Data.TypeNums

This module provides a unified interface for natural numbers, signed integers, and rationals at the type level, in a way fully compatible with existing code using type-level naturals.

Natural numbers are expressed as always, e.g. 5. Negative integers are written as Neg 3. Ratios are written as 3 :% 2.

There are some naming conflicts between this module and GHC.TypeLits, notably the comparison and arithmetic operators. This module reexports Nat, KnownNat, natVal and natVal' so you may import just this module and not GHC.TypeLits.

If you wish to use other functionality from GHC.TypeLits, this package also provides the module Data.TypeLits that includes (almost) full functionality from GHC.TypeLits, but with the conflicts resolving in this packages favour.

Type level numbers

Naturals

data Nat

(Kind) This is the kind of type-level natural numbers.

Instances

KnownNat n => KnownInt (n :: Nat)

Defined in Data.TypeNums.Ints

Methods

intSing :: SInt n

class KnownNat (n :: Nat)

This class gives the integer associated with a type-level natural. There are instances of the class for every concrete literal: 0, 1, 2, etc.

Since: base-4.7.0.0

Minimal complete definition

natSing

natVal :: KnownNat n => proxy n -> Integer

Since: base-4.7.0.0

natVal' :: KnownNat n => Proxy# n -> Integer

Since: base-4.8.0.0

data SomeNat where

This type represents unknown type-level natural numbers.

Since: base-4.10.0.0

Constructors

SomeNat :: SomeNat

Instances

Eq SomeNat

Since: base-4.7.0.0

Defined in GHC.TypeNats

Methods

(==) :: SomeNat -> SomeNat -> Bool

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

Ord SomeNat

Since: base-4.7.0.0

Defined in GHC.TypeNats

Methods

compare :: SomeNat -> SomeNat -> Ordering

(<) :: SomeNat -> SomeNat -> Bool

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

(>) :: SomeNat -> SomeNat -> Bool

(>=) :: SomeNat -> SomeNat -> Bool

max :: SomeNat -> SomeNat -> SomeNat

min :: SomeNat -> SomeNat -> SomeNat

Read SomeNat

Since: base-4.7.0.0

Defined in GHC.TypeNats

Methods

readsPrec :: Int -> ReadS SomeNat

readList :: ReadS [SomeNat]

readPrec :: ReadPrec SomeNat

readListPrec :: ReadPrec [SomeNat]

Show SomeNat

Since: base-4.7.0.0

Defined in GHC.TypeNats

Methods

showsPrec :: Int -> SomeNat -> ShowS

show :: SomeNat -> String

showList :: [SomeNat] -> ShowS

someNatVal :: Integer -> Maybe SomeNat

Convert an integer into an unknown type-level natural.

Since: base-4.7.0.0

Integers

data TInt

(Kind) An integer that may be negative.

Constructors

Pos Nat

Neg Nat

Instances

KnownNat n => KnownInt (Pos n :: TInt)

Defined in Data.TypeNums.Ints

Methods

intSing :: SInt (Pos n)

KnownNat n => KnownInt (Neg n :: TInt)

Defined in Data.TypeNums.Ints

Methods

intSing :: SInt (Neg n)

class KnownInt (n :: k)

This class gives the (value-level) integer associated with a type-level integer. There are instances of this class for every concrete natural: 0, 1, 2, etc. There are also instances of this class for every negated natural, such as Neg 1.

Minimal complete definition

intSing

Instances

KnownNat n => KnownInt (n :: Nat)

Defined in Data.TypeNums.Ints

Methods

intSing :: SInt n

KnownNat n => KnownInt (Pos n :: TInt)

Defined in Data.TypeNums.Ints

Methods

intSing :: SInt (Pos n)

KnownNat n => KnownInt (Neg n :: TInt)

Defined in Data.TypeNums.Ints

Methods

intSing :: SInt (Neg n)

intVal :: forall n proxy. KnownInt n => proxy n -> Integer

Get the value associated with a type-level integer

intVal' :: forall n. KnownInt n => Proxy# n -> Integer

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

data SomeInt

This type represents unknown type-level integers.

Since: typenums-0.1.1

Constructors

KnownInt n => SomeInt (Proxy n)

Instances

Eq SomeInt

Defined in Data.TypeNums.Ints

Methods

(==) :: SomeInt -> SomeInt -> Bool

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

Ord SomeInt

Defined in Data.TypeNums.Ints

Methods

compare :: SomeInt -> SomeInt -> Ordering

(<) :: SomeInt -> SomeInt -> Bool

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

(>) :: SomeInt -> SomeInt -> Bool

(>=) :: SomeInt -> SomeInt -> Bool

max :: SomeInt -> SomeInt -> SomeInt

min :: SomeInt -> SomeInt -> SomeInt

Read SomeInt

Defined in Data.TypeNums.Ints

Methods

readsPrec :: Int -> ReadS SomeInt

readList :: ReadS [SomeInt]

readPrec :: ReadPrec SomeInt

readListPrec :: ReadPrec [SomeInt]

Show SomeInt

Defined in Data.TypeNums.Ints

Methods

showsPrec :: Int -> SomeInt -> ShowS

show :: SomeInt -> String

showList :: [SomeInt] -> ShowS

someIntVal :: Integer -> SomeInt

Convert an integer into an unknown type-level integer.

Since: typenums-0.1.1

Rationals

data Rat

Type constructor for a rational

Constructors

k :% Nat

Instances

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

Defined in Data.TypeNums.Rats

Methods

ratSing :: SRat (n :% d)

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

Defined in Data.TypeNums.Rats

Methods

ratSing :: SRat (n :% 0)

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 n => KnownRat (n :: k)

Defined in Data.TypeNums.Rats

Methods

ratSing :: SRat n

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

Defined in Data.TypeNums.Rats

Methods

ratSing :: SRat (n :% d)

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

Defined in Data.TypeNums.Rats

Methods

ratSing :: SRat (n :% 0)

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: typenums-0.1.1

Constructors

KnownRat r => SomeRat (Proxy r)

Instances

Eq SomeRat

Defined in Data.TypeNums.Rats

Methods

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

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

Ord SomeRat

Defined in Data.TypeNums.Rats

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

Defined in Data.TypeNums.Rats

Methods

readsPrec :: Int -> ReadS SomeRat

readList :: ReadS [SomeRat]

readPrec :: ReadPrec SomeRat

readListPrec :: ReadPrec [SomeRat]

Show SomeRat

Defined in Data.TypeNums.Rats

Methods

showsPrec :: Int -> SomeRat -> ShowS

show :: SomeRat -> String

showList :: [SomeRat] -> ShowS

someRatVal :: Rational -> SomeRat

Convert a rational into an unknown type-level rational.

Since: typenums-0.1.1

Type level numerical operations

Comparisons

type (==?) (a :: k) (b :: k) = (==) a b infix 4

Boolean type-level equals. Useful for e.g. If (x ==? 0)

type (/=?) (a :: k) (b :: k) = Not ((==) a b) infix 4

Boolean type-level not-equals.

type (==) (a :: k) (b :: k) = (==) a b ~ True infix 4

Equality constraint, used as e.g. (x == 3) => _

type (/=) (a :: k) (b :: k) = (==) a b ~ False infix 4

Not-equal constraint

type family (a :: k1) <=? (b :: k2) :: Bool where ... infix 4

Boolean comparison of two type-level numbers

Equations

(a :: Nat) <=? (b :: Nat) = (<=?) a b

0 <=? (Neg 0) = True

(Neg a) <=? (b :: Nat) = True

(Neg a) <=? (Neg b) = (<=?) b a

(n1 :% d1) <=? (n2 :% d2) = (n1 * d1) <=? (n2 * d2)

a <=? (n :% d) = (a * d) <=? n

(n :% d) <=? b = n <=? (b * d)

type (<=) (a :: k1) (b :: k2) = (a <=? b) ~ True infix 4

type (<) (a :: k1) (b :: k2) = (b <=? a) ~ False infix 4

type (>=) (a :: k1) (b :: k2) = (b <=? a) ~ True infix 4

type (>) (a :: k1) (b :: k2) = (a <=? b) ~ False infix 4

Arithmetic

type (+) a b = Add a b infixl 6

The sum of two type-level numbers

type (-) a b = Sub a b infixl 6

The difference of two type-level numbers

type * a b = Mul a b infixl 7

The product of two type-level numbers.

Due to changes in GHC 8.6, using this operator infix and unqualified requires the NoStarIsType language extension to be active. See the GHC 8.6.x migration guide for details: https://ghc.haskell.org/trac/ghc/wiki/Migration/8.6