Numeric.NumType

Description

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

Documentation

class NumTypeI n => NumType n Source

Instances

NumTypeI n => NumType n

class PosTypeI n => PosType n Source

Instances

PosTypeI n => PosType n

class NegTypeI n => NegType n Source

Instances

NegTypeI n => NegType n

class NonZeroI n => NonZero n Source

Instances

NonZeroI n => NonZero n

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

Instances

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

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 -> aSource

Instances

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

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

Instances

NonZeroI n => Div Zero n Zero
(NegTypeI n, Negate n p', Div (Pos p') (Pos p) (Pos p''), Negate (Pos p'') (Neg n'')) => Div (Neg n) (Pos p) (Neg n'')
(NegTypeI n, NegTypeI n', Negate n p, Negate n' p', Div (Pos p) (Pos p') (Pos 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'')) => 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 -> cSource

Instances

NumTypeI n => Mul n Zero Zero
(NegTypeI n, Div c (Neg n) a) => Mul a (Neg n) c
(PosTypeI p, Div c (Pos p) a) => Mul a (Pos p) c

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

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

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

(+) :: Sum a b c => a -> b -> cSource

(-) :: Sum a b c => c -> b -> aSource

(*) :: Mul a b c => a -> b -> cSource

(/) :: Div a b c => a -> b -> cSource

Instances

Instances

Succ Zero (Pos Zero)
(PosTypeI p, Div c (Pos p) a) => Mul a (Pos p) c
(Succ a' a, PosTypeI b, Sub a' b c) => Sub a (Pos b) c
PosTypeI n => Show (Pos n)
PosTypeI n => NonZeroI (Pos n)
PosTypeI n => PosTypeI (Pos n)
PosTypeI n => NumTypeI (Pos n)
(PosTypeI a, Succ b c, Add a c d) => Add (Pos a) b d
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'')) => Div (Neg n) (Pos p) (Neg n'')
(NegTypeI n, NegTypeI n', Negate n p, Negate n' p', Div (Pos p) (Pos p') (Pos 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'')) => 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''')

Instances

(NegTypeI n, Div c (Neg n) a) => Mul a (Neg n) c
(Succ a a', NegTypeI b, Sub a' b c) => Sub a (Neg b) c
NegTypeI n => Show (Neg n)
NegTypeI n => NonZeroI (Neg n)
NegTypeI n => NegTypeI (Neg n)
NegTypeI n => NumTypeI (Neg n)
Succ (Neg Zero) Zero
(NegTypeI a, Succ c b, Add a c d) => Add (Neg a) b d
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'')) => Div (Neg n) (Pos p) (Neg n'')
(NegTypeI n, NegTypeI n', Negate n p, Negate n' p', Div (Pos p) (Pos p') (Pos 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'')) => Div (Pos p) (Neg n) (Neg n'')