-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Simple arithmetic with SI units using type-checked dimensional analysis.
--
-- Please see the README on GitHub at
-- https://github.com/groscoe/simple-units#readme
@package simple-units
@version 1.0.2
module Units.Simple
-- | A numerical quantity with some associated unit. Units are not created
-- directly with this constructor, but through the individual unit
-- functions.
--
-- Examples:
--
--
-- >>> import Units.Simple
--
-- >>> meter -- a unitary quantity associated to meters.
-- 1 m
--
-- >>> 2.5*ampere -- constructing through literal arithmetic
-- 2.5 A
--
-- >>> candela' 3.14 -- constructing through the unit constructors
-- 3.14 cd
--
-- >>> :set -XDataKinds
--
-- >>> 2 :: Quantity (SingleUnit 'Second) Rational
-- 2 % 1 s
--
--
-- Associated units are represented through a phantom parameter of the
-- Units kind synonym. These are currently implemented as a
-- type-level pair of lists representing the power to which each unit is
-- raised. Units can be inspected through showUnits.
--
-- New constructors may be written by combining the provided ones, such
-- as
--
--
-- >>> let newton = kilogram .* meter ./ (second .* second)
--
-- >>> 23*newton
-- 23.0 kg*m/s^2
--
--
-- >>> let g = 6.67408e-11 * newton .* (meter .* meter) ./ (kilogram .* kilogram)
--
-- >>> g -- gravitational constant
-- 6.67408e-11 m^3/kg*s^2
--
-- >>> let gravity m1 m2 r = g .* (m1 * kilogram) .* (m2 * kilogram) ./ (r*meter .* r*meter)
--
-- >>> let earth_mass = 5.972e24 * kilo gram
--
-- >>> let mars_mass = 6.417e23 * kilo gram
--
-- >>> let earth_radius = 6371 * kilo meter
--
-- >>> let mars_radius = 3389.5 * kilo meter
--
-- >>> let weight_on_earth mass = gravity mass earth_mass earth_radius
--
-- >>> let weight_on_mars mass = gravity mass mars_mass mars_radius
--
-- >>> weight_on_earth (80 * kilo gram)
-- 785.5719790179963 kg*m/s^2
--
-- >>> weight_on_mars (80 * kilo gram)
-- 298.22370259533704 kg*m/s^2
--
-- >>> weight_on_mars 1 / weight_on_earth 1
-- 0.3796261966575378 <adimensional>
--
data Quantity (us :: Units) a
-- | Unwraps a Quantity, losing all unit information
fromQuantity :: Quantity us a -> a
data Unit
Meter :: Unit
Kilogram :: Unit
Second :: Unit
Ampere :: Unit
Kelvin :: Unit
Mole :: Unit
Candela :: Unit
type Units = ([Unit'], [Unit'])
type SingleUnit (u :: Unit) = '('['(u, 1)], '[])
type UnitRepr (us :: Units) = UnitRepr' (Eval (Fst us)) (Eval (Snd us))
-- | A string representation of Units. Useful for debugging.
showUnits :: forall us. KnownSymbol (UnitRepr us) => String
-- | Sums two quantities with the same units. Summing quantities with
-- different units results in a type error.
--
-- Examples:
--
--
-- >>> import Units.Simple
--
-- >>> 2 * kilo meter .+ 3 * kilo meter
-- 5000 m
--
-- >>> 2*meter .+ 1*second
--
-- <interactive>... error:
-- • Unit mismatch: m and s
-- • In the expression: 2 * meter .+ 1 * second
-- In an equation for ‘it’: it = 2 * meter .+ 1 * second
--
(.+) :: (SameUnits u1 u2, Num a) => Quantity u1 a -> Quantity u2 a -> Quantity u1 a
infixl 5 .+
-- | Subtracts two quantities with the same units. Subtracting quantities
-- with different units results in a type error.
--
-- Examples:
--
--
-- >>> import Units.Simple
--
-- >>> let newton = kilogram .* meter ./ (second .* second)
--
-- >>> 10*newton - 2*newton
-- 8.0 kg*m/s^2
--
(.-) :: (SameUnits u1 u2, Num a) => Quantity u1 a -> Quantity u2 a -> Quantity u1 a
infixl 5 .-
-- | Multiplies two quantities correctly merging their units.
--
-- Examples:
--
--
-- >>> import Units.Simple
--
-- >>> meter .* meter
-- 1 m^2
--
-- >>> let mps = meter ./ second
--
-- >>> 20*mps .* 60*second
-- 1200.0 m
--
--
-- Important: Though Quantity a has a Num
-- instance for convenience, it must not be used for anything
-- other than interacting with literals, otherwise the units will
-- not be correct:
--
--
-- >>> 2*meter * 3*meter -- note that (*) was used in place of (.*)
-- 6 m
--
-- >>> 2*meter .* 3*meter -- this is the correct usage
-- 6 m^2
--
(.*) :: Num a => Quantity us1 a -> Quantity us2 a -> Quantity (MergeUnits us1 us2) a
infixl 6 .*
-- | Divides a quantity by another correctly merging their units.
--
-- Examples:
--
--
-- >>> import Units.Simple
--
-- >>> let coulomb = second .* ampere
--
-- >>> 20*coulomb ./ 2*second
-- 10.0 A
--
(./) :: Fractional a => Quantity us1 a -> Quantity us2 a -> Quantity (MergeUnits us1 (Recip us2)) a
infixl 6 ./
-- | A Quantity with no associated dimension. Can be multiplied or
-- divided by any other Quantity, but can only be added to or
-- subtracted from another adimensional Quantity.
--
--
-- >>> 2*adim + 4*adim
-- 6 <adimensional>
--
-- >>> adim .+ meter
--
-- <interactive>... error:
-- • Unit mismatch: <adimensional> and m
-- • In the expression: adim .+ meter
-- In an equation for ‘it’: it = adim .+ meter
--
adim :: Num a => Quantity Adimensional a
adim' :: Num a => a -> Quantity Adimensional a
meter :: Num a => Quantity (SingleUnit 'Meter) a
meter' :: Num a => a -> Quantity (SingleUnit 'Meter) a
kilogram :: Num a => Quantity (SingleUnit 'Kilogram) a
kilogram' :: Num a => a -> Quantity (SingleUnit 'Kilogram) a
-- | A constructor for 1/1000th of a kilogram, to use with SI prefixes.
gram :: Fractional a => Quantity (SingleUnit 'Kilogram) a
-- | A constructor for 1/1000th of a kilogram, to use with SI prefixes.
gram' :: Fractional a => a -> Quantity (SingleUnit 'Kilogram) a
second :: Num a => Quantity (SingleUnit 'Second) a
second' :: Num a => a -> Quantity (SingleUnit 'Second) a
ampere :: Num a => Quantity (SingleUnit 'Ampere) a
ampere' :: Num a => a -> Quantity (SingleUnit 'Ampere) a
kelvin :: Num a => Quantity (SingleUnit 'Kelvin) a
kelvin' :: Num a => a -> Quantity (SingleUnit 'Kelvin) a
mole :: Num a => Quantity (SingleUnit 'Mole) a
mole' :: Num a => a -> Quantity (SingleUnit 'Mole) a
candela :: Num a => Quantity (SingleUnit 'Candela) a
candela' :: Num a => a -> Quantity (SingleUnit 'Candela) a
yocto :: Fractional a => Quantity us a -> Quantity us a
yocto' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
zepto :: Fractional a => Quantity us a -> Quantity us a
zepto' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
atto :: Fractional a => Quantity us a -> Quantity us a
atto' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
femto :: Fractional a => Quantity us a -> Quantity us a
femto' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
pico :: Fractional a => Quantity us a -> Quantity us a
pico' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
nano :: Fractional a => Quantity us a -> Quantity us a
nano' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
micro :: Fractional a => Quantity us a -> Quantity us a
micro' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
milli :: Fractional a => Quantity us a -> Quantity us a
milli' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
centi :: Fractional a => Quantity us a -> Quantity us a
centi' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
deci :: Fractional a => Quantity us a -> Quantity us a
deci' :: Fractional a => (a -> Quantity us a) -> a -> Quantity us a
deka :: Num a => Quantity us a -> Quantity us a
deka' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
hecto :: Num a => Quantity us a -> Quantity us a
hecto' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
kilo :: Num a => Quantity us a -> Quantity us a
kilo' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
mega :: Num a => Quantity us a -> Quantity us a
mega' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
giga :: Num a => Quantity us a -> Quantity us a
giga' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
tera :: Num a => Quantity us a -> Quantity us a
tera' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
peta :: Num a => Quantity us a -> Quantity us a
peta' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
exa :: Num a => Quantity us a -> Quantity us a
exa' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
zetta :: Num a => Quantity us a -> Quantity us a
zetta' :: Num a => (a -> Quantity us a) -> a -> Quantity us a
yotta :: Num a => Quantity us a -> Quantity us a
yotta' :: Num a => (a -> Quantity us a) -> a -> Quantity us a