Org.Org.Semantic.HBase.TypeCalc.IntegerType

Synopsis

data NegativeSucc n

class IntegerType a where

getIntegerTypeValue :: Type a -> Integer

type MinusOne = NegativeSucc Zero

type MinusTwo = NegativeSucc One

type MinusThree = NegativeSucc Two

type MinusFour = NegativeSucc Three

type MinusFive = NegativeSucc Four

type MinusSix = NegativeSucc Five

type MinusSeven = NegativeSucc Six

type MinusEight = NegativeSucc Seven

type MinusNine = NegativeSucc Eight

type MinusTen = NegativeSucc Nine

class Negate a b | a -> b, b -> a

class Absolute a abs sign | a -> abs sign, abs sign -> a

class GCD a b gcd | a b -> gcd

Documentation

data NegativeSucc n

represents -(n+1)

Instances

NaturalType a => IntegerType (NegativeSucc a)

Negate (Succ a) (NegativeSucc a)

Negate (NegativeSucc a) (Succ a)

AddOne (NegativeSucc (Succ a)) (NegativeSucc a)

AddOne (NegativeSucc Zero) Zero

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

(IsEven a e, Not e ne) => IsEven (NegativeSucc a) ne

(Add (NegativeSucc a) b ab, AddOne abm1 ab) => Add (NegativeSucc (Succ a)) b abm1

AddOne bm1 b => Add (NegativeSucc Zero) b bm1

(Multiply (Succ a) b ab, Negate ab nab) => Multiply (NegativeSucc a) b nab

Absolute (NegativeSucc a) (Succ a) MinusOne

(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)

class IntegerType a where

Metatype

Methods

getIntegerTypeValue :: Type a -> Integer

Instances

IntegerType Zero

NaturalType a => IntegerType (Succ a)

NaturalType a => IntegerType (NegativeSucc a)

type MinusOne = NegativeSucc Zero

type MinusTwo = NegativeSucc One

type MinusThree = NegativeSucc Two

type MinusFour = NegativeSucc Three

type MinusFive = NegativeSucc Four

type MinusSix = NegativeSucc Five

type MinusSeven = NegativeSucc Six

type MinusEight = NegativeSucc Seven

type MinusNine = NegativeSucc Eight

type MinusTen = NegativeSucc Nine

class Negate a b | a -> b, b -> a

Instances

Negate Zero Zero

Negate (Succ a) (NegativeSucc a)

Negate (NegativeSucc a) (Succ a)

class Absolute a abs sign | a -> abs sign, abs sign -> a

Instances

Absolute Zero Zero Zero

Absolute (Succ a) (Succ a) One

Absolute (NegativeSucc a) (Succ a) MinusOne

class GCD a b gcd | a b -> gcd

Instances

GCD Zero b b

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

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