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Org.Org.Semantic.HBase.TypeCalc.NaturalType

Synopsis

data Zero data Succ n class NaturalType a where getNaturalTypeValue :: Type a -> Integer class WholeType a type One = Succ Zero type Two = Succ One type Three = Succ Two type Four = Succ Three type Five = Succ Four type Six = Succ Five type Seven = Succ Six type Eight = Succ Seven type Nine = Succ Eight type Ten = Succ Nine tZero :: Type Zero tOne :: Type One tTwo :: Type Two tThree :: Type Three tFour :: Type Four tFive :: Type Five tSix :: Type Six tSeven :: Type Seven tEight :: Type Eight tNine :: Type Nine tTen :: Type Ten class AddOne a b | a -> b, b -> a class IsAtLeast a b c | a b -> c class AtLeast a b class AtLeastOne a class Add a b ab | a b -> ab, ab a -> b class Multiply a b ab | a b -> ab class IsEven a e | a -> e class Divide ab a b | ab a -> b, a b -> ab

Documentation

data Zero

Instances IntegerType Zero Negate Zero Zero Negate Zero Zero AddOne (NegativeSucc Zero) Zero AddOne (NegativeSucc Zero) Zero IsAtLeast Zero (NegativeSucc b) True IsAtLeast (NegativeSucc a) Zero False AddOne bm1 b => Add (NegativeSucc Zero) b bm1 Absolute Zero Zero Zero Absolute Zero Zero Zero Absolute Zero Zero Zero GCD Zero b b GCD (Succ a) Zero (Succ a) Nth Zero (a, list) a list NaturalType Zero AddOne Zero (Succ Zero) AddOne Zero (Succ Zero) IsAtLeast Zero Zero True IsAtLeast Zero Zero True IsAtLeast Zero (Succ b) False IsAtLeast (Succ a) Zero True Add Zero b b Multiply Zero b Zero Multiply Zero b Zero IsEven Zero True Divide Zero (Succ a) Zero Divide Zero (Succ a) Zero Divide (Succ b) (Succ Zero) (Succ b)

data Succ n

Instances NaturalType a => IntegerType (Succ a) Negate (Succ a) (NegativeSucc a) Negate (NegativeSucc a) (Succ a) AddOne (NegativeSucc (Succ a)) (NegativeSucc a) IsAtLeast (Succ a) (NegativeSucc b) True IsAtLeast (NegativeSucc a) (Succ b) False (Add (NegativeSucc a) b ab, AddOne abm1 ab) => Add (NegativeSucc (Succ a)) b abm1 Absolute (Succ a) (Succ a) One Absolute (Succ a) (Succ a) One Absolute (NegativeSucc a) (Succ a) MinusOne Divide (Succ a) (Succ b) (Succ c) => Divide (NegativeSucc a) (Succ b) (NegativeSucc c) GCD (Succ a) Zero (Succ a) GCD (Succ a) Zero (Succ a) (Add b amb a, Absolute amb diff sign, IsAtLeast Zero amb abigger, Pick abigger b a smaller, GCD (Succ smaller) diff gcd) => GCD (Succ a) (Succ b) gcd (Add b amb a, Absolute amb diff sign, IsAtLeast Zero amb abigger, Pick abigger b a smaller, GCD (Succ smaller) diff gcd) => GCD (Succ a) (Succ b) gcd Nth n list elem rest => Nth (Succ n) (a, list) elem (a, rest) NaturalType a => NaturalType (Succ a) NaturalType a => WholeType (Succ a) AddOne Zero (Succ Zero) AddOne (Succ a) (Succ (Succ a)) AddOne (Succ a) (Succ (Succ a)) AddOne (Succ a) (Succ (Succ a)) IsAtLeast Zero (Succ b) False IsAtLeast (Succ a) Zero True IsAtLeast a b c => IsAtLeast (Succ a) (Succ b) c IsAtLeast a b c => IsAtLeast (Succ a) (Succ b) c (Add a b ab, AddOne ab ab1) => Add (Succ a) b ab1 (Multiply a b ab, Add ab b abb) => Multiply (Succ a) b abb (IsEven a e, Not e ne) => IsEven (Succ a) ne Divide Zero (Succ a) Zero Divide (Succ b) (Succ Zero) (Succ b) Divide (Succ b) (Succ Zero) (Succ b) Divide (Succ b) (Succ Zero) (Succ b) (Add b amb a, Divide amb (Succ (Succ b)) c) => Divide (Succ a) (Succ (Succ b)) (Succ c) (Add b amb a, Divide amb (Succ (Succ b)) c) => Divide (Succ a) (Succ (Succ b)) (Succ c) (Add b amb a, Divide amb (Succ (Succ b)) c) => Divide (Succ a) (Succ (Succ b)) (Succ c) (Add b amb a, Divide amb (Succ (Succ b)) c) => Divide (Succ a) (Succ (Succ b)) (Succ c)

class NaturalType a where

Metatype Methods getNaturalTypeValue :: Type a -> Integer Instances NaturalType Zero NaturalType a => NaturalType (Succ a)

class WholeType a

Instances NaturalType a => WholeType (Succ a)

type One = Succ Zero

type Two = Succ One

type Three = Succ Two

type Four = Succ Three

type Five = Succ Four

type Six = Succ Five

type Seven = Succ Six

type Eight = Succ Seven

type Nine = Succ Eight

type Ten = Succ Nine

tZero :: Type Zero

tOne :: Type One

tTwo :: Type Two

tThree :: Type Three

tFour :: Type Four

tFive :: Type Five

tSix :: Type Six

tSeven :: Type Seven

tEight :: Type Eight

tNine :: Type Nine

tTen :: Type Ten

class AddOne a b | a -> b, b -> a

Instances AddOne (NegativeSucc (Succ a)) (NegativeSucc a) AddOne (NegativeSucc Zero) Zero AddOne Zero (Succ Zero) AddOne (Succ a) (Succ (Succ a))

class IsAtLeast a b c | a b -> c

Instances IsAtLeast Zero (NegativeSucc b) True IsAtLeast (Succ a) (NegativeSucc b) True IsAtLeast (NegativeSucc a) Zero False IsAtLeast (NegativeSucc a) (Succ b) False IsAtLeast b a c => IsAtLeast (NegativeSucc a) (NegativeSucc b) c IsAtLeast Zero Zero True IsAtLeast Zero (Succ b) False IsAtLeast (Succ a) Zero True IsAtLeast a b c => IsAtLeast (Succ a) (Succ b) c

class AtLeast a b

Instances IsAtLeast a b True => AtLeast a b

class AtLeastOne a

Instances WholeType a => AtLeastOne a

class Add a b ab | a b -> ab, ab a -> b

Instances (Add (NegativeSucc a) b ab, AddOne abm1 ab) => Add (NegativeSucc (Succ a)) b abm1 AddOne bm1 b => Add (NegativeSucc Zero) b bm1 Add Zero b b (Add a b ab, AddOne ab ab1) => Add (Succ a) b ab1

class Multiply a b ab | a b -> ab

Instances (Multiply (Succ a) b ab, Negate ab nab) => Multiply (NegativeSucc a) b nab Multiply Zero b Zero (Multiply a b ab, Add ab b abb) => Multiply (Succ a) b abb

class IsEven a e | a -> e

Instances (IsEven a e, Not e ne) => IsEven (NegativeSucc a) ne IsEven Zero True (IsEven a e, Not e ne) => IsEven (Succ a) ne

class Divide ab a b | ab a -> b, a b -> ab

Instances (Divide a (Succ b) c, Negate c nc) => Divide a (NegativeSucc b) nc Divide (Succ a) (Succ b) (Succ c) => Divide (NegativeSucc a) (Succ b) (NegativeSucc c) Divide Zero (Succ a) Zero Divide (Succ b) (Succ Zero) (Succ b) (Add b amb a, Divide amb (Succ (Succ b)) c) => Divide (Succ a) (Succ (Succ b)) (Succ c)

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