numeric-prelude-0.4.3.1: An experimental alternative hierarchy of numeric type classes

Safe HaskellSafe
LanguageHaskell98

Algebra.DimensionTerm

Contents

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

Documentation

class Show a => C a Source #

Instances
C Voltage Source # 
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Defined in Algebra.DimensionTerm

C Information Source # 
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C Temperature Source # 
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C Angle Source # 
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C Charge Source # 
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C Mass Source # 
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C Time Source # 
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C Length Source # 
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C Scalar Source # 
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C a => C (Recip a) Source # 
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(C a, C b) => C (Mul a b) Source # 
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noValue :: C a => a Source #

Type constructors

data Scalar Source #

Constructors

Scalar 
Instances
Show Scalar Source # 
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IsScalar Scalar Source # 
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C Scalar Source # 
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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 # 
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Defined in Algebra.DimensionTerm

data Recip a Source #

Constructors

Recip 
Instances
Show a => Show (Recip a) Source # 
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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 #

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 #

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

Basis dimensions

data Length Source #

Constructors

Length 
Instances
Show Length Source # 
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C Length Source # 
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data Time Source #

Constructors

Time 
Instances
Show Time Source # 
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Methods

showsPrec :: Int -> Time -> ShowS #

show :: Time -> String #

showList :: [Time] -> ShowS #

C Time Source # 
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Defined in Algebra.DimensionTerm

data Mass Source #

Constructors

Mass 
Instances
Show Mass Source # 
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Methods

showsPrec :: Int -> Mass -> ShowS #

show :: Mass -> String #

showList :: [Mass] -> ShowS #

C Mass Source # 
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Defined in Algebra.DimensionTerm

data Charge Source #

Constructors

Charge 
Instances
Show Charge Source # 
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C Charge Source # 
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data Angle Source #

Constructors

Angle 
Instances
Show Angle Source # 
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Defined in Algebra.DimensionTerm

Methods

showsPrec :: Int -> Angle -> ShowS #

show :: Angle -> String #

showList :: [Angle] -> ShowS #

C Angle Source # 
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data Temperature Source #

Constructors

Temperature 
Instances
Show Temperature Source # 
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C Temperature Source # 
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data Information Source #

Constructors

Information 
Instances
Show Information Source # 
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C Information Source # 
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Derived dimensions

data Voltage Source #

Constructors

Voltage 
Instances
Show Voltage Source # 
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Defined in Algebra.DimensionTerm

C Voltage Source # 
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Defined in Algebra.DimensionTerm