Replace (#) with (&)

[RyanGlScott]

Right now, we have a function (#) :: a -> (a -> b) -> b such that a # f = f a. It works, but there's been talk of using the (#) as a natural transformation instead (currently in the wakarusa repo). With this, we could define natural transformations such as:

instance Transformation Canvas IO DeviceContext where
    (#) = send

However, this would not work for things that we currently use the blank-canvas (#) for, such as grd # addColorStop(0, "#8ED6FF") and (defFont [sansSerif]) { fontSize = 30 # pt }. I think the best way to mitigate such a change would be to use the (&) :: a -> (a -> b) -> b function that was introduced in GHC 7.10 in Data.Function (if one is using an older version of GHC, it's easy to redefine it: a & f = f a). There's also a bit of history in that (&) is also used in lens, so it's not a completely arbitrary choice of name.

@andygill, what are your thoughts?

[andygill]

Idea: make grd a natural Transformation, and then grd # addColorStop(0, "#8ED6FF") can be made to work, with a bit of persuasion.

[RyanGlScott]

How would a CanvasGradient instance for Natural work? I ask since the type signature for addColorStop—(Double, Text) -> CanvasGradient -> Canvas ()—is entirely monomorphic, so I don't see how it admits an instance of Natural, which requires two parametrically polymorphic types.

[RyanGlScott]

The closest thing I can think of is

instance Transformation ((->) CanvasGradient) Identity CanvasGradient where
    grd # f = Identity (f grd)

but that would make grd # addColorStop(0, "#8ED6FF") return something of type Identity (Canvas ()), not Canvas ().

[andygill]

Currently

 addColorStop :: CanvasColor color => (Interval, color) -> CanvasGradient -> Canvas ()

Here's the trick

addColorStop :: CanvasColor color => (Interval, color) -> ColorCommand ()
type CanvasGradient = Natural ColorCommand Canvas

Thus

grd # addColorStop(0, "#8ED6FF")

[RyanGlScott]

I'm a bit confused. What is ColorCommand?

[andygill]

data ColorCommand where
  AddColorStop' :: CanvasColor color => (Interval, color) -> ColorCommand ()
addColorStop = AddColorStop'

Which means what is grd?

grd = Natural $ \ f -> case f of 
  AddColorStop' (inv,col) -> Command (AddColorStop (off,rep) <<original-grd :: CanvasGradient>>)

So the grd "adds" the original CanvasGradient, when the Natural transformation is applied.

[RyanGlScott]

Ah. So if I'm understanding you correctly, we would (1) create a separate ADT for "member functions" of CanvasGradient, (2) change CanvasGradient from a wrapper around a buffer number to a Natural, (3) change createLinearGradient and createRadialGradient to return a Natural that gives you original_grd and (4) change the type signature of addColorStop to be compatible with this scheme.

This sounds pretty promising, but it would break some existing blank-canvas code in the wild right now (e.g., diagrams-canvas currently expects addColorStop to take grd as an argument).

[andygill]

How about

grd # do addColorStop(0.0, "red")
         addColorStop(0.5, "green")
         addColorStop(1.0, "blue")

This is possible with some trickery.

[RyanGlScott]

You're right. I suppose we could use a similar trick to what Canvas does (by having Bind and Return constructors), or we could wrap it in a Free monad.