Safe Haskell	None
Language	Haskell2010

Data.TypeNat.Nat

Synopsis

Documentation

Natural numbers

Constructors

Z
S Nat

Instances

Eq Nat Source #
Methods (==) :: Nat -> Nat -> Bool # (/=) :: Nat -> Nat -> Bool #
Ord Nat Source #
Methods compare :: 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

Methods

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

Instances

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