smart-math
Safe HaskellNone
LanguageHaskell2010

Numeric.Data.Positive.Internal

Description

Provides the Positive type for enforcing a positive invariant.

Since: 0.1

Synopsis

Type

newtype Positive a Source #

Newtype wrapper that attaches a Positive invariant to some a. Positive is an ASemigroup and MGroup i.e. supports addition, multiplication, and division.

Since: 0.1

Constructors

UnsafePositive a 

Bundled Patterns

pattern MkPositive :: a -> Positive a

Unidirectional pattern synonym for Positive. This allows us to pattern match on a positive term without exposing the unsafe internal details.

Since: 0.1

Instances

Instances details
Foldable Positive Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

fold :: Monoid m => Positive m -> m #

foldMap :: Monoid m => (a -> m) -> Positive a -> m #

foldMap' :: Monoid m => (a -> m) -> Positive a -> m #

foldr :: (a -> b -> b) -> b -> Positive a -> b #

foldr' :: (a -> b -> b) -> b -> Positive a -> b #

foldl :: (b -> a -> b) -> b -> Positive a -> b #

foldl' :: (b -> a -> b) -> b -> Positive a -> b #

foldr1 :: (a -> a -> a) -> Positive a -> a #

foldl1 :: (a -> a -> a) -> Positive a -> a #

toList :: Positive a -> [a] #

null :: Positive a -> Bool #

length :: Positive a -> Int #

elem :: Eq a => a -> Positive a -> Bool #

maximum :: Ord a => Positive a -> a #

minimum :: Ord a => Positive a -> a #

sum :: Num a => Positive a -> a #

product :: Num a => Positive a -> a #

HasField "unPositive" (Positive a) a Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

getField :: Positive a -> a #

(k ~ A_Getter, x ~ a, y ~ a) => LabelOptic "unPositive" k (Positive a) (Positive a) x y Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

labelOptic :: Optic k NoIx (Positive a) (Positive a) x y Source #

Lift a => Lift (Positive a :: Type) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

lift :: Quote m => Positive a -> m Exp #

liftTyped :: forall (m :: Type -> Type). Quote m => Positive a -> Code m (Positive a) #

ASemigroup a => ASemigroup (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

(.+.) :: Positive a -> Positive a -> Positive a Source #

MetricSpace a => MetricSpace (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

diffR :: Positive a -> Positive a -> Double Source #

MEuclidean a => MEuclidean (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

mdivMod :: Positive a -> Positive a -> (Positive a, Positive a) Source #

MGroup a => MGroup (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

(.%.) :: Positive a -> Positive a -> Positive a Source #

MMonoid a => MMonoid (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

one :: Positive a Source #

MSemigroup a => MSemigroup (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

(.*.) :: Positive a -> Positive a -> Positive a Source #

Normed a => Normed (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

norm :: Positive a -> Positive a Source #

sgn :: Positive a -> Positive a Source #

(AMonoid a, FromInteger a, Ord a, Show a) => FromInteger (Positive a) Source #

WARNING: Partial

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

fromZ :: Integer -> Positive a Source #

(AMonoid a, FromRational a, Ord a, Show a) => FromRational (Positive a) Source #

WARNING: Partial

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

fromQ :: Rational -> Positive a Source #

(AMonoid a, FromReal a, Ord a, Show a) => FromReal (Positive a) Source #

WARNING: Partial

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

fromR :: Double -> Positive a Source #

ToInteger a => ToInteger (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

toZ :: Positive a -> Integer Source #

ToRational a => ToRational (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

toQ :: Positive a -> Rational Source #

ToReal a => ToReal (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

toR :: Positive a -> Double Source #

MaybeLowerBounded (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

maybeLowerBound :: Maybe (Positive a) Source #

MaybeUpperBounded a => MaybeUpperBounded (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

maybeUpperBound :: Maybe (Positive a) Source #

UpperBounded a => UpperBounded (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

upperBound :: Positive a Source #

UpperBoundless (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

NFData a => NFData (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

rnf :: Positive a -> () #

Generic (Positive a) Source # 
Instance details

Defined in Numeric.Data.Positive.Internal

Associated Types

type Rep (Positive a)

Since: smart-math-0.1

Instance details

Defined in Numeric.Data.Positive.Internal

type Rep (Positive a) = D1 ('MetaData "Positive" "Numeric.Data.Positive.Internal" "smart-math-0.1-inplace" 'True) (C1 ('MetaCons "UnsafePositive" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Positive a -> Rep (Positive a) x #

to :: Rep (Positive a) x -> Positive a #

Show a => Show (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

showsPrec :: Int -> Positive a -> ShowS #

show :: Positive a -> String #

showList :: [Positive a] -> ShowS #

Eq a => Eq (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

(==) :: Positive a -> Positive a -> Bool #

(/=) :: Positive a -> Positive a -> Bool #

Ord a => Ord (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

compare :: Positive a -> Positive a -> Ordering #

(<) :: Positive a -> Positive a -> Bool #

(<=) :: Positive a -> Positive a -> Bool #

(>) :: Positive a -> Positive a -> Bool #

(>=) :: Positive a -> Positive a -> Bool #

max :: Positive a -> Positive a -> Positive a #

min :: Positive a -> Positive a -> Positive a #

Hashable a => Hashable (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

hashWithSalt :: Int -> Positive a -> Int Source #

hash :: Positive a -> Int Source #

Show a => Display (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

Methods

displayBuilder :: Positive a -> Builder Source #

displayList :: [Positive a] -> Builder Source #

displayPrec :: Int -> Positive a -> Builder Source #

type Rep (Positive a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.Positive.Internal

type Rep (Positive a) = D1 ('MetaData "Positive" "Numeric.Data.Positive.Internal" "smart-math-0.1-inplace" 'True) (C1 ('MetaCons "UnsafePositive" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Creation

unsafePositive :: (AMonoid a, HasCallStack, Ord a, Show a) => a -> Positive a Source #

Throws an error when given a value <= 0.

WARNING: Partial

Examples

Expand
>>> unsafePositive 7
UnsafePositive 7

Since: 0.1

Misc

errMsg :: Show a => a -> String Source #

Since: 0.1