Patrick, On Mon, Oct 25, 2010 at 6:12 PM, Patrick Browne wrote:

Patrick, Thanks for taking the time to get the program running. It seems fine, but I cannot get the *md* to print out, probably missing the Show class somewhere.

"md" is a function to which you have to give a Time value, basically the Time at which you want to evaluate the Changing points' positions. Try "md 2" in ghci, it should give you the expected value. Patrick

Thanks again, Pat

Patrick LeBoutillier wrote:

...

Patrick,

I found this program interesting and decided to spend a bit of time on it, even though I'm still a newbie. I did a few things to simplify the code, here are some comments:

1) I chose to rename the arithmetic functions in the Number class instead of trying to overload the "real" ones, I'm not that good at Haskell yet...

2) The program had some errors, namely I think the definition of the Point type should be:

      data Point a = Point a a

     to allow for different types of Points.

3) The Points class seemed useless in the end, I simply defined the dist function at the top level.

4) If you import Control.Monad, it makes functions (and therefore "Changing v") into a Monad (maybe my terminology is off here...) and allows you to use the general liftM and liftM2 lifting functions instead of defining your own.

Here's the complete program:

{-# LANGUAGE TypeSynonymInstances, FlexibleInstances #-}

data Point a = Point { x ::a, y :: a } type Time = Float

-- Functor Changing, which adds time parameter t to its input value. -- For example, Changing Float indicates a changing floating number -- (i.e. a function of time). type Changing v = Time -> v

-- Lifting functions lift1 op a = \t -> op (a t) lift2 op a b = \t -> op (a t) (b t)

class Number a where  add, sub, mul :: a -> a -> a  square, squareRoot :: a -> a  square a = a `mul` a

instance Number Float where   add = (+)   sub = (-)   mul = (*)   squareRoot = sqrt

instance Number (Changing Float) where   add = lift2 add   sub = lift2 sub   mul = lift2 mul   squareRoot = lift1 squareRoot

-- The distance operation is defined as follow dist :: Number a => Point a -> Point a -> a dist a b = squareRoot $ square((x a) `sub` (x b)) `add` square ((y a) `sub` (y b))

-- Running the code -- If p1 and p2 are two 2D static points, -- their distance d is calculated as follows: p1, p2 :: Point Float p1 = Point 3.4 5.5 p2 = Point 4.5 4.5

-- distance between p1 and p2 --> 1.55 d = dist p1 p2

-- For 2D moving points mp1 and mp2, their distance md, -- which is a function of time, is calculated as follows: mp1, mp2 :: Point (Changing Float) mp1 = Point (\t -> 4.0 + 0.5 * t) (\t -> 4.0 - 0.5 * t) mp2 = Point (\t -> 0.0 + 1.0 * t) (\t -> 0.0 - 1.0 * t) --  distance between mp1 and mp2 md = dist mp1 mp2 -- distance md for time 2 ----> 5.83

...

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Patrick

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-- ===================== Patrick LeBoutillier Rosemère, Québec, Canada