Ratio.Infix

Infix operators for Rationals.

Expressions may include both Rationals and Ints. Where both operands are Rationals, we surround the operator with the '|' symbol. Where one operand is a Rational and the other an Int, we place the '|' symbol at the side of the operator adjacent to the Rational. For example (where r is a Rational and i an Int):

r |+| r

i +| r

r |+ i

Infix comparisons

Infix arithmetic

(|), (|), (|*|), (/|), (|/), (|/|)

module Ratio.Infix
    exposing
        ( (|==|)
        , (|==)
        , (|/=|)
        , (|/=)
        , (|>|)
        , (|>=|)
        , (|<|)
        , (|<=|)
        , (+|)
        , (|+)
        , (|+|)
        , (-|)
        , (|-)
        , (|-|)
        , (*|)
        , (|*)
        , (|*|)
        , (/|)
        , (|/)
        , (|/|)
        )

{-| Infix operators for Rationals.

Expressions may include both Rationals and Ints.  Where both operands are Rationals, we surround the operator with the '|' symbol.
Where one operand is a Rational and the other an Int, we place the '|' symbol at the side of the operator adjacent to the Rational.
For example (where r is a Rational and i an Int):


    r |+| r

    i +| r

    r |+ i


# Infix comparisons
@docs (|==|), (|==), (|/=|), (|/=), (|>|), (|>=|), (|<|), (|<=|)

# Infix arithmetic
@docs  (+|), (|+), (|+|), (-|), (|-), (|-|),
       (*|), (|*), (|*|), (/|), (|/), (|/|)

-}

import Ratio exposing (..)


infixl 6 |+


infixl 6 +|


infixl 6 |+|


infixl 6 |-


infixl 6 -|


infixl 6 |-|


infixl 7 |*


infixl 7 *|


infixl 7 |*|


infixl 7 |/


infixl 7 /|


infixl 7 |/|



-- comparison ops
{- we won't provide |> or <| for comparing Rationals with Ints because of
   confusion with the same infix functions in Basics
-}


{-| Synonym for Ratio.eq
-}
(|==|) : Rational -> Rational -> Bool
(|==|) a b =
    eq a b


{-| Test a Rational and an Int for equality
-}
(|==) : Rational -> Int -> Bool
(|==) a b =
    eq a (fromInt b)


{-| Synonym for Ratio.ne
-}
(|/=|) : Rational -> Rational -> Bool
(|/=|) a b =
    ne a b


{-| Test a Rational and an Int for inequality
-}
(|/=) : Rational -> Int -> Bool
(|/=) a b =
    ne a (fromInt b)


{-| Synonym for Ratio.gt
-}
(|>|) : Rational -> Rational -> Bool
(|>|) a b =
    gt a b


{-| Synonym for Ratio.ge
-}
(|>=|) : Rational -> Rational -> Bool
(|>=|) a b =
    ge a b


{-| Synonym for Ratio.lt
-}
(|<|) : Rational -> Rational -> Bool
(|<|) a b =
    lt a b


{-| Synonym for Ratio.le
-}
(|<=|) : Rational -> Rational -> Bool
(|<=|) a b =
    le a b



-- arithmetic ops


{-| Add an Int to a Rational
-}
(+|) : Int -> Rational -> Rational
(+|) i r =
    add (fromInt i) r


{-| add a Rational to an Int
-}
(|+) : Rational -> Int -> Rational
(|+) =
    flip (+|)


{-| Synonym for Ratio.add
-}
(|+|) : Rational -> Rational -> Rational
(|+|) =
    add


{-| Subtract a Rational from an Iny
-}
(-|) : Int -> Rational -> Rational
(-|) i r =
    subtract (fromInt i) r


{-| Subtract an Int from a Rational
-}
(|-) : Rational -> Int -> Rational
(|-) r i =
    subtract r (fromInt i)



{-
     -- flip not used in arithmetic because it seems to give the wrong precedence in expressions
     -- not got to the cause of this yet
   (|-) : Rational -> Int -> Rational
   (|-) =
     flip (-|)
-}


{-| Synonym for Ratio.subtract
-}
(|-|) : Rational -> Rational -> Rational
(|-|) =
    subtract


{-| Multiply an Rational by an Int
-}
(|*) : Rational -> Int -> Rational
(|*) =
    multiplyByInt


{-| Multiply an Int by a Rational
-}
(*|) : Int -> Rational -> Rational
(*|) =
    flip multiplyByInt


{-| Synonym for Ratio.multiply
-}
(|*|) : Rational -> Rational -> Rational
(|*|) =
    multiply


{-| Divide a Rational by an Int
-}
(|/) : Rational -> Int -> Rational
(|/) =
    divideByInt


{-| Divide an Int by a Rational
-}
(/|) : Int -> Rational -> Rational
(/|) =
    divideIntBy


{-| Synonym for Ratio.divide
-}
(|/|) : Rational -> Rational -> Rational
(|/|) =
    divide