dimensional-1.6.1: Statically checked physical dimensions
CopyrightCopyright (C) 2006-2018 Bjorn Buckwalter
LicenseBSD3
Maintainer[email protected]
StabilityStable
PortabilityGHC only
Safe HaskellSafe-Inferred
LanguageHaskell2010
Extensions
  • Cpp
  • BangPatterns
  • DeriveDataTypeable
  • DeriveGeneric
  • DefaultSignatures

Numeric.Units.Dimensional.Dimensions.TermLevel

Description

This module defines physical dimensions expressed in terms of the SI base dimensions, including arithmetic.

Synopsis

Type

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

Instances details
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 :: forall r r'. (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' #

Monoid Dimension' Source #

The monoid of dimensions under multiplication.

Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

mempty :: Dimension' #

mappend :: Dimension' -> Dimension' -> Dimension' #

mconcat :: [Dimension'] -> Dimension' #

Semigroup Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

(<>) :: Dimension' -> Dimension' -> Dimension' #

sconcat :: NonEmpty Dimension' -> Dimension' #

stimes :: Integral b => b -> Dimension' -> Dimension' #

Generic Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Associated Types

type Rep Dimension' 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

type Rep Dimension' = D1 ('MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.6.1-5Kh45RH4yKfKQGqcIykmmd" 'False) (C1 ('MetaCons "Dim'" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int))) :*: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int)))))

Methods

from :: Dimension' -> Rep Dimension' x #

to :: Rep Dimension' x -> Dimension' #

Show Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

showsPrec :: Int -> Dimension' -> ShowS #

show :: Dimension' -> String #

showList :: [Dimension'] -> ShowS #

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

Methods

dimension :: Dimension' -> Dimension' Source #

HasDynamicDimension Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

dynamicDimension :: Dimension' -> DynamicDimension Source #

Eq Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

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

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

Ord Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

compare :: Dimension' -> Dimension' -> Ordering #

(<) :: Dimension' -> Dimension' -> Bool #

(<=) :: Dimension' -> Dimension' -> Bool #

(>) :: Dimension' -> Dimension' -> Bool #

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

max :: Dimension' -> Dimension' -> Dimension' #

min :: Dimension' -> Dimension' -> Dimension' #

type Rep Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

type Rep Dimension' = D1 ('MetaData "Dimension'" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.6.1-5Kh45RH4yKfKQGqcIykmmd" 'False) (C1 ('MetaCons "Dim'" 'PrefixI 'False) ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int))) :*: ((S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int)) :*: (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int)))))

Access to Dimension of Dimensional Values

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.

Instances

Instances details
HasDimension Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

dimension :: Dimension' -> Dimension' Source #

HasDimension AnyUnit Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Methods

dimension :: AnyUnit -> Dimension' Source #

HasDimension (AnyQuantity a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Methods

dimension :: AnyQuantity a -> Dimension' Source #

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy ('Dim l m t i th n j)) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel

Methods

dimension :: Proxy ('Dim l m t i th n j) -> Dimension' Source #

KnownDimension d => HasDimension (Dimensional v d a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Internal

Methods

dimension :: Dimensional v d a -> Dimension' Source #

class HasDynamicDimension a where Source #

Dimensional values, or those that are only possibly dimensional, inhabit this class, which allows access to a term-level representation of their dimension.

Minimal complete definition

Nothing

Methods

dynamicDimension :: a -> DynamicDimension Source #

Gets the DynamicDimension of a dynamic dimensional value, which may be NoDimension if it does not represent a dimensional value of any Dimension.

A default implementation is available for types that are also in the HasDimension typeclass.

default dynamicDimension :: HasDimension a => a -> DynamicDimension Source #

Instances

Instances details
HasDynamicDimension Dimension' Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

dynamicDimension :: Dimension' -> DynamicDimension Source #

HasDynamicDimension DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

dynamicDimension :: DynamicDimension -> DynamicDimension Source #

HasDynamicDimension AnyUnit Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Methods

dynamicDimension :: AnyUnit -> DynamicDimension Source #

HasDynamicDimension (AnyQuantity a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Methods

dynamicDimension :: AnyQuantity a -> DynamicDimension Source #

HasDynamicDimension (DynQuantity a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dynamic

Methods

dynamicDimension :: DynQuantity a -> DynamicDimension Source #

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDynamicDimension (Proxy ('Dim l m t i th n j)) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TypeLevel

Methods

dynamicDimension :: Proxy ('Dim l m t i th n j) -> DynamicDimension Source #

KnownDimension d => HasDynamicDimension (Dimensional v d a) Source # 
Instance details

Defined in Numeric.Units.Dimensional.Internal

Methods

dynamicDimension :: Dimensional v d a -> DynamicDimension Source #

data DynamicDimension Source #

The dimension of a dynamic value, which may not have any dimension at all.

Constructors

NoDimension

The value has no valid dimension.

SomeDimension Dimension'

The value has the given dimension.

AnyDimension

The value may be interpreted as having any dimension.

Instances

Instances details
Data DynamicDimension 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) -> DynamicDimension -> c DynamicDimension #

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

toConstr :: DynamicDimension -> Constr #

dataTypeOf :: DynamicDimension -> DataType #

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

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

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

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

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

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

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

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

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

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

Generic DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Associated Types

type Rep DynamicDimension 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

type Rep DynamicDimension = D1 ('MetaData "DynamicDimension" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.6.1-5Kh45RH4yKfKQGqcIykmmd" 'False) (C1 ('MetaCons "NoDimension" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "SomeDimension" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Dimension')) :+: C1 ('MetaCons "AnyDimension" 'PrefixI 'False) (U1 :: Type -> Type)))

Methods

from :: DynamicDimension -> Rep DynamicDimension x #

to :: Rep DynamicDimension x -> DynamicDimension #

Show DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

showsPrec :: Int -> DynamicDimension -> ShowS #

show :: DynamicDimension -> String #

showList :: [DynamicDimension] -> ShowS #

NFData DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

rnf :: DynamicDimension -> () #

HasDynamicDimension DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

dynamicDimension :: DynamicDimension -> DynamicDimension Source #

Eq DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

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

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

Ord DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

Methods

compare :: DynamicDimension -> DynamicDimension -> Ordering #

(<) :: DynamicDimension -> DynamicDimension -> Bool #

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

(>) :: DynamicDimension -> DynamicDimension -> Bool #

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

max :: DynamicDimension -> DynamicDimension -> DynamicDimension #

min :: DynamicDimension -> DynamicDimension -> DynamicDimension #

type Rep DynamicDimension Source # 
Instance details

Defined in Numeric.Units.Dimensional.Dimensions.TermLevel

type Rep DynamicDimension = D1 ('MetaData "DynamicDimension" "Numeric.Units.Dimensional.Dimensions.TermLevel" "dimensional-1.6.1-5Kh45RH4yKfKQGqcIykmmd" 'False) (C1 ('MetaCons "NoDimension" 'PrefixI 'False) (U1 :: Type -> Type) :+: (C1 ('MetaCons "SomeDimension" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Dimension')) :+: C1 ('MetaCons "AnyDimension" 'PrefixI 'False) (U1 :: Type -> Type)))

Dimension Arithmetic

(*) :: Dimension' -> Dimension' -> Dimension' infixl 7 Source #

Forms the product of two dimensions.

(/) :: Dimension' -> Dimension' -> Dimension' infixl 7 Source #

Forms the quotient of two dimensions.

(^) :: Dimension' -> Int -> Dimension' infixr 8 Source #

Raises a dimension to an integer power.

recip :: Dimension' -> Dimension' Source #

Forms the reciprocal of a dimension.

nroot :: Int -> Dimension' -> Maybe Dimension' Source #

Takes the nth root of a dimension, if it exists.

n must not be zero.

nroot (negate n) d == nroot n (recip d)

sqrt :: Dimension' -> Maybe Dimension' Source #

Takes the square root of a dimension, if it exists.

sqrt d == nroot 2 d

cbrt :: Dimension' -> Maybe Dimension' Source #

Takes the cube root of a dimension, if it exists.

cbrt d == nroot 3 d

Synonyms for Base Dimensions

dOne :: Dimension' Source #

The dimension of dimensionless values.

dLength :: Dimension' Source #

dMass :: Dimension' Source #

dTime :: Dimension' Source #

dElectricCurrent :: Dimension' Source #

dThermodynamicTemperature :: Dimension' Source #

dAmountOfSubstance :: Dimension' Source #

dLuminousIntensity :: Dimension' Source #

Deconstruction

asList :: Dimension' -> [Int] Source #

Converts a dimension to a list of 7 integers, representing the exponent associated with each of the 7 SI base dimensions in the standard order.

Examining Dynamic Dimensions

matchDimensions :: DynamicDimension -> DynamicDimension -> DynamicDimension Source #

Combines two DynamicDimensions, determining the DynamicDimension of a quantity that must match both inputs.

This is the lattice meet operation for DynamicDimension.

isCompatibleWith :: HasDynamicDimension a => a -> Dimension' -> Bool Source #

Determines if a value that has a DynamicDimension is compatible with a specified Dimension'.

hasSomeDimension :: HasDynamicDimension a => a -> Bool Source #

Determines if a value that has a DynamicDimension in fact has any valid dimension at all.