Safe Haskell	Safe
Language	Haskell98

Algebra.DimensionTerm

Contents

Type constructors
Rewrites
Example dimensions

Description

We already have the dynamically checked physical units provided by Number.Physical and the statically checked ones of the dimensional package of Buckwalter, which require multi-parameter type classes with functional dependencies.

Here we provide a poor man's approach: The units are presented by type terms. There is no canonical form and thus the type checker can not automatically check for equal units. However, if two unit terms represent the same unit, then you can tell the type checker to rewrite one into the other.

You can add more dimensions by introducing more types of class C.

This approach is not entirely safe because you can write your own flawed rewrite rules. It is however more safe than with no units at all.

Synopsis

class Show a => C a
noValue :: C a => a
data Scalar = Scalar
data Mul a b = Mul
data Recip a = Recip
type Sqr a = Mul a a
appPrec :: Int
scalar :: Scalar
mul :: (C a, C b) => a -> b -> Mul a b
recip :: C a => a -> Recip a
(%*%) :: (C a, C b) => a -> b -> Mul a b
(%/%) :: (C a, C b) => a -> b -> Mul a (Recip b)
applyLeftMul :: (C u0, C u1, C v) => (u0 -> u1) -> Mul u0 v -> Mul u1 v
applyRightMul :: (C u0, C u1, C v) => (u0 -> u1) -> Mul v u0 -> Mul v u1
applyRecip :: (C u0, C u1) => (u0 -> u1) -> Recip u0 -> Recip u1
commute :: (C u0, C u1) => Mul u0 u1 -> Mul u1 u0
associateLeft :: (C u0, C u1, C u2) => Mul u0 (Mul u1 u2) -> Mul (Mul u0 u1) u2
associateRight :: (C u0, C u1, C u2) => Mul (Mul u0 u1) u2 -> Mul u0 (Mul u1 u2)
recipMul :: (C u0, C u1) => Recip (Mul u0 u1) -> Mul (Recip u0) (Recip u1)
mulRecip :: (C u0, C u1) => Mul (Recip u0) (Recip u1) -> Recip (Mul u0 u1)
identityLeft :: C u => Mul Scalar u -> u
identityRight :: C u => Mul u Scalar -> u
cancelLeft :: C u => Mul (Recip u) u -> Scalar
cancelRight :: C u => Mul u (Recip u) -> Scalar
invertRecip :: C u => Recip (Recip u) -> u
doubleRecip :: C u => u -> Recip (Recip u)
recipScalar :: Recip Scalar -> Scalar
class C dim => IsScalar dim where
data Length = Length
data Time = Time
data Mass = Mass
data Charge = Charge
data Angle = Angle
data Temperature = Temperature
data Information = Information
length :: Length
time :: Time
mass :: Mass
charge :: Charge
angle :: Angle
temperature :: Temperature
information :: Information
type Frequency = Recip Time
frequency :: Frequency
data Voltage = Voltage
type VoltageAnalytical = Mul (Mul (Sqr Length) Mass) (Recip (Mul (Sqr Time) Charge))
voltage :: Voltage
unpackVoltage :: Voltage -> VoltageAnalytical
packVoltage :: VoltageAnalytical -> Voltage

Documentation

class Show a => C a Source #

Instances

C Voltage Source #
Instance details Defined in Algebra.DimensionTerm
C Information Source #
Instance details Defined in Algebra.DimensionTerm
C Temperature Source #
Instance details Defined in Algebra.DimensionTerm
C Angle Source #
Instance details Defined in Algebra.DimensionTerm
C Charge Source #
Instance details Defined in Algebra.DimensionTerm
C Mass Source #
Instance details Defined in Algebra.DimensionTerm
C Time Source #
Instance details Defined in Algebra.DimensionTerm
C Length Source #
Instance details Defined in Algebra.DimensionTerm
C Scalar Source #
Instance details Defined in Algebra.DimensionTerm
C a => C (Recip a) Source #
Instance details Defined in Algebra.DimensionTerm
(C a, C b) => C (Mul a b) Source #
Instance details Defined in Algebra.DimensionTerm

noValue :: C a => a Source #

Type constructors

data Scalar Source #

Constructors

Scalar

Instances

Show Scalar Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Scalar -> ShowS # show :: Scalar -> String # showList :: [Scalar] -> ShowS #
IsScalar Scalar Source #
Instance details Defined in Algebra.DimensionTerm Methods toScalar :: Scalar -> Scalar Source # fromScalar :: Scalar -> Scalar Source #
C Scalar Source #
Instance details Defined in Algebra.DimensionTerm

data Mul a b Source #

Constructors

Mul

Instances

(Show a, Show b) => Show (Mul a b) Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Mul a b -> ShowS # show :: Mul a b -> String # showList :: [Mul a b] -> ShowS #
(C a, C b) => C (Mul a b) Source #
Instance details Defined in Algebra.DimensionTerm

data Recip a Source #

Constructors

Recip

Instances

Show a => Show (Recip a) Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Recip a -> ShowS # show :: Recip a -> String # showList :: [Recip a] -> ShowS #
C a => C (Recip a) Source #
Instance details Defined in Algebra.DimensionTerm

type Sqr a = Mul a a Source #

appPrec :: Int Source #

scalar :: Scalar Source #

mul :: (C a, C b) => a -> b -> Mul a b Source #

recip :: C a => a -> Recip a Source #

(%*%) :: (C a, C b) => a -> b -> Mul a b infixl 7 Source #

(%/%) :: (C a, C b) => a -> b -> Mul a (Recip b) infixl 7 Source #

Rewrites

applyLeftMul :: (C u0, C u1, C v) => (u0 -> u1) -> Mul u0 v -> Mul u1 v Source #

applyRightMul :: (C u0, C u1, C v) => (u0 -> u1) -> Mul v u0 -> Mul v u1 Source #

applyRecip :: (C u0, C u1) => (u0 -> u1) -> Recip u0 -> Recip u1 Source #

commute :: (C u0, C u1) => Mul u0 u1 -> Mul u1 u0 Source #

associateLeft :: (C u0, C u1, C u2) => Mul u0 (Mul u1 u2) -> Mul (Mul u0 u1) u2 Source #

associateRight :: (C u0, C u1, C u2) => Mul (Mul u0 u1) u2 -> Mul u0 (Mul u1 u2) Source #

recipMul :: (C u0, C u1) => Recip (Mul u0 u1) -> Mul (Recip u0) (Recip u1) Source #

mulRecip :: (C u0, C u1) => Mul (Recip u0) (Recip u1) -> Recip (Mul u0 u1) Source #

identityLeft :: C u => Mul Scalar u -> u Source #

identityRight :: C u => Mul u Scalar -> u Source #

cancelLeft :: C u => Mul (Recip u) u -> Scalar Source #

cancelRight :: C u => Mul u (Recip u) -> Scalar Source #

invertRecip :: C u => Recip (Recip u) -> u Source #

doubleRecip :: C u => u -> Recip (Recip u) Source #

recipScalar :: Recip Scalar -> Scalar Source #

Example dimensions

Scalar

class C dim => IsScalar dim where Source #

This class allows defining instances that are exclusively for Scalar dimension. You won't want to define instances by yourself.

Minimal complete definition

toScalar, fromScalar

Methods

toScalar :: dim -> Scalar Source #

fromScalar :: Scalar -> dim Source #

Instances

IsScalar Scalar Source #
Instance details Defined in Algebra.DimensionTerm Methods toScalar :: Scalar -> Scalar Source # fromScalar :: Scalar -> Scalar Source #

Basis dimensions

data Length Source #

Constructors

Length

Instances

Show Length Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Length -> ShowS # show :: Length -> String # showList :: [Length] -> ShowS #
C Length Source #
Instance details Defined in Algebra.DimensionTerm

data Time Source #

Constructors

Time

Instances

Show Time Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Time -> ShowS # show :: Time -> String # showList :: [Time] -> ShowS #
C Time Source #
Instance details Defined in Algebra.DimensionTerm

data Mass Source #

Constructors

Mass

Instances

Show Mass Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Mass -> ShowS # show :: Mass -> String # showList :: [Mass] -> ShowS #
C Mass Source #
Instance details Defined in Algebra.DimensionTerm

data Charge Source #

Constructors

Charge

Instances

Show Charge Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Charge -> ShowS # show :: Charge -> String # showList :: [Charge] -> ShowS #
C Charge Source #
Instance details Defined in Algebra.DimensionTerm

data Angle Source #

Constructors

Angle

Instances

Show Angle Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Angle -> ShowS # show :: Angle -> String # showList :: [Angle] -> ShowS #
C Angle Source #
Instance details Defined in Algebra.DimensionTerm

data Temperature Source #

Constructors

Temperature

Instances

Show Temperature Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Temperature -> ShowS # show :: Temperature -> String # showList :: [Temperature] -> ShowS #
C Temperature Source #
Instance details Defined in Algebra.DimensionTerm

data Information Source #

Constructors

Information

Instances

Show Information Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Information -> ShowS # show :: Information -> String # showList :: [Information] -> ShowS #
C Information Source #
Instance details Defined in Algebra.DimensionTerm

length :: Length Source #

time :: Time Source #

mass :: Mass Source #

charge :: Charge Source #

angle :: Angle Source #

temperature :: Temperature Source #

information :: Information Source #

Derived dimensions

type Frequency = Recip Time Source #

frequency :: Frequency Source #

data Voltage Source #

Constructors

Voltage

Instances

Show Voltage Source #
Instance details Defined in Algebra.DimensionTerm Methods showsPrec :: Int -> Voltage -> ShowS # show :: Voltage -> String # showList :: [Voltage] -> ShowS #
C Voltage Source #
Instance details Defined in Algebra.DimensionTerm

type VoltageAnalytical = Mul (Mul (Sqr Length) Mass) (Recip (Mul (Sqr Time) Charge)) Source #

voltage :: Voltage Source #

unpackVoltage :: Voltage -> VoltageAnalytical Source #

packVoltage :: VoltageAnalytical -> Voltage Source #