Numeric.NumType

Please refer to the literate Haskell code for documentation of both API and implementation.

Documentation

class NumTypeI n => NumType n

Instances

NumTypeI n => NumType n

class PosTypeI n => PosType n

Instances

PosTypeI n => PosType n

class NegTypeI n => NegType n

Instances

NegTypeI n => NegType n

class NonZeroI n => NonZero n

Instances

NonZeroI n => NonZero n

class (NumTypeI a, NumTypeI b) => Succ a b | a -> b, b -> a

Instances

Succ Zero (Pos Zero)

Succ (Neg Zero) Zero

NegTypeI a => Succ (Neg (Neg a)) (Neg a)

PosTypeI a => Succ (Pos a) (Pos (Pos a))

class (NumTypeI a, NumTypeI b) => Negate a b | a -> b, b -> a

Instances

Negate Zero Zero

(NegTypeI a, PosTypeI b, Negate a b) => Negate (Neg a) (Pos b)

(PosTypeI a, NegTypeI b, Negate a b) => Negate (Pos a) (Neg b)

class (Add a b c, Sub c b a) => Sum a b c | a b -> c, a c -> b, b c -> a

Instances

(Add a b c, Sub c b a, Sub c a b) => Sum a b c

class (NumTypeI a, NonZeroI b, NumTypeI c) => Div a b c | a b -> c, c b -> a

Instances

NonZeroI n => Div Zero n Zero

(NegTypeI n, Negate n p', Div (Pos p') (Pos p) (Pos p''), Negate (Pos p'') (Neg n''), PosTypeI p) => Div (Neg n) (Pos p) (Neg n'')

(NegTypeI n, NegTypeI n', Negate n p, Negate n' p', Div (Pos p) (Pos p') (Pos p''), PosTypeI p'') => Div (Neg n) (Neg n') (Pos p'')

(NegTypeI n, Negate n p', Div (Pos p) (Pos p') (Pos p''), Negate (Pos p'') (Neg n''), PosTypeI p) => Div (Pos p) (Neg n) (Neg n'')

(Sum n' (Pos n'') (Pos n), Div n'' (Pos n') n''', PosTypeI n''') => Div (Pos n) (Pos n') (Pos n''')

class (NumTypeI a, NumTypeI b, NumTypeI c) => Mul a b c | a b -> c

Instances

NumTypeI n => Mul n Zero Zero

(NumTypeI a, NumTypeI c, NegTypeI n, Div c (Neg n) a) => Mul a (Neg n) c

(NumTypeI a, NumTypeI c, PosTypeI p, Div c (Pos p) a) => Mul a (Pos p) c

toNum :: (NumTypeI n, Num a) => n -> a

incr :: Succ a b => a -> b

decr :: Succ a b => b -> a

negate :: Negate a b => a -> b

(+) :: Sum a b c => a -> b -> c infixl 6

(-) :: Sum a b c => c -> b -> a infixl 6

(*) :: Mul a b c => a -> b -> c infixl 7

(/) :: Div a b c => a -> b -> c infixl 7

data Zero

Instances

Show Zero

Methods

showsPrec :: Int -> Zero -> ShowS

show :: Zero -> String

showList :: [Zero] -> ShowS

Negate Zero Zero

NumTypeI n => Mul n Zero Zero

NonZeroI n => Div Zero n Zero

Succ Zero (Pos Zero)

Succ (Neg Zero) Zero

data Pos n

Instances

Succ Zero (Pos Zero)

(NumTypeI a, NumTypeI c, PosTypeI p, Div c (Pos p) a) => Mul a (Pos p) c

PosTypeI n => Show (Pos n)

Methods

showsPrec :: Int -> Pos n -> ShowS

show :: Pos n -> String

showList :: [Pos n] -> ShowS

PosTypeI a => Succ (Pos a) (Pos (Pos a))

(NegTypeI a, PosTypeI b, Negate a b) => Negate (Neg a) (Pos b)

(PosTypeI a, NegTypeI b, Negate a b) => Negate (Pos a) (Neg b)

(NegTypeI n, Negate n p', Div (Pos p') (Pos p) (Pos p''), Negate (Pos p'') (Neg n''), PosTypeI p) => Div (Neg n) (Pos p) (Neg n'')

(NegTypeI n, NegTypeI n', Negate n p, Negate n' p', Div (Pos p) (Pos p') (Pos p''), PosTypeI p'') => Div (Neg n) (Neg n') (Pos p'')

(NegTypeI n, Negate n p', Div (Pos p) (Pos p') (Pos p''), Negate (Pos p'') (Neg n''), PosTypeI p) => Div (Pos p) (Neg n) (Neg n'')

(Sum n' (Pos n'') (Pos n), Div n'' (Pos n') n''', PosTypeI n''') => Div (Pos n) (Pos n') (Pos n''')

data Neg n

Instances

(NumTypeI a, NumTypeI c, NegTypeI n, Div c (Neg n) a) => Mul a (Neg n) c

NegTypeI n => Show (Neg n)

Methods

showsPrec :: Int -> Neg n -> ShowS

show :: Neg n -> String

showList :: [Neg n] -> ShowS

Succ (Neg Zero) Zero

NegTypeI a => Succ (Neg (Neg a)) (Neg a)

(NegTypeI a, PosTypeI b, Negate a b) => Negate (Neg a) (Pos b)

(PosTypeI a, NegTypeI b, Negate a b) => Negate (Pos a) (Neg b)

(NegTypeI n, Negate n p', Div (Pos p') (Pos p) (Pos p''), Negate (Pos p'') (Neg n''), PosTypeI p) => Div (Neg n) (Pos p) (Neg n'')

(NegTypeI n, NegTypeI n', Negate n p, Negate n' p', Div (Pos p) (Pos p') (Pos p''), PosTypeI p'') => Div (Neg n) (Neg n') (Pos p'')

(NegTypeI n, Negate n p', Div (Pos p) (Pos p') (Pos p''), Negate (Pos p'') (Neg n''), PosTypeI p) => Div (Pos p) (Neg n) (Neg n'')

type Pos1 = Pos Zero

type Pos2 = Pos Pos1

type Pos3 = Pos Pos2

type Pos4 = Pos Pos3

type Pos5 = Pos Pos4

type Neg1 = Neg Zero

type Neg2 = Neg Neg1

type Neg3 = Neg Neg2

type Neg4 = Neg Neg3

type Neg5 = Neg Neg4

zero :: Zero

pos1 :: Pos1

pos2 :: Pos2

pos3 :: Pos3

pos4 :: Pos4

pos5 :: Pos5

neg1 :: Neg1

neg2 :: Neg2

neg3 :: Neg3

neg4 :: Neg4

neg5 :: Neg5