On Oct 24, 2010, at 15:12, Patrick Browne wrote:
hi, I am trying to run and understand a lifting program from [1]. The program lifts points to moving points that vary their position over time. I made some effort to run the progrm but I do not know how to overide the +,-,*,sqr, and sqrt from the Num class. Below is my current attempt.
I do not wish to change or imporve the code, rather I wish to understand it as it stands and find out what needs to be added to get the outputs shown below i.e. distance between points p1 and p2 --> 1.55 and the distance between moving points mp1 and mp2 for time 2 ----> 5.83.
I got pretty close with {-# LANGUAGE TypeSynonymInstances, FlexibleInstances #-} import Prelude hiding ((+), (-), (*), sqrt) import qualified Prelude data Point a = Point a a type Time = Float type Changing v = Time -> v lift0 a = \t -> a lift1 op a = \t -> op (a t) lift2 op a b = \t -> op (a t) (b t) class PlusMinus a where (+), (-) :: a -> a -> a instance PlusMinus Float where (+) = (Prelude.+) (-) = (Prelude.-) instance PlusMinus s => PlusMinus (Point s) where (+) (Point x y) (Point x' y') = Point (x+x') (y+y') (-) (Point x y) (Point x' y') = Point (x-x') (y-y') class PlusMinus a => Number a where (*) :: a -> a -> a sqr, sqrt :: a -> a sqr a = a * a instance Number Float where (*) = (Prelude.*) sqrt = Prelude.sqrt class Number s => Points s where x, y :: Point s -> s x (Point x' y') = x' y (Point x' y') = y' dist :: Point s -> Point s -> s dist (Point x y) (Point x' y') = sqrt $ sqr (x-x') + sqr (y-y') instance Points Float instance PlusMinus v => PlusMinus (Changing v) where (+) = lift2 (+) (-) = lift2 (-) instance Number v => Number (Changing v) where (*) = lift2 (*) sqrt = lift1 sqrt instance Points (Changing Float)
[1] A Mathematical Tool to Extend 2D Spatial Operations to Higher Dimensions: by Farid Karimipour1,2, Mahmoud R. Delavar1, and Andrew U. Frank2
Cheers, Bastian