From 776762298b1bcdcbeed08097f6f3b8cf1aabd27e Mon Sep 17 00:00:00 2001 From: Kiana Sheibani Date: Sat, 3 Sep 2022 19:39:56 -0400 Subject: [PATCH] Create Data.Ratio --- ratio.ipkg | 10 ++++++ src/Data/Ratio.idr | 90 ++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 100 insertions(+) create mode 100644 ratio.ipkg create mode 100644 src/Data/Ratio.idr diff --git a/ratio.ipkg b/ratio.ipkg new file mode 100644 index 0000000..1f426b3 --- /dev/null +++ b/ratio.ipkg @@ -0,0 +1,10 @@ +package ratio +version = 1.0.0 + +authors = "Kiana Sheibani" +license = "MIT" + +sourcedir = "src" +readme = "README.md" + +modules = Data.Ratio diff --git a/src/Data/Ratio.idr b/src/Data/Ratio.idr new file mode 100644 index 0000000..63ef2a0 --- /dev/null +++ b/src/Data/Ratio.idr @@ -0,0 +1,90 @@ +module Data.Ratio + +infix 10 // + +export +record Ratio a where + constructor MkRatio + nm, dn : a + +public export +Rational : Type +Rational = Ratio Integer + + +gcd : (Eq a, Integral a) => a -> a -> a +gcd x y = + if x == 0 then y + else if y == 0 then x + else gcd y (x `mod` y) + +export +reduce : (Eq a, Integral a) => Ratio a -> Ratio a +reduce (MkRatio n d) = + let g = gcd n d in MkRatio (n `div` g) (d `div` g) + + +export partial +(//) : (Eq a, Integral a) => a -> a -> Ratio a +n // d = case d /= 0 of + True => reduce $ MkRatio n d + + +namespace Ratio + export %inline + numer : Ratio a -> a + numer = nm + + export %inline + (.numer) : Ratio a -> a + (.numer) = nm + + export %inline + denom : Ratio a -> a + denom = dn + + export %inline + (.denom) : Ratio a -> a + (.denom) = dn + + +export +Eq a => Eq (Ratio a) where + MkRatio n d == MkRatio m b = n == m && d == b + +export +(Ord a, Num a) => Ord (Ratio a) where + compare (MkRatio n d) (MkRatio m b) = + flipIfNeg (b*d) $ compare (n*b) (m*d) + where + flipIfNeg : a -> Ordering -> Ordering + flipIfNeg x EQ = EQ + flipIfNeg x LT = if x >= 0 then LT else GT + flipIfNeg x GT = if x >= 0 then GT else LT + +export +Show a => Show (Ratio a) where + showPrec p (MkRatio n d) = + let p' = User 10 + in showParens (p >= p') (showPrec p' n ++ " // " ++ showPrec p' d) + +export +(Eq a, Integral a) => Num (Ratio a) where + MkRatio n d + MkRatio m b = reduce $ MkRatio (n*b + m*d) (d*b) + MkRatio n d * MkRatio m b = reduce $ MkRatio (n*m) (d*b) + fromInteger x = MkRatio (fromInteger x) 1 + +export +(Eq a, Integral a, Neg a) => Neg (Ratio a) where + negate (MkRatio n d) = MkRatio (-n) d + MkRatio n d - MkRatio m b = reduce $ MkRatio (n*b - m*d) (d*b) + +export +(Eq a, Integral a, Abs a) => Abs (Ratio a) where + abs (MkRatio n d) = MkRatio (abs n) (abs d) + +export +(Eq a, Integral a) => Fractional (Ratio a) where + recip (MkRatio n d) = case n /= 0 of True => MkRatio d n + MkRatio n d / MkRatio m b = case m /= 0 of + True => reduce $ MkRatio (n*b) (m*d)