TypeUnary.Nat

Experiment in length-typed vectors

Documentation

module TypeUnary.TyNat

Value-typed natural numbers

data Nat where

Constructors

Zero :: Nat Z

Succ :: IsNat n => Nat n -> Nat (S n)

Instances

Show (Nat n)

zero :: Nat N0

one :: Nat N1

two :: Nat N2

three :: Nat N3

four :: Nat N4

withIsNat :: (IsNat n => Nat n -> a) -> Nat n -> a

natSucc :: Nat n -> Nat (S n)

natIsNat :: Nat n -> IsNat n => Nat n

natToZ :: Nat n -> Integer

Interpret a Nat as an Integer

natEq :: Nat m -> Nat n -> Maybe (m :=: n)

Equality test

natAdd :: Nat m -> Nat n -> Nat (m :+: n)

Sum of naturals

class IsNat n where

Is n a natural number type?

Methods

nat :: Nat n

Instances

IsNat Z

IsNat n => IsNat (S n)

Inequality proofs and indices

data m :<: n where

Proof that m < n

Constructors

ZLess :: Z :<: S n

SLess :: (m :<: n) -> S m :<: S n

data Index lim

A number under the given limit, with proof

Constructors

forall n . IsNat n => Index (n :<: lim) (Nat n)

Instances

Eq (Index lim)

succI :: Index m -> Index (S m)

index0 :: Index (N1 :+: m)

index1 :: Index (N2 :+: m)

index2 :: Index (N3 :+: m)

index3 :: Index (N4 :+: m)

coerceToIndex :: (Integral i, IsNat m) => i -> Index m

Index generation from integer. Can fail dynamically if the integer is too large.