smart-math
Safe HaskellNone
LanguageHaskell2010

Numeric.Data.NonZero

Description

Provides the NonZero type for enforcing a non-zero invariant.

Since: 0.1

Synopsis

Type

data NonZero a where Source #

Smart-constructor for creating a "non-zero" a.

Since: 0.1

Bundled Patterns

pattern MkNonZero :: a -> NonZero a

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

Since: 0.1

Instances

Instances details
Foldable NonZero Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

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

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

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

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

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

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

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

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

toList :: NonZero a -> [a] #

null :: NonZero a -> Bool #

length :: NonZero a -> Int #

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

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

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

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

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

HasField "unNonZero" (NonZero a) a Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

getField :: NonZero a -> a #

(k ~ A_Getter, x ~ a, y ~ a) => LabelOptic "unNonZero" k (NonZero a) (NonZero a) x y Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

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

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

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

MetricSpace a => MetricSpace (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

MEuclidean a => MEuclidean (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

MGroup a => MGroup (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

MMonoid a => MMonoid (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

one :: NonZero a Source #

MSemigroup a => MSemigroup (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

Normed a => Normed (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

norm :: NonZero a -> NonZero a Source #

sgn :: NonZero a -> NonZero a Source #

(AMonoid a, Eq a, FromInteger a) => FromInteger (NonZero a) Source #

WARNING: Partial

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

fromZ :: Integer -> NonZero a Source #

(AMonoid a, Eq a, FromRational a) => FromRational (NonZero a) Source #

WARNING: Partial

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

fromQ :: Rational -> NonZero a Source #

(AMonoid a, Eq a, FromReal a) => FromReal (NonZero a) Source #

WARNING: Partial

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

fromR :: Double -> NonZero a Source #

ToInteger a => ToInteger (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

toZ :: NonZero a -> Integer Source #

ToRational a => ToRational (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

toQ :: NonZero a -> Rational Source #

ToReal a => ToReal (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

toR :: NonZero a -> Double Source #

NFData a => NFData (NonZero a) Source #

Since: 0.1.0.0

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

rnf :: NonZero a -> () #

Generic (NonZero a) Source # 
Instance details

Defined in Numeric.Data.NonZero.Internal

Associated Types

type Rep (NonZero a)

Since: smart-math-0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

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

Methods

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

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

Show a => Show (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

show :: NonZero a -> String #

showList :: [NonZero a] -> ShowS #

Eq a => Eq (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

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

Ord a => Ord (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

compare :: NonZero a -> NonZero a -> Ordering #

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

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

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

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

max :: NonZero a -> NonZero a -> NonZero a #

min :: NonZero a -> NonZero a -> NonZero a #

Hashable a => Hashable (NonZero a) Source #

Since: 0.1.0.0

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

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

hash :: NonZero a -> Int Source #

Show a => Display (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

Methods

displayBuilder :: NonZero a -> Builder Source #

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

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

type Rep (NonZero a) Source #

Since: 0.1

Instance details

Defined in Numeric.Data.NonZero.Internal

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

Creation

mkNonZero :: (AMonoid a, Eq a) => a -> Either String (NonZero a) Source #

Smart constructor for NonZero.

Examples

Expand
>>> mkNonZero 7
Right (UnsafeNonZero 7)

>>> mkNonZero 0
Left "Numeric.Data.NonZero: Received zero"

Since: 0.1

mkNonZeroTH :: (AMonoid a, Eq a, Lift a) => a -> Code Q (NonZero a) Source #

Template-haskell version of mkNonZero for creating NonZero at compile-time.

Examples

Expand
>>> $$(mkNonZeroTH 7)
UnsafeNonZero 7

Since: 0.1

unsafeNonZero :: (AMonoid a, Eq a, HasCallStack) => a -> NonZero a Source #

Throws an error when given 0.

WARNING: Partial

Examples

Expand
>>> unsafeNonZero 7
UnsafeNonZero 7

Since: 0.1

reallyUnsafeNonZero :: a -> NonZero a Source #

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

Since: 0.1

Elimination

unNonZero :: NonZero a -> a Source #

Since: 0.1

Optics

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

Examples

Expand
>>> :set -XOverloadedLabels
>>> import Optics.Core (view)
>>> let n = $$(mkNonZeroTH 7)
>>> view #unNonZero n
7

_MkNonZero :: (AMonoid a, Eq a) => ReversedPrism' (NonZero a) a Source #

ReversedPrism' that enables total elimination and partial construction.

Examples

Expand
>>> import Optics.Core (view)
>>> nz = $$(mkNonZeroTH 7)
>>> view _MkNonZero nz
7

>>> rmatching _MkNonZero 3
Right (UnsafeNonZero 3)

>>> rmatching _MkNonZero 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