TypeNat-0.5.0.0: Some Nat-indexed types for GHC

Data.TypeNat.Nat

Synopsis

Documentation

data Nat Source #

Natural numbers

Constructors

 Z S Nat

Instances

 Source # Methods(==) :: Nat -> Nat -> Bool #(/=) :: Nat -> Nat -> Bool # Source # Methodscompare :: Nat -> Nat -> Ordering #(<) :: Nat -> Nat -> Bool #(<=) :: Nat -> Nat -> Bool #(>) :: Nat -> Nat -> Bool #(>=) :: Nat -> Nat -> Bool #max :: Nat -> Nat -> Nat #min :: Nat -> Nat -> Nat #

class IsNat n where Source #

Proof that a given type is a Nat. With this fact, you can do type-directed computation.

Minimal complete definition

natRecursion

Methods

natRecursion :: (forall m. b -> a m -> a (S m)) -> (b -> a Z) -> (b -> b) -> b -> a n Source #

Instances

 Source # MethodsnatRecursion :: (forall m. b -> a m -> a (S m)) -> (b -> a Z) -> (b -> b) -> b -> a Z Source # IsNat n => IsNat (S n) Source # MethodsnatRecursion :: (forall m. b -> a m -> a (S m)) -> (b -> a Z) -> (b -> b) -> b -> a (S n) Source #

class LTE n m where Source #

Nat n is less than or equal to nat m. Comes with functions to do type-directed computation for Nat-indexed datatypes.

Minimal complete definition

Methods

lteInduction :: StrongLTE m l => Proxy l -> (forall k. LTE (S k) l => d k -> d (S k)) -> d n -> d m Source #

lteRecursion :: (forall k. LTE n k => d (S k) -> d k) -> d m -> d n Source #

Instances

 LTE n n Source # MethodslteInduction :: StrongLTE n l => Proxy Nat l -> (forall k. LTE (S k) l => d k -> d (S k)) -> d n -> d n Source #lteRecursion :: (forall k. LTE n k => d (S k) -> d k) -> d n -> d n Source # LTE n m => LTE n (S m) Source # MethodslteInduction :: StrongLTE (S m) l => Proxy Nat l -> (forall k. LTE (S k) l => d k -> d (S k)) -> d n -> d (S m) Source #lteRecursion :: (forall k. LTE n k => d (S k) -> d k) -> d (S m) -> d n Source #

type family StrongLTE (n :: Nat) (m :: Nat) :: Constraint where ... Source #

A constrint which includes LTE k m for every k <= m.

Equations

 StrongLTE Z m = LTE Z m StrongLTE (S n) m = (LTE (S n) m, StrongLTE n m)

type Zero = Z Source #

type One = S Z Source #

type Two = S One Source #

type Three = S Two Source #

type Five = S Four Source #

type Six = S Five Source #

type Seven = S Six Source #

type Ten = S Nine Source #