Solving the expression problem in Harmonia (with structural typing through row-polymorphism and multi-methods)

expression-problem.hs

module Expression using: Platform where
 
  open Platform Math expose [sqrt, +, -, *, /, π]
  open Platform IO   expose [print]
 
  type Circle = { radius :: Double }
  type Square = { side :: Double }
 
  let { _ | side: s } area = s * s           -- inferred type: { a | side :: Double } -> Double
  let { _ | radius: r } area = π * r * r     -- inferred type: { a | radius :: Double } -> Double
 
  -- Adding a new Triangle type
  type Triangle = { adjacent :: Double, opposite :: Double, hypotenuse :: Double }
 
  let { _ | adjacent: a, opposite: b, hypotenuse: h } area = p * (p - a) * (p - b) * (p - c) |> sqrt
                                                             where 
                                                               p = (a + b + c) / 2
                                                        
 
  -- Adding a new `perimeter` operation to all types
  let { _ | side: s } perimeter = 4 * s
  let { _ | radius: r } perimeter = 2 * π * r
  let { _ | adjacent: a, opposite: b, hypotenuse: h } perimeter = a + b + h
 
  -- Using it
  let (a, b, c) triangle = { adjacent: a, opposite: b, hypotenuse: c }
  let main = do
    { side: 10 } perimeter print.       -- 40
    { side: 5 } area print.             -- 25
    { radius: 3 } perimeter print.      -- 18.84955592153876
    { radius: 5 } area print.           -- 28.274333882308138
    (2, 3, 4) triangle area print.      -- 8.4375
    (2, 3, 4) triangle perimeter print. -- 9
  end
 
end