Data.Monoid.Statistics.Class

Monoid Type class and helpers

class Monoid m => StatMonoid m a where

This type class is used to express parallelizable constant space algorithms for calculation of statistics. Statistic is function of type [a]→b which does not depend on order of elements. (for example: mean, sum, number of elements, variance, etc).

For many statistics it's possible to possible to construct constant space algorithm which is expressed as fold. Additionally it's usually possible to write function which combine state of fold accumulator to get statistic for union of two samples.

Thus for such algorithm we have value which corresponds to empty sample, function which which corresponds to merging of two samples, and single step of fold. Last one allows to evaluate statistic given data sample and first two form a monoid and allow parallelization: split data into parts, build estimate for each by folding and then merge them using mappend.

Instance must satisfy following laws. If floating point arithmetics is used then equality should be understood as approximate.

1. addValue (addValue y mempty) x  == addValue mempty x <> addValue mempty y
2. x <> y == y <> x

Minimal complete definition

addValue | singletonMonoid

Methods

addValue :: m -> a -> m

Add one element to monoid accumulator. It's step of fold.

singletonMonoid :: a -> m

State of accumulator corresponding to 1-element sample.

Instances

Real a => StatMonoid KahanSum a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: KahanSum -> a -> KahanSum

singletonMonoid :: a -> KahanSum

Real a => StatMonoid KBNSum a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: KBNSum -> a -> KBNSum

singletonMonoid :: a -> KBNSum

Real a => StatMonoid KB2Sum a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: KB2Sum -> a -> KB2Sum

singletonMonoid :: a -> KB2Sum

Real a => StatMonoid WelfordMean a

Defined in Data.Monoid.Statistics.Extra

Methods

addValue :: WelfordMean -> a -> WelfordMean

singletonMonoid :: a -> WelfordMean

Real a => StatMonoid MeanKahan a

Defined in Data.Monoid.Statistics.Extra

Methods

addValue :: MeanKahan -> a -> MeanKahan

singletonMonoid :: a -> MeanKahan

Real a => StatMonoid MeanKB2 a

Defined in Data.Monoid.Statistics.Extra

Methods

addValue :: MeanKB2 -> a -> MeanKB2

singletonMonoid :: a -> MeanKB2

StatMonoid BinomAcc Bool

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: BinomAcc -> Bool -> BinomAcc

singletonMonoid :: Bool -> BinomAcc

a ~ Double => StatMonoid MaxD a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MaxD -> a -> MaxD

singletonMonoid :: a -> MaxD

a ~ Double => StatMonoid MinD a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MinD -> a -> MinD

singletonMonoid :: a -> MinD

Real a => StatMonoid Variance a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: Variance -> a -> Variance

singletonMonoid :: a -> Variance

Real a => StatMonoid MeanKBN a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MeanKBN -> a -> MeanKBN

singletonMonoid :: a -> MeanKBN

Real a => StatMonoid MeanNaive a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MeanNaive -> a -> MeanNaive

singletonMonoid :: a -> MeanNaive

(Real w, Real a) => StatMonoid WMeanKBN (Weighted w a)

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: WMeanKBN -> Weighted w a -> WMeanKBN

singletonMonoid :: Weighted w a -> WMeanKBN

(Real w, Real a) => StatMonoid WMeanNaive (Weighted w a)

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: WMeanNaive -> Weighted w a -> WMeanNaive

singletonMonoid :: Weighted w a -> WMeanNaive

(Num a, a ~ a') => StatMonoid (Sum a) a'

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Sum a -> a' -> Sum a

singletonMonoid :: a' -> Sum a

(Num a, a ~ a') => StatMonoid (Product a) a'

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Product a -> a' -> Product a

singletonMonoid :: a' -> Product a

(Ord a, a ~ a') => StatMonoid (Max a) a'

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: Max a -> a' -> Max a

singletonMonoid :: a' -> Max a

(Ord a, a ~ a') => StatMonoid (Min a) a'

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: Min a -> a' -> Min a

singletonMonoid :: a' -> Min a

Integral a => StatMonoid (CountG a) b

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: CountG a -> b -> CountG a

singletonMonoid :: b -> CountG a

(StatMonoid m1 a, StatMonoid m2 a) => StatMonoid (m1, m2) a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: (m1, m2) -> a -> (m1, m2)

singletonMonoid :: a -> (m1, m2)

(StatMonoid a x, StatMonoid b x) => StatMonoid (Pair a b) x

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Pair a b -> x -> Pair a b

singletonMonoid :: x -> Pair a b

(StatMonoid m1 a, StatMonoid m2 a, StatMonoid m3 a) => StatMonoid (m1, m2, m3) a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: (m1, m2, m3) -> a -> (m1, m2, m3)

singletonMonoid :: a -> (m1, m2, m3)

(StatMonoid m1 a, StatMonoid m2 a, StatMonoid m3 a, StatMonoid m4 a) => StatMonoid (m1, m2, m3, m4) a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: (m1, m2, m3, m4) -> a -> (m1, m2, m3, m4)

singletonMonoid :: a -> (m1, m2, m3, m4)

reduceSample :: forall m a f. (StatMonoid m a, Foldable f) => f a -> m

Calculate statistic over Foldable. It's implemented in terms of foldl'. Note that in cases when accumulator is immediately consumed by polymorphic function such as callMeam its type becomes ambiguous. TypeApplication then could be used to disambiguate.

>>> reduceSample @Mean [1,2,3,4]
MeanKBN 4 (KBNSum 10.0 0.0)
>>> calcMean $ reduceSample @Mean [1,2,3,4] :: Maybe Double
Just 2.5

reduceSampleVec :: forall m a v. (StatMonoid m a, Vector v a) => v a -> m

Calculate statistic over vector. Works in same was as reduceSample but works for vectors.

Ad-hoc type classes for select statistics

Type classes defined here allows to extract common statistics from estimators. it's assumed that quantities in question are already computed so extraction is cheap.

Error handling

Computation of statistics may fail. For example mean is not defined for an empty sample. Maybe could be seen as easy way to handle this situation. But in many cases most convenient way to handle failure is to throw an exception. So failure is encoded by using polymorphic function of type MonadThrow m ⇒ a → m X.

Maybe types has instance, such as Maybe, Either SomeException, IO and most transformers wrapping it. Notably this library defines Partial monad which allows to convert failures to exception in pure setting.

>>> calcMean $ reduceSample @Mean []
*** Exception: EmptySample "Data.Monoid.Statistics.Numeric.MeanKBN: calcMean"

>>> calcMean $ reduceSample @Mean [] :: Maybe Double
Nothing

>>> import Control.Exception
>>> calcMean $ reduceSample @Mean [] :: Either SomeException Double
Left (EmptySample "Data.Monoid.Statistics.Numeric.MeanKBN: calcMean")

Last example uses IO

>>> calcMean $ reduceSample @Mean []
*** Exception: EmptySample "Data.Monoid.Statistics.Numeric.MeanKBN: calcMean"

Deriving instances

Type classes come in two variants, one that allow failure and one for use in cases when quantity is always defined. This is not the case for estimators, but true for distributions and intended for such use cases. In that case CalcViaHas could be used to derive necessary instances.

>>> :{
data NormalDist = NormalDist !Double !Double
  deriving (CalcMean,CalcVariance) via CalcViaHas NormalDist
instance HasMean NormalDist where
  getMean (NormalDist mu _) = mu
instance HasVariance NormalDist where
  getVariance   (NormalDist _ s) = s
  getVarianceML (NormalDist _ s) = s
:}

class CalcCount a where

Value from which we can efficiently extract number of elements in sample it represents.

Methods

calcCount :: a -> Int

Assumed O(1). Number of elements in sample.

Instances

CalcCount WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

calcCount :: WelfordMean -> Int

CalcCount MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

calcCount :: MeanKahan -> Int

CalcCount Variance

Defined in Data.Monoid.Statistics.Numeric

Methods

calcCount :: Variance -> Int

CalcCount MeanKBN

Defined in Data.Monoid.Statistics.Numeric

Methods

calcCount :: MeanKBN -> Int

CalcCount MeanNaive

Defined in Data.Monoid.Statistics.Numeric

Methods

calcCount :: MeanNaive -> Int

CalcCount (CountG Int)

Defined in Data.Monoid.Statistics.Numeric

Methods

calcCount :: CountG Int -> Int

class CalcMean a where

Value from which we can efficiently calculate mean of sample or distribution.

Methods

calcMean :: MonadThrow m => a -> m Double

Assumed O(1) Returns Nothing if there isn't enough data to make estimate or distribution doesn't have defined mean.

\[ \bar{x} = \frac{1}{N}\sum_{i=1}^N{x_i} \]

Instances

CalcMean WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

calcMean :: MonadThrow m => WelfordMean -> m Double

CalcMean MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

calcMean :: MonadThrow m => MeanKahan -> m Double

CalcMean MeanKB2

Defined in Data.Monoid.Statistics.Extra

Methods

calcMean :: MonadThrow m => MeanKB2 -> m Double

CalcMean Variance

Defined in Data.Monoid.Statistics.Numeric

Methods

calcMean :: MonadThrow m => Variance -> m Double

CalcMean WMeanKBN

Defined in Data.Monoid.Statistics.Numeric

Methods

calcMean :: MonadThrow m => WMeanKBN -> m Double

CalcMean WMeanNaive

Defined in Data.Monoid.Statistics.Numeric

Methods

calcMean :: MonadThrow m => WMeanNaive -> m Double

CalcMean MeanKBN

Defined in Data.Monoid.Statistics.Numeric

Methods

calcMean :: MonadThrow m => MeanKBN -> m Double

CalcMean MeanNaive

Defined in Data.Monoid.Statistics.Numeric

Methods

calcMean :: MonadThrow m => MeanNaive -> m Double

HasMean a => CalcMean (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

calcMean :: MonadThrow m => CalcViaHas a -> m Double

class CalcMean a => HasMean a where

Same as CalcMean but should never fail

Methods

getMean :: a -> Double

Instances

HasMean a => HasMean (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

getMean :: CalcViaHas a -> Double

class CalcVariance a where

Values from which we can efficiently compute estimate of sample variance or distribution variance. It has two methods: one which applies bias correction to estimate and another that returns maximul likelyhood estimate. For distribution they should return same value.

Minimal complete definition

calcVariance, calcVarianceML | calcStddev, calcStddevML

Methods

calcVariance :: MonadThrow m => a -> m Double

Assumed O(1) Calculate unbiased estimate of variance:

\[ \sigma^2 = \frac{1}{N-1}\sum_{i=1}^N(x_i - \bar{x})^2 \]

calcVarianceML :: MonadThrow m => a -> m Double

Assumed O(1) Calculate maximum likelihood estimate of variance:

\[ \sigma^2 = \frac{1}{N}\sum_{i=1}^N(x_i - \bar{x})^2 \]

calcStddev :: MonadThrow m => a -> m Double

Calculate sample standard deviation from unbiased estimation of variance.

calcStddevML :: MonadThrow m => a -> m Double

Calculate sample standard deviation from maximum likelihood estimation of variance.

Instances

CalcVariance Variance

Defined in Data.Monoid.Statistics.Numeric

Methods

calcVariance :: MonadThrow m => Variance -> m Double

calcVarianceML :: MonadThrow m => Variance -> m Double

calcStddev :: MonadThrow m => Variance -> m Double

calcStddevML :: MonadThrow m => Variance -> m Double

HasVariance a => CalcVariance (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

calcVariance :: MonadThrow m => CalcViaHas a -> m Double

calcVarianceML :: MonadThrow m => CalcViaHas a -> m Double

calcStddev :: MonadThrow m => CalcViaHas a -> m Double

calcStddevML :: MonadThrow m => CalcViaHas a -> m Double

class CalcVariance a => HasVariance a where

Same as CalcVariance but never fails

Minimal complete definition

getVariance, getVarianceML | getStddev, getStddevML

Methods

getVariance :: a -> Double

getVarianceML :: a -> Double

getStddev :: a -> Double

getStddevML :: a -> Double

Instances

HasVariance a => HasVariance (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

getVariance :: CalcViaHas a -> Double

getVarianceML :: CalcViaHas a -> Double

getStddev :: CalcViaHas a -> Double

getStddevML :: CalcViaHas a -> Double

newtype CalcViaHas a

Constructors

CalcViaHas a

Instances

HasVariance a => HasVariance (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

getVariance :: CalcViaHas a -> Double

getVarianceML :: CalcViaHas a -> Double

getStddev :: CalcViaHas a -> Double

getStddevML :: CalcViaHas a -> Double

HasVariance a => CalcVariance (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

calcVariance :: MonadThrow m => CalcViaHas a -> m Double

calcVarianceML :: MonadThrow m => CalcViaHas a -> m Double

calcStddev :: MonadThrow m => CalcViaHas a -> m Double

calcStddevML :: MonadThrow m => CalcViaHas a -> m Double

HasMean a => HasMean (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

getMean :: CalcViaHas a -> Double

HasMean a => CalcMean (CalcViaHas a)

Defined in Data.Monoid.Statistics.Class

Methods

calcMean :: MonadThrow m => CalcViaHas a -> m Double

Exception handling

newtype Partial a

Identity monad which is used to encode partial functions for MonadThrow based error handling. Its MonadThrow instance just throws normal exception.

Constructors

Partial a

Instances

Monad Partial

Defined in Data.Monoid.Statistics.Class

Methods

(>>=) :: Partial a -> (a -> Partial b) -> Partial b

(>>) :: Partial a -> Partial b -> Partial b

return :: a -> Partial a

Functor Partial

Defined in Data.Monoid.Statistics.Class

Methods

fmap :: (a -> b) -> Partial a -> Partial b

(<$) :: a -> Partial b -> Partial a

Applicative Partial

Defined in Data.Monoid.Statistics.Class

Methods

pure :: a -> Partial a

(<*>) :: Partial (a -> b) -> Partial a -> Partial b

liftA2 :: (a -> b -> c) -> Partial a -> Partial b -> Partial c

(*>) :: Partial a -> Partial b -> Partial b

(<*) :: Partial a -> Partial b -> Partial a

MonadThrow Partial

Defined in Data.Monoid.Statistics.Class

Methods

throwM :: Exception e => e -> Partial a

Eq a => Eq (Partial a)

Defined in Data.Monoid.Statistics.Class

Methods

(==) :: Partial a -> Partial a -> Bool

(/=) :: Partial a -> Partial a -> Bool

Data a => Data (Partial a)

Defined in Data.Monoid.Statistics.Class

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Partial a -> c (Partial a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Partial a)

toConstr :: Partial a -> Constr

dataTypeOf :: Partial a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Partial a))

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

gmapT :: (forall b. Data b => b -> b) -> Partial a -> Partial a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Partial a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Partial a -> r

gmapQ :: (forall d. Data d => d -> u) -> Partial a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Partial a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Partial a -> m (Partial a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Partial a -> m (Partial a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Partial a -> m (Partial a)

Ord a => Ord (Partial a)

Defined in Data.Monoid.Statistics.Class

Methods

compare :: Partial a -> Partial a -> Ordering

(<) :: Partial a -> Partial a -> Bool

(<=) :: Partial a -> Partial a -> Bool

(>) :: Partial a -> Partial a -> Bool

(>=) :: Partial a -> Partial a -> Bool

max :: Partial a -> Partial a -> Partial a

min :: Partial a -> Partial a -> Partial a

Read a => Read (Partial a)

Defined in Data.Monoid.Statistics.Class

Methods

readsPrec :: Int -> ReadS (Partial a)

readList :: ReadS [Partial a]

readPrec :: ReadPrec (Partial a)

readListPrec :: ReadPrec [Partial a]

Show a => Show (Partial a)

Defined in Data.Monoid.Statistics.Class

Methods

showsPrec :: Int -> Partial a -> ShowS

show :: Partial a -> String

showList :: [Partial a] -> ShowS

Generic (Partial a)

Defined in Data.Monoid.Statistics.Class

Associated Types

type Rep (Partial a) :: Type -> Type

Methods

from :: Partial a -> Rep (Partial a) x

to :: Rep (Partial a) x -> Partial a

type Rep (Partial a)

Defined in Data.Monoid.Statistics.Class

type Rep (Partial a) = D1 ('MetaData "Partial" "Data.Monoid.Statistics.Class" "monoid-statistics-1.1.1-Et52IJUUy4YDKplMeouIOs" 'True) (C1 ('MetaCons "Partial" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

partial :: HasCallStack => Partial a -> a

Convert error to IO exception. This way one could for example convert case when some statistics is not defined to an exception:

>>> calcMean $ reduceSample @Mean []
*** Exception: EmptySample "Data.Monoid.Statistics.Numeric.MeanKBN: calcMean"

data SampleError

Exception which is thrown when we can't compute some value

Constructors

EmptySample String

EmptySample function: We're trying to compute quantity that is undefined for empty sample.

InvalidSample String String

InvalidSample function descripton quantity in question could not be computed for some other reason

Instances

Show SampleError

Defined in Data.Monoid.Statistics.Class

Methods

showsPrec :: Int -> SampleError -> ShowS

show :: SampleError -> String

showList :: [SampleError] -> ShowS

Exception SampleError

Defined in Data.Monoid.Statistics.Class

Methods

toException :: SampleError -> SomeException

fromException :: SomeException -> Maybe SampleError

displayException :: SampleError -> String

Data types

data Pair a b

Strict pair. It allows to calculate two statistics in parallel

Constructors

Pair !a !b

Instances

(Unbox a, Unbox b) => Vector Vector (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Pair a b) -> m (Vector (Pair a b))

basicUnsafeThaw :: PrimMonad m => Vector (Pair a b) -> m (Mutable Vector (PrimState m) (Pair a b))

basicLength :: Vector (Pair a b) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Pair a b) -> Vector (Pair a b)

basicUnsafeIndexM :: Monad m => Vector (Pair a b) -> Int -> m (Pair a b)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Pair a b) -> Vector (Pair a b) -> m ()

elemseq :: Vector (Pair a b) -> Pair a b -> b0 -> b0

(Unbox a, Unbox b) => MVector MVector (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

basicLength :: MVector s (Pair a b) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Pair a b) -> MVector s (Pair a b)

basicOverlaps :: MVector s (Pair a b) -> MVector s (Pair a b) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Pair a b))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Pair a b) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Pair a b -> m (MVector (PrimState m) (Pair a b))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Pair a b) -> Int -> m (Pair a b)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Pair a b) -> Int -> Pair a b -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Pair a b) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Pair a b) -> Pair a b -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Pair a b) -> MVector (PrimState m) (Pair a b) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Pair a b) -> MVector (PrimState m) (Pair a b) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Pair a b) -> Int -> m (MVector (PrimState m) (Pair a b))

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

Defined in Data.Monoid.Statistics.Class

Methods

(==) :: Pair a b -> Pair a b -> Bool

(/=) :: Pair a b -> Pair a b -> Bool

(Data a, Data b) => Data (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Pair a b -> c (Pair a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Pair a b)

toConstr :: Pair a b -> Constr

dataTypeOf :: Pair a b -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Pair a b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Pair a b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Pair a b -> Pair a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Pair a b -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Pair a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Pair a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Pair a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Pair a b -> m (Pair a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Pair a b -> m (Pair a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Pair a b -> m (Pair a b)

(Ord a, Ord b) => Ord (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

compare :: Pair a b -> Pair a b -> Ordering

(<) :: Pair a b -> Pair a b -> Bool

(<=) :: Pair a b -> Pair a b -> Bool

(>) :: Pair a b -> Pair a b -> Bool

(>=) :: Pair a b -> Pair a b -> Bool

max :: Pair a b -> Pair a b -> Pair a b

min :: Pair a b -> Pair a b -> Pair a b

(Show a, Show b) => Show (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

showsPrec :: Int -> Pair a b -> ShowS

show :: Pair a b -> String

showList :: [Pair a b] -> ShowS

Generic (Pair a b)

Defined in Data.Monoid.Statistics.Class

Associated Types

type Rep (Pair a b) :: Type -> Type

Methods

from :: Pair a b -> Rep (Pair a b) x

to :: Rep (Pair a b) x -> Pair a b

(Semigroup a, Semigroup b) => Semigroup (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

(<>) :: Pair a b -> Pair a b -> Pair a b

sconcat :: NonEmpty (Pair a b) -> Pair a b

stimes :: Integral b0 => b0 -> Pair a b -> Pair a b

(Monoid a, Monoid b) => Monoid (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

mempty :: Pair a b

mappend :: Pair a b -> Pair a b -> Pair a b

mconcat :: [Pair a b] -> Pair a b

(Unbox a, Unbox b) => Unbox (Pair a b)

Defined in Data.Monoid.Statistics.Class

(StatMonoid a x, StatMonoid b x) => StatMonoid (Pair a b) x

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Pair a b -> x -> Pair a b

singletonMonoid :: x -> Pair a b

newtype MVector s (Pair a b)

Defined in Data.Monoid.Statistics.Class

newtype MVector s (Pair a b) = MV_Pair (MVector s (a, b))

type Rep (Pair a b)

Defined in Data.Monoid.Statistics.Class

type Rep (Pair a b) = D1 ('MetaData "Pair" "Data.Monoid.Statistics.Class" "monoid-statistics-1.1.1-Et52IJUUy4YDKplMeouIOs" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 b)))

newtype Vector (Pair a b)

Defined in Data.Monoid.Statistics.Class

newtype Vector (Pair a b) = V_Pair (Vector (a, b))