dimensional-0.7.3: Statically checked physical dimensions. Source code Contents Index

Numeric.NumType Portability GHC only? Stability Stable Maintainer bjorn.buckwalter@gmail.com

Description

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

Documentation

class NumTypeI n => NumType n Source

class PosTypeI n => PosType n Source

class NegTypeI n => NegType n Source

class NonZeroI n => NonZero n Source

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

Instances Succ Zero (Pos Zero) Succ Zero (Pos Zero) Succ (Neg Zero) 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 Source

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

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

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, 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, 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'') (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 -> c Source

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 -> a Source

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

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

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

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

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

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

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

data Zero Source

Instances Show Zero NegTypeI Zero PosTypeI Zero NumTypeI Zero Negate Zero Zero NumTypeI n => Mul n Zero Zero NonZeroI n => Div Zero n Zero NumType a => Sub a Zero a NumTypeI a => Add Zero a a Succ Zero (Pos Zero) Succ (Neg Zero) Zero

data Pos n Source

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''')

data Neg n Source

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'')

type Pos1 = Pos Zero Source

type Pos2 = Pos Pos1 Source

type Pos3 = Pos Pos2 Source

type Pos4 = Pos Pos3 Source

type Pos5 = Pos Pos4 Source

type Neg1 = Neg Zero Source

type Neg2 = Neg Neg1 Source

type Neg3 = Neg Neg2 Source

type Neg4 = Neg Neg3 Source

type Neg5 = Neg Neg4 Source

zero :: Zero Source

pos1 :: Pos1 Source

pos2 :: Pos2 Source

pos3 :: Pos3 Source

pos4 :: Pos4 Source

pos5 :: Pos5 Source

neg1 :: Neg1 Source

neg2 :: Neg2 Source

neg3 :: Neg3 Source

neg4 :: Neg4 Source

neg5 :: Neg5 Source

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