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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 (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 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) 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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