Data.TypeNums.Rats

Type level rational numbers expressed as a ratio between a type-level integer and a type-level natural. For example Neg 3 :% 2.

See also: Data.TypeInts

Construction

data Rat

Type constructor for a rational

Constructors

k :% Nat

Instances

(KnownInt k n, KnownNat d, (/=) Nat d 0) => KnownRat Rat ((:%) k n d)

Methods

ratSing :: SRat ((k :% n) d) r

TypeError Constraint (Text "Denominator must not equal 0") => KnownRat Rat ((:%) k n 0)

Methods

ratSing :: SRat ((k :% n) 0) r

Linking type and value level

class KnownRat r

This class gives the (value-level) rational associated with a type-level rational. There are instances of this class for every combination of a concrete integer and concrete natural.

Minimal complete definition

ratSing

Instances

KnownInt k n => KnownRat k n

Methods

ratSing :: SRat n r

(KnownInt k n, KnownNat d, (/=) Nat d 0) => KnownRat Rat ((:%) k n d)

Methods

ratSing :: SRat ((k :% n) d) r

TypeError Constraint (Text "Denominator must not equal 0") => KnownRat Rat ((:%) k n 0)

Methods

ratSing :: SRat ((k :% n) 0) r

ratVal :: forall proxy r. KnownRat r => proxy r -> Rational

Get the value associated with a type-level rational

ratVal' :: forall r. KnownRat r => Proxy# r -> Rational

Get the value associated with a type-level rational. The difference between this function and ratVal is that it takes a Proxy# parameter, which has zero runtime representation and so is entirely free.

data SomeRat

This type represents unknown type-level integers.

Since: 0.1.1

Constructors

KnownRat r => SomeRat (Proxy r)

Instances

Eq SomeRat

Methods

(==) :: SomeRat -> SomeRat -> Bool

(/=) :: SomeRat -> SomeRat -> Bool

Ord SomeRat

Methods

compare :: SomeRat -> SomeRat -> Ordering

(<) :: SomeRat -> SomeRat -> Bool

(<=) :: SomeRat -> SomeRat -> Bool

(>) :: SomeRat -> SomeRat -> Bool

(>=) :: SomeRat -> SomeRat -> Bool

max :: SomeRat -> SomeRat -> SomeRat

min :: SomeRat -> SomeRat -> SomeRat

Read SomeRat

Methods

readsPrec :: Int -> ReadS SomeRat

readList :: ReadS [SomeRat]

readPrec :: ReadPrec SomeRat

readListPrec :: ReadPrec [SomeRat]

Show SomeRat

Methods

showsPrec :: Int -> SomeRat -> ShowS

show :: SomeRat -> String

showList :: [SomeRat] -> ShowS

someRatVal :: Rational -> SomeRat

Convert a rational into an unknown type-level rational.

Since: 0.1.1