Composability and/or associativity for scaling

[smilack]

Composability

Potentially a Semigroupoid instance:

Semigroupoid

class Semigroupoid a where

A Semigroupoid is similar to a Category but does not require an identity element identity, just composable morphisms.

Semigroupoids must satisfy the following law:

• Associativity: p <<< (q <<< r) = (p <<< q) <<< r

One example of a Semigroupoid is the function type constructor (->), with (<<<) defined as function composition.

Members

• compose :: forall d c b. a c d -> a b c -> a b d

If it will be possible to create arbitrary Scalers (#50), then chaining them may become a problem. Consider an application containing a certain area that should be treated as a cartesian graph:

• canvas ⇄ drawing
• drawing ⇄ graph

Going between canvas and graph requires two conversions:

(graphCoords *~> drawing) *~> canvas

I believe that the scaling functions should be composable, so that this would be equivalent:

graphToCanvas = drawing >>> canvas
graphCoords *~> graphToCanvas

Problem

A Semigroupoid instance would require Scaler to have a newtype or data definition, and type parameters for the from and to types. Something like:

import Gesso.Geometry (Scaler, Canvas, Drawing, mkScaler)

data Graph

graphToDrawing :: Scaler Graph Drawing 
graphToDrawing = _.b $ mkScaler graphRect drawing.rect

-- assuming `scalers` is in context
graphToCanvas :: Scaler Graph Canvas
graphToCanvas = graphToDrawing >>> scalers.canvas

But the convenience fields would become less convenient, e.g.:

graphRect = getX drawingToGraph
-- or:
_.x $ unwrap $ drawingToGraph

Alternative

Composition doesn't necessarily require Semigroupoid. Nothing prevents this:

compose :: Scaler -> Scaler -> Scaler
compose aToB bToC = bToC
  { scaling
      { all = aToB.all >>> bToC.all
      , x = aToB.x >>> bToC.x
      , y = aToB.y >>> bToC.y
      , length = aToB.length >>> bToC.length
      }
  }

Associativity

Alternately, or in addition, the scaling operators could be changed from infix to infixr or infixl.

(graphCoords *~> drawing) *~> canvas -- fine
graphCoords *~> (drawing *~> canvas) -- not fine

canvas <~* (drawing <~* graphCoords) -- fine
(canvas <~* drawing) <~* graphCoords -- not fine

canvas <~* graphCoords *~> drawing -- definitely not fine