I have a problem with a function which I want to make very polymorphic. I would like to integrate functions, either analytically or numerically. When integrating analytically I provide the result. In the numeric case I would like to use various methods, for now, the tanhsinh routine from tanhsinh. I also want to learn more about gadts, so I tried to find a solution using them.
So far I have the following:
import qualified Data.VectorSpace as DV
import Numeric.Integration.TanhSinh
data IntegrationType a b where
MkAnalytic :: (DV.AdditiveGroup b) => (c -> b) -> c -> c -> IntegrationType Analytic b
MkNumeric :: NumericType -> IntegrationType Numeric [Result]
data Analytic = Analytic
data Numeric = Numeric
data Method = Trapez | Simpson
data IntBounds = Closed | NegInfPosInf | ZeroInf
data NumericType = MkSingleCoreTanhSinh IntBounds Method (Double -> Double) Double Double
| MkParallelTanhSinhExplicit IntBounds (Strategy [Double]) Method (Double -> Double) Double Double
| MkParallelTanhSinh IntBounds Method (Double -> Double) Double Double
integrate :: IntegrationType a b -> b
integrate (MkAnalytic f l h) = f h DV.^-^ f l
integrate (MkNumeric (MkSingleCoreTanhSinh Closed Trapez f l h )) = trap f l h
integrate (MkNumeric (MkSingleCoreTanhSinh Closed Simpson f l h )) = simpson f l h
This code compiles , because I expicitly state in the constructor MkNumeric that the type variable b is
[Result]
Why do I have to do this? Can I not leave the type variable b as in
data IntegrationType a b where
MkNumeric :: NumericType -> IntegrationType Numeric b
When I do this I get an error:
Could not deduce (b ~ [Result])
from the context (a ~ Numeric)
bound by a pattern with constructor
MkNumeric :: forall b. NumericType -> IntegrationType Numeric b,
in an equation for `integrate'
at test-classes-new-programm.hs:139:12-64
`b' is a rigid type variable bound by
the type signature for integrate :: IntegrationType a b -> b
at test-classes-new-programm.hs:137:14
Relevant bindings include
integrate :: IntegrationType a b -> b
(bound at test-classes-new-programm.hs:138:1)
In the expression: trap f l h
In an equation for `integrate':
integrate (MkNumeric (MkSingleCoreTanhSinh Closed Trapez f l h))
= trap f l h