[Haskell-beginners] Return type from class method
PATRICK BROWNE
patrick.browne at dit.ie
Mon Oct 9 15:53:42 UTC 2017
David,
Thanks very much for clarifying my confusion.
I would never have thought of the rather subtle import nor the instance
Number P.Float.
Your help is greatly appreciated,
Pat
On 9 October 2017 at 13:53, David McBride <toad3k at gmail.com> wrote:
> Here's a direct translation of the original code. What is missing is an
> instance for Number for Prelude.Float. That is because it is using 4.0 +
> 0.5 * (t :: Time), where Time must be a P.Float, or else if it is a data
> type it must having instances for Fractional, Num, and Floating, so that it
> can be represented as a floating point literal (ie. 4.0).
>
> It might be easier in the long run if you got rid of the Number class and
> just used Prelude's Num class instead. You would have to do some slightly
> different handling to deal with sqrt. Admittedly that might be difficult.
>
> {-# LANGUAGE NoImplicitPrelude, MultiParamTypeClasses, FlexibleInstances
> #-}
>
> import qualified Prelude as P ((+), (-), (*), sqrt, Float)
>
> class Number a where
> (+), (-), (*) :: a -> a -> a
> sqr, sqrt :: a -> a
> sqr a = a * a
>
> type Time = P.Float
>
> type Moving v = Time -> v
>
> instance Number P.Float where
> (+) = (P.+)
> (-) = (P.-)
> (*) = (P.*)
> sqrt = P.sqrt
>
>
> 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)
>
> class Number s => Points p s where
> x, y :: p s -> s
> xy :: s -> s -> p s
> dist :: p s -> p s -> s
> dist a b = sqrt (sqr ((x a) - (x b)) + sqr ((y a) - (y b)))
>
> data Point f = Point f f
>
> instance Number v => Points Point v where
> x (Point x1 y1) = x1
> y (Point x1 y1) = y1
> xy x1 y1 = Point x1 y1
>
> instance Number v => Number (Point v) where
> a + b = xy (x a + x b) (y a + y b)
> a - b = xy (x a - x b) (y a - y b)
>
>
> np1 :: Point (Moving P.Float)
> np1 = xy (\t -> 4.0 + 0.5 * t) (\t -> 4.0 - 0.5 * t)
> np2 = xy (\t -> 0.0 + 1.0 * t) (\t -> 0.0 - 1.0 * t)
> movingDist_1_2 = dist np1 np2
> dist_at_1 = movingDist_1_2 1.0
>
>
> On Sun, Oct 8, 2017 at 1:24 AM, PATRICK BROWNE <patrick.browne at dit.ie>
> wrote:
>
>> Thomas,
>> Thanks for your response. I agree that using (+) in this manner leads to
>> name clashes.
>> My question is prompted by a research paper [1] where a form of lifting
>> is attempted using type classes.
>> I think that the original code in paper (below) is intended to be
>> illustrative rather than practical.
>> I have edited the code to compile and run (after a fashion, see below).
>> But I cannot get the functions to return the lifted type.
>> Also I have a problem compiling the lines with two lambdas, e.g. (np1 =
>> xy (\t -> 4.0 + 0.5 * t) (\t -> 4.0 - 0.5 * t))
>> Regards,
>> Pat
>> ------------------------------------------------------------
>> ---------------------------------
>> Original code [1]:
>> ------------------------------------------------------------
>> ------------------------------
>> class Number a where
>> (+), (-), (*) :: a -> a -> a
>> sqr, sqrt :: a -> a
>> sqr a = a * a
>>
>> type Moving v = Time -> v
>>
>> 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)
>>
>> class Number s => Points p s where
>> x, y :: p s -> s
>> xy :: s -> s -> p s
>> dist :: p s -> p s -> s
>> dist a b = sqrt (sqr ((x a) - (x b)) +
>> sqr ((y a) - (y b)))
>>
>> data Point f = Point f f
>>
>> instance Number v => Points Point v where
>> x (Point x1 y1) = x1
>> y (Point x1 y1) = y1
>> xy x1 y1 = Point x1 y1
>>
>> instance Number v => (Point v) where
>> (+) a b = xy (x a + x b) (y a + y b)
>> (-) a b = xy (x a - x b) (y a - y b)
>>
>>
>> np1, np2 :: Point (Moving Float)
>> np1 = xy (\t -> 4.0 + 0.5 * t) (\t -> 4.0 - 0.5 * t)
>> np2 = xy (\t -> 0.0 + 1.0 * t) (\t -> 0.0 - 1.0 * t)
>> movingDist_1_2 = dist np1 np2
>> dist_at_1 = movingDist_1_2 1.0
>>
>>
>> ------------------------------------------------------------
>> ----------------------------------
>> My attempt at getting above code to run:
>> ------------------------------------------------------------
>> -----------------------------------
>> {-# LANGUAGE MultiParamTypeClasses #-}
>> {-# LANGUAGE FlexibleInstances #-}
>> {-# LANGUAGE TypeSynonymInstances #-}
>> module Moving where
>> data Time = Time Double
>> type Moving v = Time -> v
>> data Point v = Point v v deriving Show
>>
>> class Number a where
>> (+),(-),(*) :: a -> a -> a
>> sqrt :: a -> a
>>
>>
>> instance (Fractional a,Floating a) => Number (Moving a) 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))
>> sqrt a = \t -> Prelude.sqrt (a t)
>>
>> a,b :: Moving Double
>> a (Time x) = 4.0
>> b (Time x) = 4.0
>> testPlus ::(Moving Double)
>> testPlus = (a Moving.+ b)
>> testPlusArg = (a Moving.+ b) (Time 2.0)
>> testSqrt = (Moving.sqrt a) (Time 2.0)
>>
>>
>>
>> class (Number s) => Points p s where
>> x, y :: p s -> s
>> xy :: s -> s -> p s
>> dist :: p s -> p s -> s
>> dist a b = Moving.sqrt (sqr ((x a) Moving.- (x b)) Moving.+ sqr ((y a)
>> Moving.- (y b)))
>> where sqr z = z Moving.* z
>>
>>
>>
>> -- instance (Floating v,Number v) => Points Point v where
>> instance (Number s) => Points Point s where
>> x (Point x1 y1) = x1
>> y (Point x1 y1) = y1
>> xy x1 y1 = Point x1 y1
>>
>> instance Number v => Number (Point v) where
>> (+) a b = xy (x a Moving.+ x b) (y a Moving.+ y b)
>> (-) a b = xy (x a Moving.- x b) (y a Moving.- y b)
>>
>>
>> md1,md2,md3,md4 :: Moving Double
>> md1 (Time x) = 0.0
>> md2 (Time x) = 0.0
>> md3 (Time x) = 10.0
>> md4 (Time x) = 10.0
>> testMD1 = (md1 (Time 2.0))
>> testX = x (Point md1 md2) (Time 2.0)
>> testY = y (Point md1 md2) (Time 2.0)
>> testXY = (xy md1 md2)::(Point (Moving Double))
>> testX' = x testXY (Time 1.0)
>> testD = dist (Point md1 md2) (Point md3 md4) (Time 1.0)
>>
>> --- I cannot get the rest to work
>>
>> [1] Ontology for Spatio-temporal Databases
>> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.113
>> .9804&rep=rep1&type=pdf
>>
>> On 7 October 2017 at 23:30, Thomas Jakway <tjakway at nyu.edu> wrote:
>>
>>> You could hide Prelude and define it yourself in a different module but
>>> that would be a pretty bad idea. Everyone who wanted to use it would have
>>> to import your module qualified and refer to it as MyModule.+, which
>>> defeats the point of making it (+) and not `myAdditionFunction` in the
>>> first place.
>>>
>>> Haskell deliberately doesn't allow overloading. Having (+) return
>>> something other than Num would be extremely confusing.
>>>
>>> On 10/07/2017 05:07 AM, PATRICK BROWNE wrote:
>>>
>>> Hi,
>>> Is there a way rewriting the definition of (+) so that testPlusArg
>>> returns a (Moving Double). My current intuition is that the signature [(+)
>>> :: a -> a -> a] says that the type should be the same as the arguments.
>>> And indeed (:t testPlus) confirms this. But the type of testPlusArg is a
>>> Double.
>>> Can I make it (Moving Double) ?
>>> Thanks,
>>> Pat
>>>
>>>
>>> {-# LANGUAGE FlexibleInstances #-}
>>> {-# LANGUAGE TypeSynonymInstances #-}
>>> module Moving where
>>> data Time = Time Double
>>> type Moving v = Time -> v
>>>
>>> class Number a where
>>> (+) :: a -> a -> a
>>>
>>> instance Number (Moving Double) where
>>> (+) a b = \t -> ((a t) Prelude.+ (b t))
>>>
>>> a,b :: Moving Double
>>> a (Time x) = 2.0
>>> b (Time x) = 2.0
>>> testPlus ::(Moving Double)
>>> testPlus = (a Moving.+ b)
>>> testPlusArg = (a Moving.+ b) (Time 2.0)
>>>
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