dimensional-1.3: Statically checked physical dimensions, using Type Families and Data Kinds.

CopyrightCopyright (C) 2006-2018 Bjorn Buckwalter
LicenseBSD3
Maintainerbjorn@buckwalter.se
StabilityStable
PortabilityGHC only
Safe HaskellNone
LanguageHaskell2010

Numeric.Units.Dimensional.Prelude

Description

Summary

This module supplies a convenient set of imports for working with the dimensional package, including aliases for common Quantitys and Dimensions, and a comprehensive set of SI units and units accepted for use with the SI.

It re-exports the Prelude, hiding arithmetic functions whose names collide with the dimensionally-typed versions supplied by this package.

Synopsis

Documentation

class HasDynamicDimension a => HasDimension a where Source #

Dimensional values inhabit this class, which allows access to a term-level representation of their dimension.

Methods

dimension :: a -> Dimension' Source #

Obtains a term-level representation of a value's dimension.

data Dimension' Source #

A physical dimension, encoded as 7 integers, representing a factorization of the dimension into the 7 SI base dimensions. By convention they are stored in the same order as in the Dimension data kind.

Constructors

Dim' !Int !Int !Int !Int !Int !Int !Int 
Instances
Eq Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Data Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dimension' -> c Dimension' #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Dimension' #

toConstr :: Dimension' -> Constr #

dataTypeOf :: Dimension' -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Dimension') #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Dimension') #

gmapT :: (forall b. Data b => b -> b) -> Dimension' -> Dimension' #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dimension' -> r #

gmapQ :: (forall d. Data d => d -> u) -> Dimension' -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dimension' -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension' -> m Dimension' #

Ord Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Show Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Generic Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Associated Types

type Rep Dimension' :: Type -> Type #

Semigroup Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Monoid Dimension' Source #

The monoid of dimensions under multiplication.

Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

NFData Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

rnf :: Dimension' -> () #

HasDimension Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

HasDynamicDimension Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

type Rep Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

type KnownDimension (d :: Dimension) = HasDimension (Proxy d) Source #

A KnownDimension is one for which we can construct a term-level representation. Each validly constructed type of kind Dimension has a KnownDimension instance.

While KnownDimension is a constraint synonym, the presence of KnownDimension d in a context allows use of dimension :: Proxy d -> Dimension'.

type Cbrt d = NRoot d Pos3 Source #

Cube root is a special case of NRoot with order 3.

type Sqrt d = NRoot d Pos2 Source #

Square root is a special case of NRoot with order 2.

type family NRoot (d :: Dimension) (x :: TypeInt) where ... Source #

Roots of dimensions corresponds to division of the base dimensions' exponents by the order of the root.

Equations

NRoot DOne x = DOne 
NRoot d Pos1 = d 
NRoot (Dim l m t i th n j) x = Dim (l / x) (m / x) (t / x) (i / x) (th / x) (n / x) (j / x) 

type family (d :: Dimension) ^ (x :: TypeInt) where ... infixr 8 Source #

Powers of dimensions corresponds to multiplication of the base dimensions' exponents by the exponent.

We limit ourselves to integer powers of Dimensionals as fractional powers make little physical sense.

Equations

DOne ^ x = DOne 
d ^ Zero = DOne 
d ^ Pos1 = d 
(Dim l m t i th n j) ^ x = Dim (l * x) (m * x) (t * x) (i * x) (th * x) (n * x) (j * x) 

type Recip (d :: Dimension) = DOne / d Source #

The reciprocal of a dimension is defined as the result of dividing DOne by it, or of negating each of the base dimensions' exponents.

type family (a :: Dimension) / (d :: Dimension) where ... infixl 7 Source #

Division of dimensions corresponds to subtraction of the base dimensions' exponents.

Equations

d / DOne = d 
d / d = DOne 
(Dim l m t i th n j) / (Dim l' m' t' i' th' n' j') = Dim (l - l') (m - m') (t - t') (i - i') (th - th') (n - n') (j - j') 

type family (a :: Dimension) * (b :: Dimension) where ... infixl 7 Source #

Multiplication of dimensions corresponds to adding of the base dimensions' exponents.

Equations

DOne * d = d 
d * DOne = d 
(Dim l m t i th n j) * (Dim l' m' t' i' th' n' j') = Dim (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j') 

type DOne = Dim Zero Zero Zero Zero Zero Zero Zero Source #

The type-level dimension of dimensionless values.

data Dimension Source #

Represents a physical dimension in the basis of the 7 SI base dimensions, where the respective dimensions are represented by type variables using the following convention:

  • l: Length
  • m: Mass
  • t: Time
  • i: Electric current
  • th: Thermodynamic temperature
  • n: Amount of substance
  • j: Luminous intensity

For the equivalent term-level representation, see Dimension'

data Metricality Source #

Encodes whether a unit is a metric unit, that is, whether it can be combined with a metric prefix to form a related unit.

Constructors

Metric

Capable of receiving a metric prefix.

NonMetric

Incapable of receiving a metric prefix.

Instances
Eq Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

Data Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Metricality -> c Metricality #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Metricality #

toConstr :: Metricality -> Constr #

dataTypeOf :: Metricality -> DataType #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Metricality) #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Metricality) #

gmapT :: (forall b. Data b => b -> b) -> Metricality -> Metricality #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Metricality -> r #

gmapQ :: (forall d. Data d => d -> u) -> Metricality -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Metricality -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Metricality -> m Metricality #

Ord Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

Generic Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

Associated Types

type Rep Metricality :: Type -> Type #

NFData Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

Methods

rnf :: Metricality -> () #

type Rep Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

type Rep Metricality = D1 (MetaData "Metricality" "Numeric.Units.Dimensional.Variants" "dimensional-1.3-7Gh1mp5ZBGaGfkDr7lUYf2" False) (C1 (MetaCons "Metric" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "NonMetric" PrefixI False) (U1 :: Type -> Type))

class KnownVariant (v :: Variant) Source #

A KnownVariant is one whose term-level Dimensional values we can represent with an associated data family instance and manipulate with certain functions, not all of which are exported from the package.

Each validly constructed type of kind Variant has a KnownVariant instance.

Minimal complete definition

extractValue, extractName, injectValue, dmap

Associated Types

data Dimensional v :: Dimension -> Type -> Type Source #

A dimensional value, either a Quantity or a Unit, parameterized by its Dimension and representation.

Instances
KnownVariant (DQuantity s) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Internal

Associated Types

data Dimensional (DQuantity s) a b :: Type Source #

type ScaleFactor (DQuantity s) :: ExactPi'

Typeable m => KnownVariant (DUnit m) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Internal

Associated Types

data Dimensional (DUnit m) a b :: Type Source #

type ScaleFactor (DUnit m) :: ExactPi'

type Quantity = SQuantity One Source #

A dimensional quantity.

type Unit (m :: Metricality) = Dimensional (DUnit m) Source #

A unit of measurement.

siUnit :: forall d a. (KnownDimension d, Num a) => Unit NonMetric d a Source #

A polymorphic Unit which can be used in place of the coherent SI base unit of any dimension. This allows polymorphic quantity creation and destruction without exposing the Dimensional constructor.

showIn :: (Show a, Fractional a) => Unit m d a -> Quantity d a -> String Source #

Shows the value of a Quantity expressed in a specified Unit of the same Dimension.

Uses non-breaking spaces between the value and the unit, and within the unit name.

>>> putStrLn $ showIn watt $ (37 *~ volt) * (4 *~ ampere)
148.0 W

name :: Unit m d a -> UnitName m Source #

Extracts the UnitName of a Unit.

exactValue :: Unit m d a -> ExactPi Source #

Extracts the exact value of a Unit, expressed in terms of the SI coherent derived unit (see siUnit) of the same Dimension.

Note that the actual value may in some cases be approximate, for example if the unit is defined by experiment.

weaken :: Unit m d a -> Unit NonMetric d a Source #

Discards potentially unwanted type level information about a Unit.

strengthen :: Unit m d a -> Maybe (Unit Metric d a) Source #

Attempts to convert a Unit which may or may not be Metric to one which is certainly Metric.

exactify :: Unit m d a -> Unit m d ExactPi Source #

Forms the exact version of a Unit.

(*~) :: Num a => a -> Unit m d a -> Quantity d a infixl 7 Source #

Forms a Quantity by multipliying a number and a unit.

(/~) :: Fractional a => Quantity d a -> Unit m d a -> a infixl 7 Source #

Divides a Quantity by a Unit of the same physical dimension, obtaining the numerical value of the quantity expressed in that unit.

(*) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 * v2), Num a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 * v2) (d1 * d2) a infixl 7 Source #

Multiplies two Quantitys or two Units.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NonMetric.

(/) :: (KnownVariant v1, KnownVariant v2, KnownVariant (v1 / v2), Fractional a) => Dimensional v1 d1 a -> Dimensional v2 d2 a -> Dimensional (v1 / v2) (d1 / d2) a infixl 7 Source #

Divides one Quantity by another or one Unit by another.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NotPrefixable.

recip :: Fractional a => Quantity d a -> Quantity (Recip d) a Source #

Forms the reciprocal of a Quantity, which has the reciprocal dimension.

>>> recip $ 47 *~ hertz
2.127659574468085e-2 s

(^) :: (Fractional a, KnownTypeInt i, KnownVariant v, KnownVariant (Weaken v)) => Dimensional v d1 a -> Proxy i -> Dimensional (Weaken v) (d1 ^ i) a infixr 8 Source #

Raises a Quantity or Unit to an integer power.

Because the power chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the exponent in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

The intimidating type signature captures the similarity between these operations and ensures that composite Units are NotPrefixable.

negate :: Num a => Quantity d a -> Quantity d a Source #

Negates the value of a Quantity.

(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #

Adds two Quantitys.

(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a infixl 6 Source #

Subtracts one Quantity from another.

abs :: Num a => Quantity d a -> Quantity d a Source #

Takes the absolute value of a Quantity.

signum :: Num a => Quantity d a -> Dimensionless a Source #

Takes the sign of a Quantity. The functions abs and signum satisy the law that:

abs x * signum x == x

The sign is either negate _1 (negative), _0 (zero), or _1 (positive).

nroot :: (KnownTypeInt n, Floating a) => Proxy n -> Quantity d a -> Quantity (NRoot d n) a Source #

Computes the nth root of a Quantity using **.

The NRoot type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.

Because the root chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the root in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

n must not be zero. Negative roots are defined such that nroot (Proxy :: Proxy (Negate n)) x == nroot (Proxy :: Proxy n) (recip x).

Also available in operator form, see ^/.

sqrt :: Floating a => Quantity d a -> Quantity (Sqrt d) a Source #

Computes the square root of a Quantity using **.

The NRoot type family will prevent application where the supplied quantity does not have a square dimension.

(x :: Area Double) >= _0 ==> sqrt x == nroot pos2 x

cbrt :: Floating a => Quantity d a -> Quantity (Cbrt d) a Source #

Computes the cube root of a Quantity using **.

The NRoot type family will prevent application where the supplied quantity does not have a cubic dimension.

(x :: Volume Double) >= _0 ==> cbrt x == nroot pos3 x

(^/) :: (KnownTypeInt n, Floating a) => Quantity d a -> Proxy n -> Quantity (NRoot d n) a infixr 8 Source #

Computes the nth root of a Quantity using **.

The NRoot type family will prevent application of this operator where the result would have a fractional dimension or where n is zero.

Because the root chosen impacts the Dimension of the result, it is necessary to supply a type-level representation of the root in the form of a Proxy to some TypeInt. Convenience values pos1, pos2, neg1, ... are supplied by the Numeric.NumType.DK.Integers module. The most commonly used ones are also reexported by Numeric.Units.Dimensional.Prelude.

Also available in prefix form, see nroot.

(*~~) :: (Functor f, Num a) => f a -> Unit m d a -> f (Quantity d a) infixl 7 Source #

Applies *~ to all values in a functor.

(/~~) :: forall f m d a. (Functor f, Fractional a) => f (Quantity d a) -> Unit m d a -> f a infixl 7 Source #

Applies /~ to all values in a functor.

sum :: (Num a, Foldable f) => f (Quantity d a) -> Quantity d a Source #

The sum of all elements in a foldable structure.

>>> sum ([] :: [Mass Double])
0.0 kg
>>> sum [12.4 *~ meter, 1 *~ foot]
12.7048 m

product :: (Num a, Foldable f) => f (Dimensionless a) -> Dimensionless a Source #

The product of all elements in a foldable structure.

>>> product ([] :: [Dimensionless Double])
1.0
>>> product [pi, _4, 0.36 *~ one]
4.523893421169302

mean :: (Fractional a, Foldable f) => f (Quantity d a) -> Quantity d a Source #

The arithmetic mean of all elements in a foldable structure.

>>> mean [pi, _7]
5.070796326794897

dimensionlessLength :: (Num a, Foldable f) => f b -> Dimensionless a Source #

The length of the foldable data structure as a Dimensionless. This can be useful for purposes of e.g. calculating averages.

>>> dimensionlessLength ["foo", "bar"]
2

nFromTo Source #

Arguments

:: (Fractional a, Integral b) 
=> Quantity d a

The initial value.

-> Quantity d a

The final value.

-> b

The number of intermediate values. If less than one, no intermediate values will result.

-> [Quantity d a] 

Returns a list of quantities between given bounds.

n <= 0 ==> nFromTo (x :: Mass Double) (y :: Mass Double) n == [x, y]
(x :: Length Double) <= (y :: Length Double) ==> all (\z -> x <= z && z <= y) (nFromTo x y n)
>>> nFromTo _0 _3 2
[0.0,1.0,2.0,3.0]
>>> nFromTo _1 _0 7
[1.0,0.875,0.75,0.625,0.5,0.375,0.25,0.125,0.0]
>>> nFromTo _0 _1 (-5)
[0.0,1.0]

(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a infixr 8 Source #

Raises a dimensionless quantity to a dimensionless power.

logBase :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a Source #

Takes the logarithm of the second argument in the base of the first.

>>> logBase _2 _8
3.0

atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a Source #

The standard two argument arctangent function. Since it interprets its two arguments in comparison with one another, the input may have any dimension.

>>> atan2 _0 _1
0.0
>>> atan2 _1 _0
1.5707963267948966
>>> atan2 _0 (negate _1)
3.141592653589793
>>> atan2 (negate _1) _0
-1.5707963267948966

one :: Num a => Unit NonMetric DOne a Source #

The unit one has dimension DOne and is the base unit of dimensionless values.

As detailed in 7.10 "Values of quantities expressed simply as numbers: the unit one, symbol 1" of [1] the unit one generally does not appear in expressions. However, for us it is necessary to use one as we would any other unit to perform the "boxing" of dimensionless values.

_0 :: Num a => Quantity d a Source #

The constant for zero is polymorphic, allowing it to express zero Length or Capacitance or Velocity etc, in addition to the Dimensionless value zero.

tau :: Floating a => Dimensionless a Source #

Twice pi.

For background on tau see http://tauday.com/tau-manifesto (but also feel free to review http://www.thepimanifesto.com).

changeRep :: (KnownVariant v, Real a, Fractional b) => Dimensional v d a -> Dimensional v d b Source #

Convenient conversion between numerical types while retaining dimensional information.

>>> let x = (37 :: Rational) *~ poundMass
>>> changeRep x :: Mass Double
16.78291769 kg

changeRepApproximate :: (KnownVariant v, Floating b) => Dimensional v d ExactPi -> Dimensional v d b Source #

Convenient conversion from exactly represented values while retaining dimensional information.

asLens :: Fractional a => Unit m d a -> forall f. Functor f => (a -> f a) -> Quantity d a -> f (Quantity d a) Source #

Converts a Unit into a lens from Quantitys to values.

mkUnitR :: Floating a => UnitName m -> ExactPi -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is irrational or Approximate. See mkUnitQ for when it is rational and mkUnitZ for when it is an integer.

Note that supplying zero as a definining quantity is invalid, as the library relies upon units forming a group under multiplication.

Supplying negative defining quantities is allowed and handled gracefully, but is discouraged on the grounds that it may be unexpected by other readers.

mkUnitQ :: Fractional a => UnitName m -> Rational -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is rational. See mkUnitZ for when it is an integer and mkUnitR for the general case.

For more information see mkUnitR.

mkUnitZ :: Num a => UnitName m -> Integer -> Unit m1 d a -> Unit m d a Source #

Forms a new atomic Unit by specifying its UnitName and its definition as a multiple of another Unit.

Use this variant when the scale factor of the resulting unit is an integer. See mkUnitQ for when it is rational and mkUnitR for the general case.

For more information see mkUnitR.

class Category (cat :: k -> k -> Type) where #

A class for categories. Instances should satisfy the laws

f . id  =  f  -- (right identity)
id . f  =  f  -- (left identity)
f . (g . h)  =  (f . g) . h  -- (associativity)

Methods

id :: cat a a #

the identity morphism

(.) :: cat b c -> cat a b -> cat a c infixr 9 #

morphism composition

Instances
Category (Coercion :: k -> k -> Type)

Since: base-4.7.0.0

Instance details

Defined in Control.Category

Methods

id :: Coercion a a #

(.) :: Coercion b c -> Coercion a b -> Coercion a c #

Category ((:~:) :: k -> k -> Type)

Since: base-4.7.0.0

Instance details

Defined in Control.Category

Methods

id :: a :~: a #

(.) :: (b :~: c) -> (a :~: b) -> a :~: c #

Category ((:~~:) :: k -> k -> Type)

Since: base-4.10.0.0

Instance details

Defined in Control.Category

Methods

id :: a :~~: a #

(.) :: (b :~~: c) -> (a :~~: b) -> a :~~: c #

Category ((->) :: Type -> Type -> Type)

Since: base-3.0

Instance details

Defined in Control.Category

Methods

id :: a -> a #

(.) :: (b -> c) -> (a -> b) -> a -> c #

maximum :: (Foldable t, Ord a) => t a -> a #

The largest element of a non-empty structure.

minimum :: (Foldable t, Ord a) => t a -> a #

The least element of a non-empty structure.

(++) :: [a] -> [a] -> [a] infixr 5 #

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

seq :: a -> b -> b #

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

filter :: (a -> Bool) -> [a] -> [a] #

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

zip :: [a] -> [b] -> [(a, b)] #

zip takes two lists and returns a list of corresponding pairs.

zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

print :: Show a => a -> IO () #

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

main = print ([(n, 2^n) | n <- [0..19]])

fst :: (a, b) -> a #

Extract the first component of a pair.

snd :: (a, b) -> b #

Extract the second component of a pair.

otherwise :: Bool #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

map :: (a -> b) -> [a] -> [b] #

map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

($) :: (a -> b) -> a -> b infixr 0 #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b #

general coercion to fractional types

class Bounded a where #

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

Methods

minBound :: a #

maxBound :: a #

Instances
Bounded Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Char

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: Int #

maxBound :: Int #

Bounded Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Bounded Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Word

Since: base-2.1

Instance details

Defined in GHC.Enum

Bounded Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Bounded VecCount

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Bounded VecElem

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Bounded ()

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: () #

maxBound :: () #

Bounded All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: All #

maxBound :: All #

Bounded Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Any #

maxBound :: Any #

Bounded Associativity

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Bounded CChar 
Instance details

Defined in Foreign.C.Types

Bounded CSChar 
Instance details

Defined in Foreign.C.Types

Bounded CUChar 
Instance details

Defined in Foreign.C.Types

Bounded CShort 
Instance details

Defined in Foreign.C.Types

Bounded CUShort 
Instance details

Defined in Foreign.C.Types

Bounded CInt 
Instance details

Defined in Foreign.C.Types

Bounded CUInt 
Instance details

Defined in Foreign.C.Types

Bounded CLong 
Instance details

Defined in Foreign.C.Types

Bounded CULong 
Instance details

Defined in Foreign.C.Types

Bounded CLLong 
Instance details

Defined in Foreign.C.Types

Bounded CULLong 
Instance details

Defined in Foreign.C.Types

Bounded CBool 
Instance details

Defined in Foreign.C.Types

Bounded CPtrdiff 
Instance details

Defined in Foreign.C.Types

Bounded CSize 
Instance details

Defined in Foreign.C.Types

Bounded CWchar 
Instance details

Defined in Foreign.C.Types

Bounded CSigAtomic 
Instance details

Defined in Foreign.C.Types

Bounded CIntPtr 
Instance details

Defined in Foreign.C.Types

Bounded CUIntPtr 
Instance details

Defined in Foreign.C.Types

Bounded CIntMax 
Instance details

Defined in Foreign.C.Types

Bounded CUIntMax 
Instance details

Defined in Foreign.C.Types

Bounded WordPtr 
Instance details

Defined in Foreign.Ptr

Bounded IntPtr 
Instance details

Defined in Foreign.Ptr

Bounded a => Bounded (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Min a #

maxBound :: Min a #

Bounded a => Bounded (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Max a #

maxBound :: Max a #

Bounded a => Bounded (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: First a #

maxBound :: First a #

Bounded a => Bounded (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

minBound :: Last a #

maxBound :: Last a #

Bounded m => Bounded (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Bounded a => Bounded (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a #

maxBound :: Dual a #

Bounded a => Bounded (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a #

maxBound :: Sum a #

Bounded a => Bounded (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

(Bounded a, Bounded b) => Bounded (a, b)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b) #

maxBound :: (a, b) #

Bounded (Proxy t)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

minBound :: Proxy t #

maxBound :: Proxy t #

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c) #

maxBound :: (a, b, c) #

Bounded a => Bounded (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

minBound :: Const a b #

maxBound :: Const a b #

(Applicative f, Bounded a) => Bounded (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

minBound :: Ap f a #

maxBound :: Ap f a #

Coercible a b => Bounded (Coercion a b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Methods

minBound :: Coercion a b #

maxBound :: Coercion a b #

a ~ b => Bounded (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

minBound :: a :~: b #

maxBound :: a :~: b #

Bounded a => Bounded (SQuantity s d a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Internal

Methods

minBound :: SQuantity s d a #

maxBound :: SQuantity s d a #

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d) #

maxBound :: (a, b, c, d) #

a ~~ b => Bounded (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

minBound :: a :~~: b #

maxBound :: a :~~: b #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e) #

maxBound :: (a, b, c, d, e) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f) #

maxBound :: (a, b, c, d, e, f) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g) #

maxBound :: (a, b, c, d, e, f, g) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h) #

maxBound :: (a, b, c, d, e, f, g, h) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i) #

maxBound :: (a, b, c, d, e, f, g, h, i) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j) #

maxBound :: (a, b, c, d, e, f, g, h, i, j) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Enum a where #

Class Enum defines operations on sequentially ordered types.

The enumFrom... methods are used in Haskell's translation of arithmetic sequences.

Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class Bounded as well as Enum, the following should hold:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a #

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a #

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a #

Convert from an Int.

fromEnum :: a -> Int #

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

enumFrom :: a -> [a] #

Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example:

  • enumFrom 4 :: [Integer] = [4,5,6,7,...]
  • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

enumFromThen :: a -> a -> [a] #

Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y For example:

  • enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
  • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

enumFromTo :: a -> a -> [a] #

Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For example:

  • enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
  • enumFromTo 42 1 :: [Integer] = []

enumFromThenTo :: a -> a -> a -> [a] #

Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y and worker s c v m | c v m = v : worker s c (s v) m | otherwise = [] For example:

  • enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
  • enumFromThenTo 6 8 2 :: [Int] = []
Instances
Enum Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Bool -> Bool #

pred :: Bool -> Bool #

toEnum :: Int -> Bool #

fromEnum :: Bool -> Int #

enumFrom :: Bool -> [Bool] #

enumFromThen :: Bool -> Bool -> [Bool] #

enumFromTo :: Bool -> Bool -> [Bool] #

enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #

Enum Char

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Char -> Char #

pred :: Char -> Char #

toEnum :: Int -> Char #

fromEnum :: Char -> Int #

enumFrom :: Char -> [Char] #

enumFromThen :: Char -> Char -> [Char] #

enumFromTo :: Char -> Char -> [Char] #

enumFromThenTo :: Char -> Char -> Char -> [Char] #

Enum Int

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Enum Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

succ :: Int8 -> Int8 #

pred :: Int8 -> Int8 #

toEnum :: Int -> Int8 #

fromEnum :: Int8 -> Int #

enumFrom :: Int8 -> [Int8] #

enumFromThen :: Int8 -> Int8 -> [Int8] #

enumFromTo :: Int8 -> Int8 -> [Int8] #

enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #

Enum Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Enum Integer

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Enum

Enum Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Word

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Word -> Word #

pred :: Word -> Word #

toEnum :: Int -> Word #

fromEnum :: Word -> Int #

enumFrom :: Word -> [Word] #

enumFromThen :: Word -> Word -> [Word] #

enumFromTo :: Word -> Word -> [Word] #

enumFromThenTo :: Word -> Word -> Word -> [Word] #

Enum Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Enum VecCount

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Enum VecElem

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Enum ()

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: () -> () #

pred :: () -> () #

toEnum :: Int -> () #

fromEnum :: () -> Int #

enumFrom :: () -> [()] #

enumFromThen :: () -> () -> [()] #

enumFromTo :: () -> () -> [()] #

enumFromThenTo :: () -> () -> () -> [()] #

Enum Associativity

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Enum CChar 
Instance details

Defined in Foreign.C.Types

Enum CSChar 
Instance details

Defined in Foreign.C.Types

Enum CUChar 
Instance details

Defined in Foreign.C.Types

Enum CShort 
Instance details

Defined in Foreign.C.Types

Enum CUShort 
Instance details

Defined in Foreign.C.Types

Enum CInt 
Instance details

Defined in Foreign.C.Types

Methods

succ :: CInt -> CInt #

pred :: CInt -> CInt #

toEnum :: Int -> CInt #

fromEnum :: CInt -> Int #

enumFrom :: CInt -> [CInt] #

enumFromThen :: CInt -> CInt -> [CInt] #

enumFromTo :: CInt -> CInt -> [CInt] #

enumFromThenTo :: CInt -> CInt -> CInt -> [CInt] #

Enum CUInt 
Instance details

Defined in Foreign.C.Types

Enum CLong 
Instance details

Defined in Foreign.C.Types

Enum CULong 
Instance details

Defined in Foreign.C.Types

Enum CLLong 
Instance details

Defined in Foreign.C.Types

Enum CULLong 
Instance details

Defined in Foreign.C.Types

Enum CBool 
Instance details

Defined in Foreign.C.Types

Enum CFloat 
Instance details

Defined in Foreign.C.Types

Enum CDouble 
Instance details

Defined in Foreign.C.Types

Enum CPtrdiff 
Instance details

Defined in Foreign.C.Types

Enum CSize 
Instance details

Defined in Foreign.C.Types

Enum CWchar 
Instance details

Defined in Foreign.C.Types

Enum CSigAtomic 
Instance details

Defined in Foreign.C.Types

Enum CClock 
Instance details

Defined in Foreign.C.Types

Enum CTime 
Instance details

Defined in Foreign.C.Types

Enum CUSeconds 
Instance details

Defined in Foreign.C.Types

Enum CSUSeconds 
Instance details

Defined in Foreign.C.Types

Enum CIntPtr 
Instance details

Defined in Foreign.C.Types

Enum CUIntPtr 
Instance details

Defined in Foreign.C.Types

Enum CIntMax 
Instance details

Defined in Foreign.C.Types

Enum CUIntMax 
Instance details

Defined in Foreign.C.Types

Enum WordPtr 
Instance details

Defined in Foreign.Ptr

Enum IntPtr 
Instance details

Defined in Foreign.Ptr

Integral a => Enum (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a #

pred :: Ratio a -> Ratio a #

toEnum :: Int -> Ratio a #

fromEnum :: Ratio a -> Int #

enumFrom :: Ratio a -> [Ratio a] #

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #

Enum (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

succ :: Fixed a -> Fixed a #

pred :: Fixed a -> Fixed a #

toEnum :: Int -> Fixed a #

fromEnum :: Fixed a -> Int #

enumFrom :: Fixed a -> [Fixed a] #

enumFromThen :: Fixed a -> Fixed a -> [Fixed a] #

enumFromTo :: Fixed a -> Fixed a -> [Fixed a] #

enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] #

Enum a => Enum (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Min a -> Min a #

pred :: Min a -> Min a #

toEnum :: Int -> Min a #

fromEnum :: Min a -> Int #

enumFrom :: Min a -> [Min a] #

enumFromThen :: Min a -> Min a -> [Min a] #

enumFromTo :: Min a -> Min a -> [Min a] #

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #

Enum a => Enum (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Max a -> Max a #

pred :: Max a -> Max a #

toEnum :: Int -> Max a #

fromEnum :: Max a -> Int #

enumFrom :: Max a -> [Max a] #

enumFromThen :: Max a -> Max a -> [Max a] #

enumFromTo :: Max a -> Max a -> [Max a] #

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #

Enum a => Enum (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: First a -> First a #

pred :: First a -> First a #

toEnum :: Int -> First a #

fromEnum :: First a -> Int #

enumFrom :: First a -> [First a] #

enumFromThen :: First a -> First a -> [First a] #

enumFromTo :: First a -> First a -> [First a] #

enumFromThenTo :: First a -> First a -> First a -> [First a] #

Enum a => Enum (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

succ :: Last a -> Last a #

pred :: Last a -> Last a #

toEnum :: Int -> Last a #

fromEnum :: Last a -> Int #

enumFrom :: Last a -> [Last a] #

enumFromThen :: Last a -> Last a -> [Last a] #

enumFromTo :: Last a -> Last a -> [Last a] #

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #

Enum a => Enum (WrappedMonoid a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Enum (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

succ :: Proxy s -> Proxy s #

pred :: Proxy s -> Proxy s #

toEnum :: Int -> Proxy s #

fromEnum :: Proxy s -> Int #

enumFrom :: Proxy s -> [Proxy s] #

enumFromThen :: Proxy s -> Proxy s -> [Proxy s] #

enumFromTo :: Proxy s -> Proxy s -> [Proxy s] #

enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] #

Enum a => Enum (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

succ :: Const a b -> Const a b #

pred :: Const a b -> Const a b #

toEnum :: Int -> Const a b #

fromEnum :: Const a b -> Int #

enumFrom :: Const a b -> [Const a b] #

enumFromThen :: Const a b -> Const a b -> [Const a b] #

enumFromTo :: Const a b -> Const a b -> [Const a b] #

enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #

Enum (f a) => Enum (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

succ :: Ap f a -> Ap f a #

pred :: Ap f a -> Ap f a #

toEnum :: Int -> Ap f a #

fromEnum :: Ap f a -> Int #

enumFrom :: Ap f a -> [Ap f a] #

enumFromThen :: Ap f a -> Ap f a -> [Ap f a] #

enumFromTo :: Ap f a -> Ap f a -> [Ap f a] #

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] #

Enum (f a) => Enum (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a #

pred :: Alt f a -> Alt f a #

toEnum :: Int -> Alt f a #

fromEnum :: Alt f a -> Int #

enumFrom :: Alt f a -> [Alt f a] #

enumFromThen :: Alt f a -> Alt f a -> [Alt f a] #

enumFromTo :: Alt f a -> Alt f a -> [Alt f a] #

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] #

Coercible a b => Enum (Coercion a b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Methods

succ :: Coercion a b -> Coercion a b #

pred :: Coercion a b -> Coercion a b #

toEnum :: Int -> Coercion a b #

fromEnum :: Coercion a b -> Int #

enumFrom :: Coercion a b -> [Coercion a b] #

enumFromThen :: Coercion a b -> Coercion a b -> [Coercion a b] #

enumFromTo :: Coercion a b -> Coercion a b -> [Coercion a b] #

enumFromThenTo :: Coercion a b -> Coercion a b -> Coercion a b -> [Coercion a b] #

a ~ b => Enum (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

succ :: (a :~: b) -> a :~: b #

pred :: (a :~: b) -> a :~: b #

toEnum :: Int -> a :~: b #

fromEnum :: (a :~: b) -> Int #

enumFrom :: (a :~: b) -> [a :~: b] #

enumFromThen :: (a :~: b) -> (a :~: b) -> [a :~: b] #

enumFromTo :: (a :~: b) -> (a :~: b) -> [a :~: b] #

enumFromThenTo :: (a :~: b) -> (a :~: b) -> (a :~: b) -> [a :~: b] #

a ~~ b => Enum (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

succ :: (a :~~: b) -> a :~~: b #

pred :: (a :~~: b) -> a :~~: b #

toEnum :: Int -> a :~~: b #

fromEnum :: (a :~~: b) -> Int #

enumFrom :: (a :~~: b) -> [a :~~: b] #

enumFromThen :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

enumFromTo :: (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

enumFromThenTo :: (a :~~: b) -> (a :~~: b) -> (a :~~: b) -> [a :~~: b] #

class Eq a where #

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:

Reflexivity
x == x = True
Symmetry
x == y = y == x
Transitivity
if x == y && y == z = True, then x == z = True
Substitutivity
if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True
Negation
x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 #

(/=) :: a -> a -> Bool infix 4 #

Instances
Eq Bool 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Char 
Instance details

Defined in GHC.Classes

Methods

(==) :: Char -> Char -> Bool #

(/=) :: Char -> Char -> Bool #

Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Eq Float

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool #

(/=) :: Float -> Float -> Bool #

Eq Int 
Instance details

Defined in GHC.Classes

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Eq Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int8 -> Int8 -> Bool #

(/=) :: Int8 -> Int8 -> Bool #

Eq Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int16 -> Int16 -> Bool #

(/=) :: Int16 -> Int16 -> Bool #

Eq Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int32 -> Int32 -> Bool #

(/=) :: Int32 -> Int32 -> Bool #

Eq Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

(==) :: Int64 -> Int64 -> Bool #

(/=) :: Int64 -> Int64 -> Bool #

Eq Integer 
Instance details

Defined in GHC.Integer.Type

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Eq Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Methods

(==) :: Natural -> Natural -> Bool #

(/=) :: Natural -> Natural -> Bool #

Eq Ordering 
Instance details

Defined in GHC.Classes

Eq Word 
Instance details

Defined in GHC.Classes

Methods

(==) :: Word -> Word -> Bool #

(/=) :: Word -> Word -> Bool #

Eq Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word8 -> Word8 -> Bool #

(/=) :: Word8 -> Word8 -> Bool #

Eq Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word16 -> Word16 -> Bool #

(/=) :: Word16 -> Word16 -> Bool #

Eq Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word32 -> Word32 -> Bool #

(/=) :: Word32 -> Word32 -> Bool #

Eq Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

(==) :: Word64 -> Word64 -> Bool #

(/=) :: Word64 -> Word64 -> Bool #

Eq SomeTypeRep 
Instance details

Defined in Data.Typeable.Internal

Eq () 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq TyCon 
Instance details

Defined in GHC.Classes

Methods

(==) :: TyCon -> TyCon -> Bool #

(/=) :: TyCon -> TyCon -> Bool #

Eq Module 
Instance details

Defined in GHC.Classes

Methods

(==) :: Module -> Module -> Bool #

(/=) :: Module -> Module -> Bool #

Eq TrName 
Instance details

Defined in GHC.Classes

Methods

(==) :: TrName -> TrName -> Bool #

(/=) :: TrName -> TrName -> Bool #

Eq BigNat 
Instance details

Defined in GHC.Integer.Type

Methods

(==) :: BigNat -> BigNat -> Bool #

(/=) :: BigNat -> BigNat -> Bool #

Eq Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

(==) :: Void -> Void -> Bool #

(/=) :: Void -> Void -> Bool #

Eq SpecConstrAnnotation

Since: base-4.3.0.0

Instance details

Defined in GHC.Exts

Eq Constr

Equality of constructors

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

(==) :: Constr -> Constr -> Bool #

(/=) :: Constr -> Constr -> Bool #

Eq DataRep

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

(==) :: DataRep -> DataRep -> Bool #

(/=) :: DataRep -> DataRep -> Bool #

Eq ConstrRep

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Eq Fixity

Since: base-4.0.0.0

Instance details

Defined in Data.Data

Methods

(==) :: Fixity -> Fixity -> Bool #

(/=) :: Fixity -> Fixity -> Bool #

Eq Unique 
Instance details

Defined in Data.Unique

Methods

(==) :: Unique -> Unique -> Bool #

(/=) :: Unique -> Unique -> Bool #

Eq Version

Since: base-2.1

Instance details

Defined in Data.Version

Methods

(==) :: Version -> Version -> Bool #

(/=) :: Version -> Version -> Bool #

Eq ThreadId

Since: base-4.2.0.0

Instance details

Defined in GHC.Conc.Sync

Eq BlockReason

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Eq ThreadStatus

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Eq AsyncException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Eq ArrayException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Eq ExitCode 
Instance details

Defined in GHC.IO.Exception

Eq IOErrorType

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Eq MaskingState

Since: base-4.3.0.0

Instance details

Defined in GHC.IO

Eq IOException

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Eq All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool #

(/=) :: All -> All -> Bool #

Eq Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool #

(/=) :: Any -> Any -> Bool #

Eq Fixity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: Fixity -> Fixity -> Bool #

(/=) :: Fixity -> Fixity -> Bool #

Eq Associativity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Eq SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq SomeSymbol

Since: base-4.7.0.0

Instance details

Defined in GHC.TypeLits

Eq SomeNat

Since: base-4.7.0.0

Instance details

Defined in GHC.TypeNats

Methods

(==) :: SomeNat -> SomeNat -> Bool #

(/=) :: SomeNat -> SomeNat -> Bool #

Eq CChar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CChar -> CChar -> Bool #

(/=) :: CChar -> CChar -> Bool #

Eq CSChar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CSChar -> CSChar -> Bool #

(/=) :: CSChar -> CSChar -> Bool #

Eq CUChar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CUChar -> CUChar -> Bool #

(/=) :: CUChar -> CUChar -> Bool #

Eq CShort 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CShort -> CShort -> Bool #

(/=) :: CShort -> CShort -> Bool #

Eq CUShort 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CUShort -> CUShort -> Bool #

(/=) :: CUShort -> CUShort -> Bool #

Eq CInt 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CInt -> CInt -> Bool #

(/=) :: CInt -> CInt -> Bool #

Eq CUInt 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CUInt -> CUInt -> Bool #

(/=) :: CUInt -> CUInt -> Bool #

Eq CLong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CLong -> CLong -> Bool #

(/=) :: CLong -> CLong -> Bool #

Eq CULong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CULong -> CULong -> Bool #

(/=) :: CULong -> CULong -> Bool #

Eq CLLong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CLLong -> CLLong -> Bool #

(/=) :: CLLong -> CLLong -> Bool #

Eq CULLong 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CULLong -> CULLong -> Bool #

(/=) :: CULLong -> CULLong -> Bool #

Eq CBool 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CBool -> CBool -> Bool #

(/=) :: CBool -> CBool -> Bool #

Eq CFloat 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CFloat -> CFloat -> Bool #

(/=) :: CFloat -> CFloat -> Bool #

Eq CDouble 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CDouble -> CDouble -> Bool #

(/=) :: CDouble -> CDouble -> Bool #

Eq CPtrdiff 
Instance details

Defined in Foreign.C.Types

Eq CSize 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CSize -> CSize -> Bool #

(/=) :: CSize -> CSize -> Bool #

Eq CWchar 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CWchar -> CWchar -> Bool #

(/=) :: CWchar -> CWchar -> Bool #

Eq CSigAtomic 
Instance details

Defined in Foreign.C.Types

Eq CClock 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CClock -> CClock -> Bool #

(/=) :: CClock -> CClock -> Bool #

Eq CTime 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CTime -> CTime -> Bool #

(/=) :: CTime -> CTime -> Bool #

Eq CUSeconds 
Instance details

Defined in Foreign.C.Types

Eq CSUSeconds 
Instance details

Defined in Foreign.C.Types

Eq CIntPtr 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CIntPtr -> CIntPtr -> Bool #

(/=) :: CIntPtr -> CIntPtr -> Bool #

Eq CUIntPtr 
Instance details

Defined in Foreign.C.Types

Eq CIntMax 
Instance details

Defined in Foreign.C.Types

Methods

(==) :: CIntMax -> CIntMax -> Bool #

(/=) :: CIntMax -> CIntMax -> Bool #

Eq CUIntMax 
Instance details

Defined in Foreign.C.Types

Eq WordPtr 
Instance details

Defined in Foreign.Ptr

Methods

(==) :: WordPtr -> WordPtr -> Bool #

(/=) :: WordPtr -> WordPtr -> Bool #

Eq IntPtr 
Instance details

Defined in Foreign.Ptr

Methods

(==) :: IntPtr -> IntPtr -> Bool #

(/=) :: IntPtr -> IntPtr -> Bool #

Eq Fingerprint

Since: base-4.4.0.0

Instance details

Defined in GHC.Fingerprint.Type

Eq SrcLoc

Since: base-4.9.0.0

Instance details

Defined in GHC.Stack.Types

Methods

(==) :: SrcLoc -> SrcLoc -> Bool #

(/=) :: SrcLoc -> SrcLoc -> Bool #

Eq ByteArray

Since: primitive-0.6.3.0

Instance details

Defined in Data.Primitive.ByteArray

Eq Addr 
Instance details

Defined in Data.Primitive.Types

Methods

(==) :: Addr -> Addr -> Bool #

(/=) :: Addr -> Addr -> Bool #

Eq DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Eq Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Eq InterchangeName Source # 
Instance details

Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames

Eq InterchangeNameAuthority Source # 
Instance details

Defined in Numeric.Units.Dimensional.UnitNames.InterchangeNames

Eq Metricality Source # 
Instance details

Defined in Numeric.Units.Dimensional.Variants

Eq Prefix Source # 
Instance details

Defined in Numeric.Units.Dimensional.UnitNames.Internal

Methods

(==) :: Prefix -> Prefix -> Bool #

(/=) :: Prefix -> Prefix -> Bool #

Eq a => Eq [a] 
Instance details

Defined in GHC.Classes

Methods

(==) :: [a] -> [a] -> Bool #

(/=) :: [a] -> [a] -> Bool #

Eq a => Eq (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

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

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

Eq a => Eq (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

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

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

Eq (StablePtr a)

Since: base-2.1

Instance details

Defined in GHC.Stable

Methods

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

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

Eq (Ptr a)

Since: base-2.1

Instance details

Defined in GHC.Ptr

Methods

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

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

Eq (FunPtr a) 
Instance details

Defined in GHC.Ptr

Methods

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

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

Eq p => Eq (Par1 p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: Par1 p -> Par1 p -> Bool #

(/=) :: Par1 p -> Par1 p -> Bool #

Eq (ForeignPtr a)

Since: base-2.1

Instance details

Defined in GHC.ForeignPtr

Methods

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

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

Eq a => Eq (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

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

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

Eq (Fixed a)

Since: base-2.1

Instance details

Defined in Data.Fixed

Methods

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

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

Eq a => Eq (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Eq a => Eq (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq (StableName a)

Since: base-2.1

Instance details

Defined in GHC.StableName

Methods

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

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

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

Methods

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

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

Eq (TVar a)

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

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

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

Eq (IORef a)

^ Pointer equality.

Since: base-4.1.0.0

Instance details

Defined in GHC.IORef

Methods

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

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

Eq a => Eq (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq a => Eq (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq a => Eq (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq a => Eq (Down a)

Since: base-4.6.0.0

Instance details

Defined in Data.Ord

Methods

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

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

Eq (MVar a)

Since: base-4.1.0.0

Instance details

Defined in GHC.MVar

Methods

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

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

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

(Eq a, PrimUnlifted a) => Eq (UnliftedArray a) 
Instance details

Defined in Data.Primitive.UnliftedArray

(Eq a, Prim a) => Eq (PrimArray a)

Since: primitive-0.6.4.0

Instance details

Defined in Data.Primitive.PrimArray

Methods

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

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

Eq a => Eq (SmallArray a) 
Instance details

Defined in Data.Primitive.SmallArray

Methods

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

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

Eq a => Eq (Array a) 
Instance details

Defined in Data.Primitive.Array

Methods

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

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

(Prim a, Eq a) => Eq (Vector a) 
Instance details

Defined in Data.Vector.Primitive

Methods

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

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

Eq (NameAtom m) Source # 
Instance details

Defined in Numeric.Units.Dimensional.UnitNames.Internal

Methods

(==) :: NameAtom m -> NameAtom m -> Bool #

(/=) :: NameAtom m -> NameAtom m -> Bool #

Eq (UnitName m) Source # 
Instance details

Defined in Numeric.Units.Dimensional.UnitNames.Internal

Methods

(==) :: UnitName m -> UnitName m -> Bool #

(/=) :: UnitName m -> UnitName m -> Bool #

Eq a => Eq (DynQuantity a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Eq a => Eq (AnyQuantity a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

(Eq a, Eq b) => Eq (Either a b)

Since: base-2.1

Instance details

Defined in Data.Either

Methods

(==) :: Either a b -> Either a b -> Bool #

(/=) :: Either a b -> Either a b -> Bool #

Eq (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: V1 p -> V1 p -> Bool #

(/=) :: V1 p -> V1 p -> Bool #

Eq (U1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: U1 p -> U1 p -> Bool #

(/=) :: U1 p -> U1 p -> Bool #

Eq (TypeRep a)

Since: base-2.1

Instance details

Defined in Data.Typeable.Internal

Methods

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

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

(Eq a, Eq b) => Eq (a, b) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b) -> (a, b) -> Bool #

(/=) :: (a, b) -> (a, b) -> Bool #

(Ix i, Eq e) => Eq (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: Array i e -> Array i e -> Bool #

(/=) :: Array i e -> Array i e -> Bool #

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool #

(/=) :: Arg a b -> Arg a b -> Bool #

Eq (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

(==) :: Proxy s -> Proxy s -> Bool #

(/=) :: Proxy s -> Proxy s -> Bool #

Eq (STRef s a)

Pointer equality.

Since: base-2.1

Instance details

Defined in GHC.STRef

Methods

(==) :: STRef s a -> STRef s a -> Bool #

(/=) :: STRef s a -> STRef s a -> Bool #

Eq (MutableUnliftedArray s a) 
Instance details

Defined in Data.Primitive.UnliftedArray

Eq (SmallMutableArray s a) 
Instance details

Defined in Data.Primitive.SmallArray

Eq (MutableArray s a) 
Instance details

Defined in Data.Primitive.Array

Methods

(==) :: MutableArray s a -> MutableArray s a -> Bool #

(/=) :: MutableArray s a -> MutableArray s a -> Bool #

(Eq1 m, Eq a) => Eq (MaybeT m a) 
Instance details

Defined in Control.Monad.Trans.Maybe

Methods

(==) :: MaybeT m a -> MaybeT m a -> Bool #

(/=) :: MaybeT m a -> MaybeT m a -> Bool #

(Eq1 m, Eq a) => Eq (ListT m a) 
Instance details

Defined in Control.Monad.Trans.List

Methods

(==) :: ListT m a -> ListT m a -> Bool #

(/=) :: ListT m a -> ListT m a -> Bool #

Eq (f p) => Eq (Rec1 f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: Rec1 f p -> Rec1 f p -> Bool #

(/=) :: Rec1 f p -> Rec1 f p -> Bool #

Eq (URec (Ptr ()) p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

Eq (URec Char p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Char p -> URec Char p -> Bool #

(/=) :: URec Char p -> URec Char p -> Bool #

Eq (URec Double p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Eq (URec Float p) 
Instance details

Defined in GHC.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool #

(/=) :: URec Float p -> URec Float p -> Bool #

Eq (URec Int p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Eq (URec Word p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: URec Word p -> URec Word p -> Bool #

(/=) :: URec Word p -> URec Word p -> Bool #

(Eq a, Eq b, Eq c) => Eq (a, b, c) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c) -> (a, b, c) -> Bool #

(/=) :: (a, b, c) -> (a, b, c) -> Bool #

Eq (STArray s i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: STArray s i e -> STArray s i e -> Bool #

(/=) :: STArray s i e -> STArray s i e -> Bool #

Eq a => Eq (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

(==) :: Const a b -> Const a b -> Bool #

(/=) :: Const a b -> Const a b -> Bool #

Eq (f a) => Eq (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(==) :: Ap f a -> Ap f a -> Bool #

(/=) :: Ap f a -> Ap f a -> Bool #

Eq (f a) => Eq (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

(==) :: Alt f a -> Alt f a -> Bool #

(/=) :: Alt f a -> Alt f a -> Bool #

Eq (Coercion a b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Coercion

Methods

(==) :: Coercion a b -> Coercion a b -> Bool #

(/=) :: Coercion a b -> Coercion a b -> Bool #

Eq (a :~: b)

Since: base-4.7.0.0

Instance details

Defined in Data.Type.Equality

Methods

(==) :: (a :~: b) -> (a :~: b) -> Bool #

(/=) :: (a :~: b) -> (a :~: b) -> Bool #

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) 
Instance details

Defined in Control.Monad.Trans.Writer.Strict

Methods

(==) :: WriterT w m a -> WriterT w m a -> Bool #

(/=) :: WriterT w m a -> WriterT w m a -> Bool #

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) 
Instance details

Defined in Control.Monad.Trans.Writer.Lazy

Methods

(==) :: WriterT w m a -> WriterT w m a -> Bool #

(/=) :: WriterT w m a -> WriterT w m a -> Bool #

(Eq1 f, Eq a) => Eq (IdentityT f a) 
Instance details

Defined in Control.Monad.Trans.Identity

Methods

(==) :: IdentityT f a -> IdentityT f a -> Bool #

(/=) :: IdentityT f a -> IdentityT f a -> Bool #

(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a) 
Instance details

Defined in Control.Monad.Trans.Except

Methods

(==) :: ExceptT e m a -> ExceptT e m a -> Bool #

(/=) :: ExceptT e m a -> ExceptT e m a -> Bool #

(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

(==) :: ErrorT e m a -> ErrorT e m a -> Bool #

(/=) :: ErrorT e m a -> ErrorT e m a -> Bool #

Eq a => Eq (Dimensional (DQuantity s) d a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Internal

Methods

(==) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool #

(/=) :: Dimensional (DQuantity s) d a -> Dimensional (DQuantity s) d a -> Bool #

Eq c => Eq (K1 i c p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: K1 i c p -> K1 i c p -> Bool #

(/=) :: K1 i c p -> K1 i c p -> Bool #

(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool #

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool #

(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: (f :*: g) p -> (f :*: g) p -> Bool #

(/=) :: (f :*: g) p -> (f :*: g) p -> Bool #

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

Methods

(==) :: Product f g a -> Product f g a -> Bool #

(/=) :: Product f g a -> Product f g a -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Sum

Methods

(==) :: Sum f g a -> Sum f g a -> Bool #

(/=) :: Sum f g a -> Sum f g a -> Bool #

Eq (a :~~: b)

Since: base-4.10.0.0

Instance details

Defined in Data.Type.Equality

Methods

(==) :: (a :~~: b) -> (a :~~: b) -> Bool #

(/=) :: (a :~~: b) -> (a :~~: b) -> Bool #

Eq (f p) => Eq (M1 i c f p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: M1 i c f p -> M1 i c f p -> Bool #

(/=) :: M1 i c f p -> M1 i c f p -> Bool #

Eq (f (g p)) => Eq ((f :.: g) p)

Since: base-4.7.0.0

Instance details

Defined in GHC.Generics

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool #

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Compose

Methods

(==) :: Compose f g a -> Compose f g a -> Bool #

(/=) :: Compose f g a -> Compose f g a -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 
Instance details

Defined in GHC.Classes

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

class Fractional a => Floating a #

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, '(+)', '(*)' and exp are customarily expected to define an exponential field and have the following properties:

  • exp (a + b) = @exp a * exp b
  • exp (fromInteger 0) = fromInteger 1

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Instances
Floating Double

Since: base-2.1

Instance details

Defined in GHC.Float

Floating Float

Since: base-2.1

Instance details

Defined in GHC.Float

Floating CFloat 
Instance details

Defined in Foreign.C.Types

Floating CDouble 
Instance details

Defined in Foreign.C.Types

Floating ExactPi 
Instance details

Defined in Data.ExactPi

KnownMinCtxt Floating 
Instance details

Defined in Data.ExactPi.TypeLevel

Methods

inj :: Floating a => Proxy Floating -> ExactPi -> a

RealFloat a => Floating (Complex a)

Since: base-2.1

Instance details

Defined in Data.Complex

Methods

pi :: Complex a #

exp :: Complex a -> Complex a #

log :: Complex a -> Complex a #

sqrt :: Complex a -> Complex a #

(**) :: Complex a -> Complex a -> Complex a #

logBase :: Complex a -> Complex a -> Complex a #

sin :: Complex a -> Complex a #

cos :: Complex a -> Complex a #

tan :: Complex a -> Complex a #

asin :: Complex a -> Complex a #

acos :: Complex a -> Complex a #

atan :: Complex a -> Complex a #

sinh :: Complex a -> Complex a #

cosh :: Complex a -> Complex a #

tanh :: Complex a -> Complex a #

asinh :: Complex a -> Complex a #

acosh :: Complex a -> Complex a #

atanh :: Complex a -> Complex a #

log1p :: Complex a -> Complex a #

expm1 :: Complex a -> Complex a #

log1pexp :: Complex a -> Complex a #

log1mexp :: Complex a -> Complex a #

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Floating a => Floating (DynQuantity a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Floating a => Floating (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

pi :: Const a b #

exp :: Const a b -> Const a b #

log :: Const a b -> Const a b #

sqrt :: Const a b -> Const a b #

(**) :: Const a b -> Const a b -> Const a b #

logBase :: Const a b -> Const a b -> Const a b #

sin :: Const a b -> Const a b #

cos :: Const a b -> Const a b #

tan :: Const a b -> Const a b #

asin :: Const a b -> Const a b #

acos :: Const a b -> Const a b #

atan :: Const a b -> Const a b #

sinh :: Const a b -> Const a b #

cosh :: Const a b -> Const a b #

tanh :: Const a b -> Const a b #

asinh :: Const a b -> Const a b #

acosh :: Const a b -> Const a b #

atanh :: Const a b -> Const a b #

log1p :: Const a b -> Const a b #

expm1 :: Const a b -> Const a b #

log1pexp :: Const a b -> Const a b #

log1mexp :: Const a b -> Const a b #

class Num a => Fractional a where #

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, '(+)' and '(*)' are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse
x * recip x = recip x * x = fromInteger 1

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Methods

fromRational :: Rational -> a #

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances
Fractional CFloat 
Instance details

Defined in Foreign.C.Types

Fractional CDouble 
Instance details

Defined in Foreign.C.Types

Fractional ExactPi 
Instance details

Defined in Data.ExactPi

Methods

(/) :: ExactPi -> ExactPi ->