uom-plugin-0.2.0.1: Units of measure as a GHC typechecker plugin

Data.UnitsOfMeasure

Description

See Data.UnitsOfMeasure.Tutorial for how to use this module.

Synopsis

# Type-level units of measure

data Unit Source

(Kind) Units of measure

type family Base b :: Unit Source

Base unit

type family One :: Unit Source

Dimensionless unit (identity element)

type family u *: v :: Unit infixl 7 Source

Multiplication for units of measure

type family u /: v :: Unit infixl 7 Source

Division for units of measure

type family u ^: n :: Unit infixr 8 Source

Exponentiation (to a positive power) for units of measure; negative exponents are not yet supported (they require an Integer kind)

Equations

 u ^: 0 = One u ^: 1 = u u ^: n = u *: (u ^: (n - 1))

# Values indexed by their units

data Quantity a u Source

A `Quantity a u` is represented identically to a value of underlying numeric type `a`, but with units `u`.

Instances

 Bounded a => Bounded (Quantity a u) Source (Enum a, (~) Unit u One) => Enum (Quantity a u) Source Eq a => Eq (Quantity a u) Source (Floating a, (~) Unit u One) => Floating (Quantity a u) Source (Fractional a, (~) Unit u One) => Fractional (Quantity a u) Source (Integral a, (~) Unit u One) => Integral (Quantity a u) Source (Num a, (~) Unit u One) => Num (Quantity a u) Source Ord a => Ord (Quantity a u) Source (Real a, (~) Unit u One) => Real (Quantity a u) Source (RealFloat a, (~) Unit u One) => RealFloat (Quantity a u) Source (RealFrac a, (~) Unit u One) => RealFrac (Quantity a u) Source Storable a => Storable (Quantity a u) Source NFData a => NFData (Quantity a u) Source

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.

Convert a `Rational` quantity into any `Fractional` type (`fromRational`).

# 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.

# TH constructor for quantities/units

The `u` quasiquoter may be used to create units or quantities; its meaning depends on the context:

• in a declaration context, it creates new base and derived units from a comma-separated list of names with optional definitions, for example `[u|kg, m, s, N = kg * m/s^2|]`;
• in a type context, it parses a single unit and converts it into the corresponding type, so `[u|m/s|]` becomes the type `Base "m" /: Base "s"` of kind `Unit`;
• in an expression context, it can be used to create a `Quantity` corresponding to a numeric literal, for example `[u|42 m|]` is an expression of type `Quantity Integer (Base "m")`, `[u|-2.2 m|]` is an expression of type `Quantity Double (Base "m")`, and `[u|m|]` alone is a function of type `a -> Quantity a (Base "m")`;
• in a pattern context, it can be used to match on a particular value of a quantity with an `Integer` or `Rational` representation type, for example `f [u| 42 m |] = True` is a (partial) function of type `Quantity Integer [u|m|] -> Bool`.

# Declaring units

Declare a canonical base unit of the given name, which must not contain any spaces, e.g.

`declareBaseUnit "m"`

produces

```type instance MkUnit "m" = Base "m"
instance HasCanonicalBaseUnit "m"```

This can also be written `[u| m |]`.

Declare a derived unit with the given name and definition, e.g.

`declareDerivedUnit "N" "kg m / s^2"`

produces

`type instance MkUnit "N" = Base "kg" *: Base "m" /: Base "s" ^: 2`

This can also be written `[u| N = kg m / s^2 |]`.

Declare a base unit of the given name, which is convertible to the canonical base unit, e.g.

`declareConvertibleUnit "kilobyte" 1024 "byte"`

produces

```type instance MkUnit "kilobyte" = Base "kilobyte"
instance HasCanonicalBaseUnit "kilobyte" where
type CanonicalBaseUnit "kilobyte" = Base "byte"
conversionBase _ = [u| 1 % 1024 kilobyte/byte |]```

This can also be written `[u| kilobyte = 1024 byte |]`. See Data.UnitsOfMeasure.Convert for more information about conversions.

# Automatic unit conversions

convert :: forall a u v. (Fractional a, Convertible u v) => Quantity a u -> Quantity a v Source

Automatically convert a quantity with units `u` so that its units are `v`, provided `u` and `v` have the same dimension.

# Pay no attention to that man behind the curtain

type family MkUnit s :: Unit Source

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.

Instances

 type MkUnit "A" = Base "A" Source type MkUnit "C" = (*:) (MkUnit "s") (MkUnit "A") Source type MkUnit "F" = (/:) (MkUnit "C") (MkUnit "V") Source type MkUnit "Hz" = (/:) One ((^:) (MkUnit "s") 1) Source type MkUnit "J" = (*:) (MkUnit "N") (MkUnit "m") Source type MkUnit "K" = Base "K" Source type MkUnit "N" = (/:) ((*:) (MkUnit "kg") (MkUnit "m")) ((^:) (MkUnit "s") 2) Source type MkUnit "Pa" = (/:) (MkUnit "N") ((^:) (MkUnit "m") 2) Source type MkUnit "V" = (/:) (MkUnit "W") (MkUnit "A") Source type MkUnit "W" = (/:) (MkUnit "J") (MkUnit "s") Source type MkUnit "au" = Base "au" Source type MkUnit "cd" = Base "cd" Source type MkUnit "d" = Base "d" Source type MkUnit "ft" = Base "ft" Source type MkUnit "g" = Base "g" Source type MkUnit "h" = Base "h" Source type MkUnit "ha" = Base "ha" Source type MkUnit "in" = Base "in" Source type MkUnit "kg" = Base "kg" Source type MkUnit "km" = Base "km" Source type MkUnit "l" = Base "l" Source type MkUnit "m" = Base "m" Source type MkUnit "mi" = Base "mi" Source type MkUnit "min" = Base "min" Source type MkUnit "mol" = Base "mol" Source type MkUnit "mph" = (/:) (MkUnit "mi") (MkUnit "h") Source type MkUnit "ohm" = (/:) (MkUnit "V") (MkUnit "A") Source type MkUnit "rad" = Base "rad" Source type MkUnit "s" = Base "s" Source type MkUnit "sr" = Base "sr" Source type MkUnit "t" = Base "t" Source

type family Pack u :: Unit 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).

Equations

 Pack (xs :/ ys) = Prod xs /: Prod ys

type family Unpack u :: UnitSyntax Symbol Source

Unpack a unit as a syntactic representation, where the order of units is deterministic. For example:

` `Unpack` `One` = [] `:/` []`
` `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.

class KnownUnit u Source

A constraint `KnownUnit u` means that `u` must be a concrete unit that is statically known but passed at runtime

Minimal complete definition

unitSing

Instances

 (KnownList xs, KnownList ys) => KnownUnit ((:/) Symbol xs ys) Source