| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Data.UnitsOfMeasure.Internal
Description
This module defines the core types used in the uom-plugin
library. Note that importing this module may allow you to violate
invariants, so you should generally work with the safe interface in
Data.UnitsOfMeasure instead.
Synopsis
- data Unit
- type family One :: Unit where ...
- type family Base b where ...
- type family u *: v where ...
- type family u /: v where ...
- type family u ^: n where ...
- newtype Quantity a (u :: Unit) = MkQuantity a
- unQuantity :: Quantity a u -> a
- zero :: Num a => Quantity a u
- mk :: a -> Quantity a One
- (+:) :: Num a => Quantity a u -> Quantity a u -> Quantity a u
- (*:) :: (Num a, w ~~ (u *: v)) => Quantity a u -> Quantity a v -> Quantity a w
- (-:) :: Num a => Quantity a u -> Quantity a u -> Quantity a u
- negate' :: Num a => Quantity a u -> Quantity a u
- abs' :: Num a => Quantity a u -> Quantity a u
- signum' :: Num a => Quantity a u -> Quantity a One
- fromInteger' :: Integral a => Quantity Integer u -> Quantity a u
- (/:) :: (Fractional a, w ~~ (u /: v)) => Quantity a u -> Quantity a v -> Quantity a w
- recip' :: (Fractional a, w ~~ (One /: u)) => Quantity a u -> Quantity a w
- fromRational' :: Fractional a => Quantity Rational u -> Quantity a u
- toRational' :: Real a => Quantity a u -> Quantity Rational u
- sqrt' :: (Floating a, w ~~ (u ^: 2)) => Quantity a w -> Quantity a u
- data UnitSyntax s = [s] :/ [s]
- type family Unpack u where ...
- type family Pack u where ...
- type family Prod xs where ...
- type family u ~~ v where ...
- type family MkUnit s
Type-level units of measure
type family u ^: n where ... infixr 8 Source #
Exponentiation (to a positive power) for units of measure; negative exponents are not yet supported (they require an Integer kind)
Values indexed by their units
newtype Quantity a (u :: Unit) Source #
A Quantity a u is represented identically to a value of
underlying numeric type a, but with units u.
Constructors
| MkQuantity a | Warning: the |
Instances
unQuantity :: Quantity a u -> a Source #
Extract the underlying value of a quantity
zero :: Num a => Quantity a u Source #
Zero is polymorphic in its units: this is required because the
Num instance constrains the quantity to be dimensionless, so
0 :: Quantity a u is not well typed.
mk :: a -> Quantity a One Source #
Construct a Quantity from a dimensionless value. Note that for
numeric literals, the Num and Fractional instances allow them
to be treated as quantities directly.
Unit-safe Num operations
(+:) :: Num a => Quantity a u -> Quantity a u -> Quantity a u infixl 6 Source #
Addition (+) of quantities requires the units to match.
(*:) :: (Num a, w ~~ (u *: v)) => Quantity a u -> Quantity a v -> Quantity a w infixl 7 Source #
Multiplication (*) of quantities multiplies the units.
(-:) :: Num a => Quantity a u -> Quantity a u -> Quantity a u infixl 6 Source #
Subtraction (-) of quantities requires the units to match.
negate' :: Num a => Quantity a u -> Quantity a u Source #
Negation (negate) of quantities is polymorphic in the units.
abs' :: Num a => Quantity a u -> Quantity a u Source #
Absolute value (abs) of quantities is polymorphic in the units.
signum' :: Num a => Quantity a u -> Quantity a One Source #
The sign (signum) of a quantity gives a dimensionless result.
fromInteger' :: Integral a => Quantity Integer u -> Quantity a u Source #
Convert an Integer quantity into any Integral type (fromInteger).
Unit-safe Fractional operations
(/:) :: (Fractional a, w ~~ (u /: v)) => Quantity a u -> Quantity a v -> Quantity a w infixl 7 Source #
Division (/) of quantities divides the units.
recip' :: (Fractional a, w ~~ (One /: u)) => Quantity a u -> Quantity a w Source #
Reciprocal (recip) of quantities reciprocates the units.
fromRational' :: Fractional a => Quantity Rational u -> Quantity a u Source #
Convert a Rational quantity into any Fractional type (fromRational).
Unit-safe Real operations
toRational' :: Real a => Quantity a u -> Quantity Rational u Source #
Convert any Real quantity into a Rational type (toRational).
Unit-safe Floating operations
sqrt' :: (Floating a, w ~~ (u ^: 2)) => Quantity a w -> Quantity a u Source #
Taking the square root (sqrt) of a quantity requires its units
to be a square. Fractional units are not currently supported.
Syntactic representation of units
data UnitSyntax s Source #
Syntactic representation of a unit as a pair of lists of base
units, for example One is represented as [] and
:/ []Base "m" /: Base "s" ^: 2["m"] .:/ ["s","s"]
Constructors
| [s] :/ [s] |
Instances
| Show s => Show (UnitSyntax s) Source # | |
Defined in Data.UnitsOfMeasure.Internal Methods showsPrec :: Int -> UnitSyntax s -> ShowS # show :: UnitSyntax s -> String # showList :: [UnitSyntax s] -> ShowS # | |
| Eq s => Eq (UnitSyntax s) Source # | |
Defined in Data.UnitsOfMeasure.Internal | |
| TestEquality SUnit Source # | |
Defined in Data.UnitsOfMeasure.Singleton | |
type family Unpack u where ... Source #
Unpack a unit as a syntactic representation, where the order of units is deterministic. For example:
UnpackOne= []:/[]
Unpack(Base"s"*:Base"m") = ["m","s"]:/[]
This does not break type soundness because
Unpack will reduce only when the unit is entirely constant, and
it does not allow the structure of the unit to be observed. The
reduction behaviour is implemented by the plugin, because we cannot
define it otherwise.
type family Pack u where ... Source #
Pack up a syntactic representation of a unit as a unit. For example:
Pack([]:/[]) =One
Pack(["m"]:/["s","s"]) =Base"m"/:Base"s" ^: 2
This is a perfectly ordinary closed type family. Pack is a left
inverse of Unpack up to the equational theory of units, but it is
not a right inverse (because there are multiple list
representations of the same unit).
Internal
type family u ~~ v where ... infix 4 Source #
This is a bit of a hack, honestly, but a good hack. Constraints
u ~~ v are just like equalities u ~ v, except solving them will
be delayed until the plugin. This may lead to better inferred types.
This type family is used for translating unit names (as
type-level strings) into units. It will be Base for base units
or expand the definition for derived units.
The instances displayed by Haddock are available only if Data.UnitsOfMeasure.Defs is imported.