o-clock-1.2.1: Type-safe time library.
Safe HaskellNone
LanguageHaskell2010

Time.Rational

Description

This module introduces Rat kind and all necessary functional.

Synopsis

Documentation

data Rat Source #

Data structure represents the rational number. Rational number can be represented as a pair of natural numbers n and m where m is nor equal to zero.

Constructors

Nat ::% Nat 

Instances

Instances details
SeriesP ('[] :: [Rat]) Source # 
Instance details

Defined in Time.Series

Methods

seriesP :: forall (someUnit :: Rat). KnownRatName someUnit => String -> Maybe (Time someUnit) Source #

SeriesF ('[] :: [Rat]) Source # 
Instance details

Defined in Time.Series

Methods

seriesF :: forall (someUnit :: Rat). KnownRatName someUnit => Time someUnit -> String Source #

(KnownRatName unit, SeriesP (nextUnit ': units), DescendingConstraint (IsDescending (unit ': (nextUnit ': units)))) => SeriesP (unit ': (nextUnit ': units)) Source # 
Instance details

Defined in Time.Series

Methods

seriesP :: forall (someUnit :: Rat). KnownRatName someUnit => String -> Maybe (Time someUnit) Source #

KnownRatName unit => SeriesP '[unit] Source # 
Instance details

Defined in Time.Series

Methods

seriesP :: forall (someUnit :: Rat). KnownRatName someUnit => String -> Maybe (Time someUnit) Source #

(KnownRatName unit, SeriesF (nextUnit ': units), DescendingConstraint (IsDescending (unit ': (nextUnit ': units)))) => SeriesF (unit ': (nextUnit ': units)) Source # 
Instance details

Defined in Time.Series

Methods

seriesF :: forall (someUnit :: Rat). KnownRatName someUnit => Time someUnit -> String Source #

KnownRatName unit => SeriesF '[unit] Source # 
Instance details

Defined in Time.Series

Methods

seriesF :: forall (someUnit :: Rat). KnownRatName someUnit => Time someUnit -> String Source #

type DivK Nat Rat Source # 
Instance details

Defined in Time.Rational

type DivK Nat Rat = Rat
type DivK Rat Nat Source # 
Instance details

Defined in Time.Rational

type DivK Rat Nat = Rat
type DivK Rat Rat Source # 
Instance details

Defined in Time.Rational

type DivK Rat Rat = Rat
type MulK Nat Rat Source # 
Instance details

Defined in Time.Rational

type MulK Nat Rat = Rat
type MulK Rat Nat Source # 
Instance details

Defined in Time.Rational

type MulK Rat Nat = Rat
type MulK Rat Rat Source # 
Instance details

Defined in Time.Rational

type MulK Rat Rat = Rat
type (a :: Nat) / (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Nat) / (b :: Rat) = DivRat (a :% 1) b
type (a :: Rat) / (b :: Nat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) / (b :: Nat)
type (a :: Rat) / (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) / (b :: Rat) = DivRat a b
type (a :: Nat) * (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Nat) * (b :: Rat)
type (a :: Rat) * (b :: Nat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) * (b :: Nat)
type (a :: Rat) * (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) * (b :: Rat)

type (:%) = '(::%) Source #

More convenient name for promoted constructor of Rat.

type family (m :: Nat) % (n :: Nat) :: Rat where ... infixl 7 Source #

Type family for normalized pair of Nats — Rat.

Equations

a % b = Normalize (a :% b) 

type family (a :: k1) * (b :: k2) :: MulK k1 k2 Source #

Overloaded multiplication.

Instances

Instances details
type (a :: Nat) * (b :: Nat) Source # 
Instance details

Defined in Time.Rational

type (a :: Nat) * (b :: Nat) = a * b
type (a :: Nat) * (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Nat) * (b :: Rat)
type (a :: Rat) * (b :: Nat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) * (b :: Nat)
type (a :: Rat) * (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) * (b :: Rat)

type family (a :: k1) / (b :: k2) :: DivK k1 k2 Source #

Overloaded division.

Instances

Instances details
type (a :: Nat) / (b :: Nat) Source # 
Instance details

Defined in Time.Rational

type (a :: Nat) / (b :: Nat) = a % b
type (a :: Nat) / (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Nat) / (b :: Rat) = DivRat (a :% 1) b
type (a :: Rat) / (b :: Nat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) / (b :: Nat)
type (a :: Rat) / (b :: Rat) Source # 
Instance details

Defined in Time.Rational

type (a :: Rat) / (b :: Rat) = DivRat a b

type family MulK (k1 :: Type) (k2 :: Type) :: Type Source #

The result kind of overloaded multiplication.

Instances

Instances details
type MulK Nat Nat Source # 
Instance details

Defined in Time.Rational

type MulK Nat Nat = Nat
type MulK Nat Rat Source # 
Instance details

Defined in Time.Rational

type MulK Nat Rat = Rat
type MulK Rat Nat Source # 
Instance details

Defined in Time.Rational

type MulK Rat Nat = Rat
type MulK Rat Rat Source # 
Instance details

Defined in Time.Rational

type MulK Rat Rat = Rat

type family DivK (k1 :: Type) (k2 :: Type) :: Type Source #

The result kind of overloaded division.

Instances

Instances details
type DivK Nat Nat Source # 
Instance details

Defined in Time.Rational

type DivK Nat Nat = Rat
type DivK Nat Rat Source # 
Instance details

Defined in Time.Rational

type DivK Nat Rat = Rat
type DivK Rat Nat Source # 
Instance details

Defined in Time.Rational

type DivK Rat Nat = Rat
type DivK Rat Rat Source # 
Instance details

Defined in Time.Rational

type DivK Rat Rat = Rat

type family Gcd (m :: Nat) (n :: Nat) :: Nat where ... Source #

Greatest common divisor for type-level naturals.

Example:

>>> :kind! Gcd 9 11
Gcd 9 11 :: Nat
= 1
>>> :kind! Gcd 9 12
Gcd 9 12 :: Nat
= 3

Equations

Gcd a 0 = a 
Gcd a b = Gcd b (a `Mod` b) 

type family Normalize (r :: Rat) :: Rat where ... Source #

Normalization of type-level rational.

Example:

>>> :kind! Normalize (9 % 11)
Normalize (9 % 11) :: Rat
= 9 :% 11
>>> :kind! Normalize (9 % 12)
Normalize (9 % 12) :: Rat
= 3 :% 4

Equations

Normalize (a :% b) = (a `Div` Gcd a b) :% (b `Div` Gcd a b) 

type family DivRat (m :: Rat) (n :: Rat) :: Rat where ... Source #

Division of type-level rationals.

If there are Rat with Nats a and b and another Rat with c d then the following formula should be applied: \[ \frac{a}{b} / \frac{c}{d} = \frac{a * d}{b * c} \]

Example:

>>> :kind! DivRat (9 % 11) (9 % 11)
DivRat (9 % 11) (9 % 11) :: Rat
= 1 :% 1

Equations

DivRat (a :% b) (c :% d) = (a * d) % (b * c) 

type family (m :: Rat) >=% (n :: Rat) :: Bool where ... infix 4 Source #

Comparison of type-level rationals, as a function.

>>> :kind! (1 :% 42) >=% (5 :% 42)
(1 :% 42) >=% (5 :% 42) :: Bool
= 'False
>>> :kind! (5 :% 42) >=% (1 :% 42)
(5 :% 42) >=% (1 :% 42) :: Bool
= 'True
>>> :kind! (42 :% 1) >=% (42 :% 1)
(42 :% 1) >=% (42 :% 1) :: Bool
= 'True

Equations

(a :% b) >=% (c :% d) = (c * b) <=? (a * d) 

type RatioNat = Ratio Natural Source #

Rational numbers, with numerator and denominator of Natural type.

class KnownRat (r :: Rat) where Source #

This class gives the integer associated with a type-level rational.

Instances

Instances details
(KnownNat a, KnownNat b) => KnownRat (a :% b) Source # 
Instance details

Defined in Time.Rational

withRuntimeDivRat :: forall (a :: Rat) (b :: Rat) r. (KnownRat a, KnownRat b) => (KnownRat (a / b) => r) -> r Source #

Performs action with introduced DivRat constraint for rational numbers.

type KnownDivRat a b = (KnownRat a, KnownRat b, KnownRat (a / b)) Source #

Constraint alias for DivRat units.