Data.Object.Dynamic.Examples.PointParticle

Here we use dynamic-object to descibe the concept of point-like particles from classical mechanics. Also read the HSpec tests : https://github.com/nushio3/dynamic-object/blob/master/test/ObjectSpec.hs for more details.

Documentation

data Vec a

First, let us create a tiny two-dimensional vector class. We make it an instance of Arbitrary to use them later for tests.

Constructors

Vec a a

Instances

Typeable1 Vec

Eq a => Eq (Vec a)

(Eq (Vec a), Ord a) => Ord (Vec a)

Show a => Show (Vec a)

Arbitrary a => Arbitrary (Vec a)

data Mass

Now, let us introduce the concepts of Mass, Velocity, Momentum and KineticEnergy. Any such concepts are described in terms of Member labels.

Constructors

Mass

Instances

Typeable Mass

(Typeable Mass, Typeable (ValType o Mass), Objective o, UseReal o) => Member o Mass

data Velocity

To define a member with compound types like vector of real numbers, we use UnderlyingReal to ask the object which real value it prefers, then put the response into the type constructors.

We also give a fallback accessor here. If the velocity field is missing, we attempt to re-calculate it from the mass and momentum. Here is how we can do that.

Constructors

Velocity

Instances

Typeable Velocity

(Typeable Velocity, Typeable (ValType o Velocity), Objective o, UseReal o, Fractional (UnderlyingReal o)) => Member o Velocity

data Momentum

If the momentum field is missing, we re-calculate it from the mass and velocity.

Constructors

Momentum

Instances

Typeable Momentum

(Typeable Momentum, Typeable (ValType o Momentum), Objective o, UseReal o, Fractional (UnderlyingReal o)) => Member o Momentum

data KineticEnergy

kineticEnergy, unless given explicitly, is defined in terms of mass and velocity .

Constructors

KineticEnergy

Instances

Typeable KineticEnergy

(Typeable KineticEnergy, Typeable (ValType o KineticEnergy), Objective o, UseReal o, Fractional (UnderlyingReal o)) => Member o KineticEnergy

mass :: MemberLens o Mass

Now we define the lenses.

velocity :: MemberLens o Velocity

momentum :: (UseReal o, Fractional (UnderlyingReal o)) => MemberLens o Momentum

kineticEnergy :: (UseReal o, Fractional (UnderlyingReal o)) => MemberLens o KineticEnergy

fromMassVelocity :: (Objective o, UseReal o, Fractional real, real ~ UnderlyingReal o) => real -> Vec real -> o

We can write functions that would construct a point particle from its mass and velocity. And we can make the function polymorphic over the representation of the real numbers the objects prefer.

fromMassMomentum :: (Objective o, UseReal o, Fractional real, real ~ UnderlyingReal o) => real -> Vec real -> o

We can also construct a point particle from its mass and momentum.

laserBeam :: (Objective o, UseReal o, Fractional real, real ~ UnderlyingReal o) => o

We define an instance of point-like particle. And again, we can keep it polymorphic, so that anyone can choose its concrete type later, according to their purpose. Thus we will achieve the polymorphic encoding of the knowledge of this world, in Haskell.

>>> (laserBeam :: Object DIT) ^? kineticEnergy
Just 1631.25
>>> (laserBeam :: Object Precise) ^? kineticEnergy
Just (6525 % 4)

Moreover, we can ask Ichiro to sign the ball. Usually, we needed to create a new data-type to add a new field. But with 'dynamic-object' we can do so without changing the type of the ball. So, we can put our precious, one-of-a-kind ball into toybox together with less uncommon balls, and with various other toys. And still, we can safely access the contents of the toybox without runtime errors, and e.g. see which toy is the heaviest.

>>> let (mySpecialBall :: Object DIT) = laserBeam & insert Autograph "Ichiro Suzuki"
>>> let toybox = [laserBeam, mySpecialBall]
>>> let toybox2 = toybox ++ [duck, lens, banana, envelope, ghost]
>>> maximum $ mapMaybe (^?mass) toybox2
5.2

duck :: (Objective o, UseReal o, Fractional real, real ~ UnderlyingReal o) => o

lens :: (Objective o, UseReal o, Fractional real, real ~ UnderlyingReal o) => o

banana :: (Objective o, UseReal o, Fractional real, real ~ UnderlyingReal o) => o

envelope :: (Objective o, UseReal o, UseString o, Fractional (UnderlyingReal o), IsString (UnderlyingString o)) => o

ghost :: Objective o => o