Copyright	Copyright (C) 2006-2015 Bjorn Buckwalter
License	BSD3
Maintainer	bjorn@buckwalter.se
Stability	Stable
Portability	GHC only
Safe Haskell	Safe
Language	Haskell2010
Extensions	MonoLocalBinds ScopedTypeVariables TypeFamilies ConstraintKinds DataKinds TypeSynonymInstances FlexibleContexts FlexibleInstances KindSignatures TypeOperators ExplicitNamespaces ExplicitForAll

Numeric.Units.Dimensional.Dimensions.TypeLevel

Contents

Kind of Type-Level Dimensions
Dimension Arithmetic
Synonyms for Base Dimensions
Conversion to Term Level

Description

This module defines type-level physical dimensions expressed in terms of the SI base dimensions using NumType for type-level integers.

Type-level arithmetic, synonyms for the base dimensions, and conversion to the term-level are included.

Synopsis

Kind of Type-Level Dimensions

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'

Constructors

Dim TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt TypeInt

Instances

(KnownTypeInt l, KnownTypeInt m, KnownTypeInt t, KnownTypeInt i, KnownTypeInt th, KnownTypeInt n, KnownTypeInt j) => HasDimension (Proxy Dimension (Dim l m t i th n j)) Source

Dimension Arithmetic

type family a * b 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 family a / d 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 d ^ x 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 = 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 Root d x Source

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

See sqrt, cbrt, and nroot for the corresponding term-level operations.

Equations

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

Synonyms for Base Dimensions

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

The type-level dimensions of dimensionless values.

type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero Source

type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero Source

type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero Source

type DElectricCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero Source

type DThermodynamicTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero Source

type DAmountOfSubstance = Dim Zero Zero Zero Zero Zero Pos1 Zero Source

type DLuminousIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1 Source

Conversion to Term Level

type KnownDimension d = 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'.