<div dir="ltr"><div><div><div><div>You can get some intuition for how this works by replacing "Moving v" with its definition "Time -> v". Let's look at the + operation.<br><br></div><div>class Number a where<br></div><div> (+) :: a -> a -> a<br>instance Number v => Number (Moving v)<br>instance Number v => Number (Time -> v)<br></div><div>(+) :: Number v => (Time -> v) -> (Time -> v) -> (Time -> v)<br><br></div><div>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.<br><br></div><div>(+) a b = \t -> (a t) Prelude.+ (b t)<br><br></div>data Time = Time Double -- For example.<br><br></div><div>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:<br><br></div><div>balldistance :: Moving Double<br></div><div>balldistance (Time f) = f * 1.2<br></div><div><br></div><div>ball1 :: Moving Double<br></div>ball1 = balldistance <br><br><div>ball2 :: Moving Double<br></div>ball2 = balldistance<br><br></div><div>-- the combined distance of both balls at time f<br></div><div>bothballs :: Moving Double<br></div><div>bothballs = ball1 + ball2<br><br></div><div>Then you can get the combined distance of both balls after 12 seconds, for example.<br><br></div><div>test :: Double<br></div><div>test = bothballs (Time 12.0)<br></div><div><br></div></div><br><div><div><div><div><div> <br></div><div><br></div></div></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Oct 3, 2017 at 9:07 AM, PATRICK BROWNE <span dir="ltr"><<a href="mailto:patrick.browne@dit.ie" target="_blank">patrick.browne@dit.ie</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Hi,</div><div>I am trying to compile, run, and understand the following code from [1].</div><div><br></div><div>type Moving v = Time -> v</div><div><br></div><div>class Number a where</div><div>(+), (-), (*) :: a -> a -> a</div><div>sqr, sqrt :: a -> a</div><div>sqr a = a * a</div><div><br></div><div>instance Number v => Number (Moving v) where</div><div> (+) a b = \t -> (a t) + (b t)</div><div> (-) a b = \t -> (a t) - (b t)</div><div> (*) a b = \t -> (a t) * (b t)</div><div> sqrt a = \t -> sqrt (a t)</div><div><br></div><div>I followed the compiler advice to produce the following version which compiles:</div><div><br></div><div>{-# LANGUAGE FlexibleInstances #-}</div><div>{-# LANGUAGE TypeSynonymInstances #-}</div><div>module MovingPoint where</div><div>type Time = Float -- Type synonym assumed, could it be data type??</div><div>type Moving v = Time -> v</div><div><br></div><div>class Number a where</div><div> (+), (-), (*) :: a -> a -> a</div><div> sqr :: a -> a</div><div> sqrt :: a -> a</div><div><br></div><div>instance (Floating v) => Number (Moving v) where</div><div> (+) a b = \t -> (a t) Prelude.+ (b t)</div><div> (-) a b = \t -> (a t) Prelude.- (b t)</div><div> (*) a b = \t -> (a t) Prelude.* (b t)</div><div> sqr a = \t -> (a t) Prelude.* (a t)</div><div> sqrt a = \t -> Prelude.sqrt (a t)</div><div><br></div><div>I do not know how to invoke any of the operations. In general I do know how to execute lambdas.</div><div>I do not understand the bracketed pairs e.g. (a t).</div><div>Any help on understanding and running the program would be appreciated.</div><div>Thanks,</div><div>Pat</div><div><br></div><div><br></div><div>[1] Ontology for Spatio-temporal Databases</div><div><a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.113.9804&rep=rep1&type=pdf" target="_blank">http://citeseerx.ist.psu.edu/<wbr>viewdoc/download?doi=10.1.1.<wbr>113.9804&rep=rep1&type=pdf</a></div></div>
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