[Haskell-cafe] running and understanding a lifting program

[Patrick LeBoutillier]

Patrick,

On Mon, Oct 25, 2010 at 6:12 PM, Patrick Browne <patrick.browne at dit.ie> 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