You can get some intuition for how this works by replacing "Moving v" with
its definition "Time -> v". Let's look at the + operation.
class Number a where
(+) :: a -> a -> a
instance Number v => Number (Moving v)
instance Number v => Number (Time -> v)
(+) :: Number v => (Time -> v) -> (Time -> v) -> (Time -> v)
So each argument of + must take a Time, the end result must also take a
Time, and whatever each argument returns must be a Number (and thus has +
defined for it). So you can sort of see how it works. + for a Moving v
takes a time, then passes that time to each of its arguments, then adds the
result.
(+) a b = \t -> (a t) Prelude.+ (b t)
data Time = Time Double -- For example.
Then you can make formulas that are rooted in time. For example
(contrived) if you are throwing a ball, the distance of the ball from you
at time f could be something like the following:
balldistance :: Moving Double
balldistance (Time f) = f * 1.2
ball1 :: Moving Double
ball1 = balldistance
ball2 :: Moving Double
ball2 = balldistance
-- the combined distance of both balls at time f
bothballs :: Moving Double
bothballs = ball1 + ball2
Then you can get the combined distance of both balls after 12 seconds, for
example.
test :: Double
test = bothballs (Time 12.0)
On Tue, Oct 3, 2017 at 9:07 AM, PATRICK BROWNE
Hi, I am trying to compile, run, and understand the following code from [1].
type Moving v = Time -> v
class Number a where (+), (-), (*) :: a -> a -> a sqr, sqrt :: a -> a sqr a = a * a
instance Number v => Number (Moving v) where (+) a b = \t -> (a t) + (b t) (-) a b = \t -> (a t) - (b t) (*) a b = \t -> (a t) * (b t) sqrt a = \t -> sqrt (a t)
I followed the compiler advice to produce the following version which compiles:
{-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE TypeSynonymInstances #-} module MovingPoint where type Time = Float -- Type synonym assumed, could it be data type?? type Moving v = Time -> v
class Number a where (+), (-), (*) :: a -> a -> a sqr :: a -> a sqrt :: a -> a
instance (Floating v) => Number (Moving v) where (+) a b = \t -> (a t) Prelude.+ (b t) (-) a b = \t -> (a t) Prelude.- (b t) (*) a b = \t -> (a t) Prelude.* (b t) sqr a = \t -> (a t) Prelude.* (a t) sqrt a = \t -> Prelude.sqrt (a t)
I do not know how to invoke any of the operations. In general I do know how to execute lambdas. I do not understand the bracketed pairs e.g. (a t). Any help on understanding and running the program would be appreciated. Thanks, Pat
[1] Ontology for Spatio-temporal Databases http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1. 113.9804&rep=rep1&type=pdf
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