositive s

type AsHaskell PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type AsHaskell PPositive = AsHaskell (DeriveNewtypePLiftable PPositive Positive)

type PlutusRepr PPositive Source #

Instance details

Defined in Plutarch.Internal.Numeric

type PlutusRepr PPositive = PlutusRepr (DeriveNewtypePLiftable PPositive Positive)

type PInner PPositive Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type PInner PPositive = PInner (DeriveNewtypePlutusType PPositive)

type PTryFromExcess PInteger PPositive Source #

Instance details

Defined in Plutarch.Internal.TryFrom

type PTryFromExcess PInteger PPositive = Const () :: S -> Type

type PTryFromExcess PData (PAsData PPositive) Source #

Instance details

Defined in Plutarch.Internal.TryFrom

type PTryFromExcess PData (PAsData PPositive) = PTryFromExcess PData (PInner (PAsData PPositive))

type Rep (PPositive s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Rep (PPositive s) = D1 ('MetaData "PPositive" "Plutarch.Internal.Numeric" "plutarch-1.14.0-6fw3gqGsL7f3TFINWPu1lG" 'True) (C1 ('MetaCons "PPositive" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Term s PNatural))))

type Code (PPositive s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Code (PPositive s) = GCode (PPositive s)

data Positive Source #

Since: 1.10.0

Instances

Instances details

Arbitrary Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods arbitrary :: Gen Positive shrink :: Positive -> [Positive]
CoArbitrary Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods coarbitrary :: Positive -> Gen b -> Gen b
Function Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods function :: (Positive -> b) -> Positive :-> b
Show Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods showsPrec :: Int -> Positive -> ShowS Source # show :: Positive -> String Source # showList :: [Positive] -> ShowS Source #
Eq Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (==) :: Positive -> Positive -> Bool Source # (/=) :: Positive -> Positive -> Bool Source #
Ord Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods compare :: Positive -> Positive -> Ordering Source # (<) :: Positive -> Positive -> Bool Source # (<=) :: Positive -> Positive -> Bool Source # (>) :: Positive -> Positive -> Bool Source # (>=) :: Positive -> Positive -> Bool Source # max :: Positive -> Positive -> Positive Source # min :: Positive -> Positive -> Positive Source #
Pretty Positive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pretty :: Positive -> Doc ann prettyList :: [Positive] -> Doc ann

data PNatural (s :: S) Source #

Since: 1.10.0

Instances

Instances details

PEq PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#==) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PBool Source #

PIsData PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pfromDataImpl :: forall (s :: S). Term s (PAsData PNatural) -> Term s PNatural Source #

pdataImpl :: forall (s :: S). Term s PNatural -> Term s PData Source #

PLiftable PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type AsHaskell PNatural
Instance details Defined in Plutarch.Internal.Numeric type AsHaskell PNatural = Natural
type PlutusRepr PNatural
Instance details Defined in Plutarch.Internal.Numeric type PlutusRepr PNatural = Integer

Methods

haskToRepr :: AsHaskell PNatural -> PlutusRepr PNatural Source #

reprToHask :: PlutusRepr PNatural -> Either LiftError (AsHaskell PNatural) Source #

reprToPlut :: forall (s :: S). PlutusRepr PNatural -> PLifted s PNatural Source #

plutToRepr :: (forall (s :: S). PLifted s PNatural) -> Either LiftError (PlutusRepr PNatural) Source #

PAdditiveMonoid PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pzero :: forall (s :: S). Term s PNatural Source #

pscaleNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PAdditiveSemigroup PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#+) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

pscalePositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #

PMultiplicativeMonoid PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

pone :: forall (s :: S). Term s PNatural Source #

ppowNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PMultiplicativeSemigroup PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#*) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

ppowPositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #

POrd PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

Methods

(#<=) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PBool Source #

(#<) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PBool Source #

pmax :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

pmin :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #

PlutusType PNatural Source #

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type PInner PNatural	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type PInner PNatural = PInner (DeriveNewtypePlutusType PNatural)

Methods

pcon' :: forall (s :: S). PNatural s -> Term s (PInner PNatural) Source #

pmatch' :: forall (s :: S) (b :: S -> Type). Term s (PInner PNatural) -> (PNatural s -> Term s b) -> Term s b Source #

PShow PNatural Source #

Since: 1.13.0

Instance details

Defined in Plutarch.Internal.Show

Methods

pshow' :: forall (s :: S). Bool -> Term s PNatural -> Term s PString Source #

PTryFrom PData (PAsData PNatural) Source #

Since: 3.4.0

Instance details

Defined in Plutarch.Internal.TryFrom

Associated Types

type PTryFromExcess PData (PAsData PNatural)
Instance details Defined in Plutarch.Internal.TryFrom type PTryFromExcess PData (PAsData PNatural) = PTryFromExcess PData (PInner (PAsData PNatural))

Methods

ptryFrom' :: forall (s :: S) (r :: S -> Type). Term s PData -> ((Term s (PAsData PNatural), Reduce (PTryFromExcess PData (PAsData PNatural) s)) -> Term s r) -> Term s r Source #

Generic (PNatural s) Source #

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Rep (PNatural s)	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type Rep (PNatural s) = D1 ('MetaData "PNatural" "Plutarch.Internal.Numeric" "plutarch-1.14.0-6fw3gqGsL7f3TFINWPu1lG" 'True) (C1 ('MetaCons "PNatural" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Term s PInteger))))

Methods

from :: PNatural s -> Rep (PNatural s) x Source #

to :: Rep (PNatural s) x -> PNatural s Source #

Generic (PNatural s) Source #

Instance details

Defined in Plutarch.Internal.Numeric

Associated Types

type Code (PNatural s)	Since: plutarch-1.10.0
Instance details Defined in Plutarch.Internal.Numeric type Code (PNatural s) = GCode (PNatural s)

Methods

from :: PNatural s -> Rep (PNatural s)

to :: Rep (PNatural s) -> PNatural s

type AsHaskell PNatural Source #

Instance details

Defined in Plutarch.Internal.Numeric

type AsHaskell PNatural = Natural

type PlutusRepr PNatural Source #

Instance details

Defined in Plutarch.Internal.Numeric

type PlutusRepr PNatural = Integer

type PInner PNatural Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type PInner PNatural = PInner (DeriveNewtypePlutusType PNatural)

type PTryFromExcess PData (PAsData PNatural) Source #

Instance details

Defined in Plutarch.Internal.TryFrom

type PTryFromExcess PData (PAsData PNatural) = PTryFromExcess PData (PInner (PAsData PNatural))

type Rep (PNatural s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Rep (PNatural s) = D1 ('MetaData "PNatural" "Plutarch.Internal.Numeric" "plutarch-1.14.0-6fw3gqGsL7f3TFINWPu1lG" 'True) (C1 ('MetaCons "PNatural" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Term s PInteger))))

type Code (PNatural s) Source #

Since: 1.10.0

Instance details

Defined in Plutarch.Internal.Numeric

type Code (PNatural s) = GCode (PNatural s)

Type classes

class PAdditiveSemigroup (a :: S -> Type) where Source #

The addition operation, and the notion of scaling by a positive.

Laws

x #+ y = y #+ x (commutativity of #+)
x #+ (y #+ z) = (x #+ y) #+ z (associativity of #+)

If you define a custom pscalePositive, ensure the following also hold:

pscalePositive x pone = x
(pscalePositive x n) #+ (pscalePositive x m) = pscalePositive x (n #+ m)
pscalePositive (pscalePositive x n) m = pscalePositive x (n #* m)

The default implementation ensures these laws are satisfied.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

(#+) :: forall (s :: S). Term s a -> Term s a -> Term s a infix 6 Source #

default (#+) :: forall (s :: S). PAdditiveSemigroup (PInner a) => Term s a -> Term s a -> Term s a Source #

pscalePositive :: forall (s :: S). Term s a -> Term s PPositive -> Term s a Source #

This defaults to exponentiation-by-squaring, which in general is the best we can do.

Instances

Instances details

PAdditiveSemigroup PBuiltinBLS12_381_G1_Element Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#+) :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element Source # pscalePositive :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PPositive -> Term s PBuiltinBLS12_381_G1_Element Source #
PAdditiveSemigroup PBuiltinBLS12_381_G2_Element Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#+) :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element Source # pscalePositive :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PPositive -> Term s PBuiltinBLS12_381_G2_Element Source #
PAdditiveSemigroup PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#+) :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source # pscalePositive :: forall (s :: S). Term s PInteger -> Term s PPositive -> Term s PInteger Source #
PAdditiveSemigroup PNatural Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#+) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source # pscalePositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #
PAdditiveSemigroup PPositive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#+) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source # pscalePositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #
PAdditiveSemigroup PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods (#+) :: forall (s :: S). Term s PRational -> Term s PRational -> Term s PRational Source # pscalePositive :: forall (s :: S). Term s PRational -> Term s PPositive -> Term s PRational Source #
PAdditiveSemigroup a => PAdditiveSemigroup (PPullArray a) Source #	Since: 1.12.0
Instance details Defined in Plutarch.Array Methods (#+) :: forall (s :: S). Term s (PPullArray a) -> Term s (PPullArray a) -> Term s (PPullArray a) Source # pscalePositive :: forall (s :: S). Term s (PPullArray a) -> Term s PPositive -> Term s (PPullArray a) Source #

class PAdditiveSemigroup a => PAdditiveMonoid (a :: S -> Type) where Source #

The notion of zero, as well as a way to scale by naturals.

Laws

pzero #+ x = x (pzero is the identity of #+)
pscalePositive pzero n = pzero (pzero does not scale up)

If you define pscaleNatural, ensure the following as well:

pscaleNatural x (ppositiveToNatural # p) = pscalePositive x p
pscaleNatural x pzero = pzero

The default implementation of pscaleNatural ensures these laws hold.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

pzero :: forall (s :: S). Term s a Source #

default pzero :: forall (s :: S). PAdditiveMonoid (PInner a) => Term s a Source #

pscaleNatural :: forall (s :: S). Term s a -> Term s PNatural -> Term s a Source #

Instances

Instances details

PAdditiveMonoid PBuiltinBLS12_381_G1_Element Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pzero :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element Source # pscaleNatural :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PNatural -> Term s PBuiltinBLS12_381_G1_Element Source #
PAdditiveMonoid PBuiltinBLS12_381_G2_Element Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pzero :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element Source # pscaleNatural :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PNatural -> Term s PBuiltinBLS12_381_G2_Element Source #
PAdditiveMonoid PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pzero :: forall (s :: S). Term s PInteger Source # pscaleNatural :: forall (s :: S). Term s PInteger -> Term s PNatural -> Term s PInteger Source #
PAdditiveMonoid PNatural Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pzero :: forall (s :: S). Term s PNatural Source # pscaleNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #
PAdditiveMonoid PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods pzero :: forall (s :: S). Term s PRational Source # pscaleNatural :: forall (s :: S). Term s PRational -> Term s PNatural -> Term s PRational Source #

class PAdditiveMonoid a => PAdditiveGroup (a :: S -> Type) where Source #

The notion of additive inverses, and the subtraction operation.

Laws

If you define pnegate, the following laws must hold:

(pnegate # x) #+ x = pzero (pnegate is an additive inverse)
pnegate #$ pnegate # x = x (pnegate is self-inverting)

If you define #-, the following law must hold:

x #- x = pzero

Additionally, the following 'consistency laws' must hold. Default implementations of both pnegate and #- uphold these.

pnegate # x = pzero #- x
x #- y = x #+ (pnegate # y)

Lastly, if you define a custom pscaleInteger, the following laws must hold:

pscaleInteger x pzero = pzero
pscaleInteger x (pnegate # y) = pnegate # (pscaleInteger x y)

Since: 1.10.0

Minimal complete definition

pnegate | (#-)

Methods

pnegate :: forall (s :: S). Term s (a :--> a) Source #

(#-) :: forall (s :: S). Term s a -> Term s a -> Term s a infix 6 Source #

pscaleInteger :: forall (s :: S). Term s a -> Term s PInteger -> Term s a Source #

Instances

Instances details

PAdditiveGroup PBuiltinBLS12_381_G1_Element Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pnegate :: forall (s :: S). Term s (PBuiltinBLS12_381_G1_Element :--> PBuiltinBLS12_381_G1_Element) Source # (#-) :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element -> Term s PBuiltinBLS12_381_G1_Element Source # pscaleInteger :: forall (s :: S). Term s PBuiltinBLS12_381_G1_Element -> Term s PInteger -> Term s PBuiltinBLS12_381_G1_Element Source #
PAdditiveGroup PBuiltinBLS12_381_G2_Element Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pnegate :: forall (s :: S). Term s (PBuiltinBLS12_381_G2_Element :--> PBuiltinBLS12_381_G2_Element) Source # (#-) :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element -> Term s PBuiltinBLS12_381_G2_Element Source # pscaleInteger :: forall (s :: S). Term s PBuiltinBLS12_381_G2_Element -> Term s PInteger -> Term s PBuiltinBLS12_381_G2_Element Source #
PAdditiveGroup PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pnegate :: forall (s :: S). Term s (PInteger :--> PInteger) Source # (#-) :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source # pscaleInteger :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source #
PAdditiveGroup PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods pnegate :: forall (s :: S). Term s (PRational :--> PRational) Source # (#-) :: forall (s :: S). Term s PRational -> Term s PRational -> Term s PRational Source # pscaleInteger :: forall (s :: S). Term s PRational -> Term s PInteger -> Term s PRational Source #

class PMultiplicativeSemigroup (a :: S -> Type) where Source #

The multiplication operation.

Laws

x #* (y #* z) = (x #* y) #* z (associativity of #*)

If you define a custom ppowPositive, ensure the following also hold:

ppowPositive x pone = x
(ppowPositive x n) #* (ppowPositive x m) = ppowPositive x (n #+ m)
ppowPositive (ppowPositive x n) m = ppowPositive x (n #* m)

The default implementation ensures these laws are satisfied.

Note

Unlike PAdditiveSemigroup, the multiplication operation doesn't need to be commutative. Currently, all Plutarch-provided instances are, but this need not be true for other instances.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

(#*) :: forall (s :: S). Term s a -> Term s a -> Term s a infix 6 Source #

default (#*) :: forall (s :: S). PMultiplicativeSemigroup (PInner a) => Term s a -> Term s a -> Term s a Source #

ppowPositive :: forall (s :: S). Term s a -> Term s PPositive -> Term s a Source #

Instances

Instances details

PMultiplicativeSemigroup PBuiltinBLS12_381_MlResult Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#*) :: forall (s :: S). Term s PBuiltinBLS12_381_MlResult -> Term s PBuiltinBLS12_381_MlResult -> Term s PBuiltinBLS12_381_MlResult Source # ppowPositive :: forall (s :: S). Term s PBuiltinBLS12_381_MlResult -> Term s PPositive -> Term s PBuiltinBLS12_381_MlResult Source #
PMultiplicativeSemigroup PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#*) :: forall (s :: S). Term s PInteger -> Term s PInteger -> Term s PInteger Source # ppowPositive :: forall (s :: S). Term s PInteger -> Term s PPositive -> Term s PInteger Source #
PMultiplicativeSemigroup PNatural Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#*) :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source # ppowPositive :: forall (s :: S). Term s PNatural -> Term s PPositive -> Term s PNatural Source #
PMultiplicativeSemigroup PPositive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods (#*) :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source # ppowPositive :: forall (s :: S). Term s PPositive -> Term s PPositive -> Term s PPositive Source #
PMultiplicativeSemigroup PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods (#*) :: forall (s :: S). Term s PRational -> Term s PRational -> Term s PRational Source # ppowPositive :: forall (s :: S). Term s PRational -> Term s PPositive -> Term s PRational Source #
PMultiplicativeSemigroup a => PMultiplicativeSemigroup (PPullArray a) Source #	Since: 1.12.0
Instance details Defined in Plutarch.Array Methods (#*) :: forall (s :: S). Term s (PPullArray a) -> Term s (PPullArray a) -> Term s (PPullArray a) Source # ppowPositive :: forall (s :: S). Term s (PPullArray a) -> Term s PPositive -> Term s (PPullArray a) Source #

class PMultiplicativeSemigroup a => PMultiplicativeMonoid (a :: S -> Type) where Source #

The notion of one (multiplicative identity), and exponentiation by - naturals.

Laws

pone #* x = x (pone is the left identity of #*)
x #* pone = x (pone is the right identity of #*)
ppowPositive pone p = pone (pone does not scale up)

If you define ppowNatural, ensure the following as well:

ppowNatural x (ppositiveToNatural # p) = ppowPositive x p
ppowNatural x pzero = pone

Since: 1.10.0

Minimal complete definition

Nothing

Methods

pone :: forall (s :: S). Term s a Source #

default pone :: forall (s :: S). PMultiplicativeMonoid (PInner a) => Term s a Source #

ppowNatural :: forall (s :: S). Term s a -> Term s PNatural -> Term s a Source #

Instances

Instances details

PMultiplicativeMonoid PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pone :: forall (s :: S). Term s PInteger Source # ppowNatural :: forall (s :: S). Term s PInteger -> Term s PNatural -> Term s PInteger Source #
PMultiplicativeMonoid PNatural Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pone :: forall (s :: S). Term s PNatural Source # ppowNatural :: forall (s :: S). Term s PNatural -> Term s PNatural -> Term s PNatural Source #
PMultiplicativeMonoid PPositive Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pone :: forall (s :: S). Term s PPositive Source # ppowNatural :: forall (s :: S). Term s PPositive -> Term s PNatural -> Term s PPositive Source #
PMultiplicativeMonoid PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods pone :: forall (s :: S). Term s PRational Source # ppowNatural :: forall (s :: S). Term s PRational -> Term s PNatural -> Term s PRational Source #

class (PAdditiveGroup a, PMultiplicativeMonoid a) => PRing (a :: S -> Type) where Source #

Laws

pfromInteger 0 = pzero
pfromInteger 1 = pone
pfromInteger (x + y) = pfromInteger x #+ pfromInteger y
pfromInteger (x * y) = pfromInteger x #* pfromInteger y

Additionally, the following 'interaction laws' must hold between the instances of PAdditiveGroup and PMultiplicativeMonoid for a:

x #* (y #+ z) = (x #* y) #+ (x #* z) (#* left-distributes over #+)
(y #+ z) #* x = (y #* x) #+ (z #* x) (#* right-distributes over #+)

Since: 1.10.0

Minimal complete definition

Nothing

Methods

pfromInteger :: forall (s :: S). Integer -> Term s a Source #

default pfromInteger :: forall (s :: S). PRing (PInner a) => Integer -> Term s a Source #

Instances

Instances details

PRing PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods pfromInteger :: forall (s :: S). Integer -> Term s PInteger Source #
PRing PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods pfromInteger :: forall (s :: S). Integer -> Term s PRational Source #

class (PRing a, POrd a) => PIntegralDomain (a :: S -> Type) where Source #

Laws

Pedantry note

Technically, the requirements here are too strong: we demand an ordered ring, which integral domains don't necessarily have to be. However, in our case, our hand is forced by expected semantics: in abstract algebra, both the absolute value and the signum are real numbers (which are always totally ordered) but in our case, both must be elements of the integral domain itself. Thus, in order for the laws to make any sense, we have to ensure a total order on the integral domain. Since all of our integral domains are 'at least as big' as the integers, this doesn't pose a huge problem.

Since: 1.10.0

Minimal complete definition

Nothing

Methods

psignum :: forall (s :: S). Term s (a :--> a) Source #

default psignum :: forall (s :: S). Term s (a :--> a) Source #

pabs :: forall (s :: S). Term s (a :--> a) Source #

default pabs :: forall (s :: S). Term s (a :--> a) Source #

Instances

Instances details

PIntegralDomain PInteger Source #	Since: 1.10.0
Instance details Defined in Plutarch.Internal.Numeric Methods psignum :: forall (s :: S). Term s (PInteger :--> PInteger) Source # pabs :: forall (s :: S). Term s (PInteger :--> PInteger) Source #
PIntegralDomain PRational Source #	Since: 1.10.0
Instance details Defined in Plutarch.Rational Methods psignum :: forall (s :: S). Term s (PRational :--> PRational) Source # pabs :: forall (s :: S). Term s (PRational :--> PRational) Source #

Functions

positiveToInteger :: Positive -> Integer Source #

Since: 1.10.0

toPositiveAbs :: Integer -> Positive Source #

Converts negative Integers into their absolute values, positive Integers into their Positive equivalents. Errors on 0.

Since: 1.10.0

ptryPositive :: forall (s :: S). Term s (PInteger :--> PPositive) Source #

Partial version of ppositive. Errors if argument is not positive.

Since: 1.10.0

ppositive :: forall (s :: S). Term s (PInteger :--> PMaybe PPositive) Source #

Build a PPositive from a PInteger. Yields PNothing if argument is not positive.

ptryNatural :: forall (s :: S). Term s (PInteger :--> PNatural) Source #

Partial version of pnatural. Errors if argument is negative.

Since: 1.10.0

pnatural :: forall (s :: S). Term s (PInteger :--> PMaybe PNatural) Source #

Build a PNatural from a PInteger. Yields PNothing if given a negative value.

Since: 1.10.0

ppositiveToNatural :: forall (s :: S). Term s (PPositive :--> PNatural) Source #

'Relax' a PPositive to PNatural. This uses punsafeCoerce underneath, but because any positive is also a natural, is safe.

Since: 1.10.0

pnaturalToPositiveCPS :: forall (a :: S -> Type) (s :: S). Term s a -> (Term s PPositive -> Term s a) -> Term s PNatural -> Term s a Source #

Specialized form of pmaybe for PNatural. Given a default, and a way to turn a PPositive into an answer, produce the default when given pzero, and apply the function otherwise.

Since: 1.10.0

pbySquaringDefault :: forall (a :: S -> Type) (s :: S). (forall (s' :: S). Term s' a -> Term s' a -> Term s' a) -> Term s a -> Term s PPositive -> Term s a Source #

A default implementation of exponentiation-by-squaring with a strictly-positive exponent.

Important note

This implementation assumes that the operation argument is associative.

Since: 1.10.0

pdiv :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

pmod :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

pquot :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

prem :: forall (s :: S). Term s (PInteger :--> (PInteger :--> PInteger)) Source #

Since: 1.10.0

Orphan instances

PIntegralDomain a => Num (Term s a) Source #
Instance details Methods (+) :: Term s a -> Term s a -> Term s a Source # (-) :: Term s a -> Term s a -> Term s a Source # (*) :: Term s a -> Term s a -> Term s a Source # negate :: Term s a -> Term s a Source # abs :: Term s a -> Term s a Source # signum :: Term s a -> Term s a Source # fromInteger :: Integer -> Term s a Source #