basement-0.0.2: Foundation scrap box of array & string

Basement.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

natValNatural :: forall n proxy. KnownNat n => proxy n -> Natural #

natValCountOf :: forall n ty proxy. (KnownNat n, NatWithinBound (CountOf ty) n) => proxy n -> CountOf ty #

natValOffset :: forall n ty proxy. (KnownNat n, NatWithinBound (Offset ty) n) => proxy n -> Offset ty #

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

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

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

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

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

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

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

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

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

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

# Maximum bounds

type family NatNumMaxBound ty where ... #

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

Equations

 NatNumMaxBound Char = 1114111 NatNumMaxBound Char7 = 127 NatNumMaxBound Int64 = 9223372036854775807 NatNumMaxBound Int32 = 2147483647 NatNumMaxBound Int16 = 32767 NatNumMaxBound Int8 = 127 NatNumMaxBound Word256 = 115792089237316195423570985008687907853269984665640564039457584007913129639935 NatNumMaxBound Word128 = 340282366920938463463374607431768211455 NatNumMaxBound Word64 = 18446744073709551615 NatNumMaxBound Word32 = 4294967295 NatNumMaxBound Word16 = 65535 NatNumMaxBound Word8 = 255 NatNumMaxBound Int = NatNumMaxBound Int64 NatNumMaxBound Word = NatNumMaxBound Word64 NatNumMaxBound (CountOf x) = NatNumMaxBound Int NatNumMaxBound (Offset x) = NatNumMaxBound Int

# Constraint

type family NatInBoundOf ty n where ... #

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 ... #

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))