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
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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