Safe Haskell	None
Language	Haskell2010

Numeric.Data.Positive

Contents

Type
Creation
Elimination
Functions
Optics

Description

Provides the Positive type for enforcing a positive invariant.

Since: 0.1

Synopsis

data Positive a where
- pattern MkPositive :: a -> Positive a
mkPositiveTH :: (AMonoid a, Lift a, Ord a, Show a) => a -> Code Q (Positive a)
mkPositive :: (AMonoid a, Ord a, Show a) => a -> Either String (Positive a)
unsafePositive :: (AMonoid a, HasCallStack, Ord a, Show a) => a -> Positive a
(+!) :: (AMonoid a, HasCallStack, Ord a, Show a) => a -> Positive a
reallyUnsafePositive :: a -> Positive a
unPositive :: Positive a -> a
positiveToNonZero :: Positive a -> NonZero (Positive a)
_MkPositive :: (AMonoid a, Ord a, Show a) => ReversedPrism' (Positive a) a
rmatching :: (Is (ReversedOptic k) An_AffineTraversal, ReversibleOptic k) => Optic k NoIx b a t s -> s -> Either t a

Type

data Positive a where 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

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

mkPositiveTH :: (AMonoid a, Lift a, Ord a, Show a) => a -> Code Q (Positive a) Source #

Template haskell for creating a Positive at compile-time.

Examples

Expand

>>> $$(mkPositiveTH 1)
UnsafePositive 1

Since: 0.1

mkPositive :: (AMonoid a, Ord a, Show a) => a -> Either String (Positive a) Source #

Smart constructor for Positive. Returns Nothing if the second parameter is <= 0.

Examples

Expand

>>> mkPositive 7
Right (UnsafePositive 7)

>>> mkPositive 0
Left "Numeric.Data.Positive: Received value <= zero: 0"

Since: 0.1

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

(+!) :: (AMonoid a, HasCallStack, Ord a, Show a) => a -> Positive a infixl 7 Source #

Postfix operator for unsafePositive.

WARNING: Partial

Examples

Expand

>>> (7 +!)
UnsafePositive 7

Since: 0.1

reallyUnsafePositive :: a -> Positive a Source #

This function is an alias for the unchecked constructor UnsafePositive i.e. it allows us to construct a Positive without checking the invariant. This is intended only for when we absolutely know the invariant holds and a branch (i.e. unsafePositive) is undesirable for performance reasons. Exercise extreme caution.

Since: 0.1

Elimination

unPositive :: Positive a -> a Source #

Since: 0.1

Functions

positiveToNonZero :: Positive a -> NonZero (Positive a) Source #

Convenience function for adding a NonZero proof to our Positive.

Examples

Expand

>>> positiveToNonZero $ unsafePositive 3
UnsafeNonZero (UnsafePositive 3)

Since: 0.1

Optics

We provide a ReversedPrism' _MkPositive that allows for total elimination and partial construction, along with a LabelOptic Getter for #unPositive.

Examples

Expand

>>> :set -XOverloadedLabels
>>> import Optics.Core (view)
>>> let n = $$(mkPositiveTH 2)
>>> view #unPositive n
2

_MkPositive :: (AMonoid a, Ord a, Show a) => ReversedPrism' (Positive a) a Source #

ReversedPrism' that enables total elimination and partial construction.

Examples

Expand

>>> import Optics.Core (view)
>>> pos = $$(mkPositiveTH 2)
>>> view _MkPositive pos
2

>>> rmatching _MkPositive 3
Right (UnsafePositive 3)

>>> rmatching _MkPositive 0
Left 0

Since: 0.1

rmatching :: (Is (ReversedOptic k) An_AffineTraversal, ReversibleOptic k) => Optic k NoIx b a t s -> s -> Either t a Source #

Reversed matching. Useful with smart-constructor optics.

Since: 0.1