Copyright	(c) Nils Anders Danielsson 2004-2020
License	See the file LICENCE.
Maintainer	http://www.cse.chalmers.se/~nad/
Stability	experimental
Portability	non-portable (GHC-specific)
Safe Haskell	None
Language	Haskell2010

Test.ChasingBottoms.Nat

Description

A simple implementation of natural numbers on top of Integers. Note that since Integers are used there is no infinite natural number; in other words, succ is strict.

Synopsis

data Nat
isSucc :: Nat -> Bool
fromSucc :: Nat -> Maybe Nat
natrec :: a -> (Nat -> a -> a) -> Nat -> a
foldN :: a -> (a -> a) -> Nat -> a

Documentation

data Nat Source #

Natural numbers.

No Data instance is provided, because the implementation should be abstract.

Instances

Instances details

Enum Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods succ :: Nat -> Nat pred :: Nat -> Nat toEnum :: Int -> Nat fromEnum :: Nat -> Int enumFrom :: Nat -> [Nat] enumFromThen :: Nat -> Nat -> [Nat] enumFromTo :: Nat -> Nat -> [Nat] enumFromThenTo :: Nat -> Nat -> Nat -> [Nat]
Eq Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods (==) :: Nat -> Nat -> Bool (/=) :: Nat -> Nat -> Bool
Integral Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods quot :: Nat -> Nat -> Nat rem :: Nat -> Nat -> Nat div :: Nat -> Nat -> Nat mod :: Nat -> Nat -> Nat quotRem :: Nat -> Nat -> (Nat, Nat) divMod :: Nat -> Nat -> (Nat, Nat) toInteger :: Nat -> Integer
Num Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods (+) :: Nat -> Nat -> Nat (-) :: Nat -> Nat -> Nat (*) :: Nat -> Nat -> Nat negate :: Nat -> Nat abs :: Nat -> Nat signum :: Nat -> Nat fromInteger :: Integer -> Nat
Ord Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat 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
Real Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods toRational :: Nat -> Rational
Show Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods showsPrec :: Int -> Nat -> ShowS show :: Nat -> String showList :: [Nat] -> ShowS
Arbitrary Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods arbitrary :: Gen Nat shrink :: Nat -> [Nat]
CoArbitrary Nat Source #
Instance details Defined in Test.ChasingBottoms.Nat Methods coarbitrary :: Nat -> Gen b -> Gen b

isSucc :: Nat -> Bool Source #

isSucc 0 == False, for other total natural numbers it is True.

fromSucc :: Nat -> Maybe Nat Source #

fromSucc 0 == Nothing, fromSucc (n+1) == Just n for a total natural number n.

natrec :: a -> (Nat -> a -> a) -> Nat -> a Source #

natrec performs primitive recursion on natural numbers.

foldN :: a -> (a -> a) -> Nat -> a Source #

foldN is a fold on natural numbers:

 foldN g h = natrec g (curry $ h . snd)