foundation-0.0.5: Alternative prelude with batteries and no dependencies

Foundation.Primitive.Nat

Synopsis

# Documentation

data Nat :: * #

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

Instances

 type (==) Nat a b type (==) Nat a b = EqNat a b

class KnownNat n #

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: 4.7.0.0

Minimal complete definition

natSing

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

Since: 4.7.0.0

type (<=) x y = (~) Bool ((<=?) x y) True infix 4 #

Comparison of type-level naturals, as a constraint.

type family (a :: Nat) <=? (b :: Nat) :: Bool where ... infix 4 #

Comparison of type-level naturals, as a function. NOTE: The functionality for this function should be subsumed by CmpNat, so this might go away in the future. Please let us know, if you encounter discrepancies between the two.

type family (a :: Nat) + (b :: Nat) :: Nat where ... infixl 6 #

type family (a :: Nat) * (b :: Nat) :: Nat where ... infixl 7 #

Multiplication of type-level naturals.

type family (a :: Nat) ^ (b :: Nat) :: Nat where ... infixr 8 #

Exponentiation of type-level naturals.

type family (a :: Nat) - (b :: Nat) :: Nat where ... infixl 6 #

Subtraction of type-level naturals.

Since: 4.7.0.0

type family CmpNat (a :: Nat) (b :: Nat) :: Ordering where ... #

Comparison of type-level naturals, as a function.

Since: 4.7.0.0

# Nat convertion

natValInt :: forall n proxy. (KnownNat n, NatWithinBound Int n) => proxy n -> Int Source #

natValInt8 :: forall n proxy. (KnownNat n, NatWithinBound Int8 n) => proxy n -> Int8 Source #

natValInt16 :: forall n proxy. (KnownNat n, NatWithinBound Int16 n) => proxy n -> Int16 Source #

natValInt32 :: forall n proxy. (KnownNat n, NatWithinBound Int32 n) => proxy n -> Int32 Source #

natValInt64 :: forall n proxy. (KnownNat n, NatWithinBound Int64 n) => proxy n -> Int64 Source #

natValWord :: forall n proxy. (KnownNat n, NatWithinBound Word n) => proxy n -> Word Source #

natValWord8 :: forall n proxy. (KnownNat n, NatWithinBound Word8 n) => proxy n -> Word8 Source #

natValWord16 :: forall n proxy. (KnownNat n, NatWithinBound Word16 n) => proxy n -> Word16 Source #

natValWord32 :: forall n proxy. (KnownNat n, NatWithinBound Word32 n) => proxy n -> Word32 Source #

natValWord64 :: forall n proxy. (KnownNat n, NatWithinBound Word64 n) => proxy n -> Word64 Source #

# Maximum bounds

type family NatNumMaxBound ty where ... Source #

Get Maximum bounds of different Integral / Natural types related to Nat

Equations

 NatNumMaxBound Int64 = 9223372036854775807 NatNumMaxBound Int32 = 2147483647 NatNumMaxBound Int16 = 32767 NatNumMaxBound Int8 = 127 NatNumMaxBound Word64 = 18446744073709551615 NatNumMaxBound Word32 = 4294967295 NatNumMaxBound Word16 = 65535 NatNumMaxBound Word8 = 255 NatNumMaxBound Int = NatNumMaxBound Int64 NatNumMaxBound Word = NatNumMaxBound Word64

# Constraint

type family NatInBoundOf ty n where ... Source #

Check if a Nat is in bounds of another integral / natural types

Equations

 NatInBoundOf Integer n = True NatInBoundOf Natural n = True NatInBoundOf ty n = n <=? NatNumMaxBound ty

type family NatWithinBound ty (n :: Nat) where ... Source #

Constraint to check if a natural is within a specific bounds of a type.

i.e. given a Nat n, is it possible to convert it to ty without losing information

Equations

 NatWithinBound ty n = If (NatInBoundOf ty n) (() ~ ()) (TypeError (((Text "Natural " :<>: ShowType n) :<>: Text " is out of bounds for ") :<>: ShowType ty))