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Musings on the fatality of infinite loops and other stuff.

Approximating PI With PureScript

Oh, it is Pi day! To be honest, I had not known about it until today but it somehow made it into my Twitter stream. Well, after some relaxed Saturday morning browsing I stumbled across the Wolfram Pi approximation demonstration. It looks like this:

Pi is approximated by computing the area of the inscribed polygon and by dividing that area by the square of the circle radius – after all, the area of a circle is r²π. Obviously, that idea is that beautiful and so simple that Pi has thus been approximated thousands of years ago (of course, there are many better and faster ways!), so I decided to implement it myself.


Some days ago I stumbled across PureScript which compiles to JavaScript. It is heavily influenced by Haskell and shares its quality of static typing. However, it has been designed to target JavaScript from the getgo such that it incorporates the strict evaluation semantics of JavaScript. In addition, it provides a syntax similar to native JavaScript for accessing object properties. Given some Haskell knowledge, PureScript seems to be a decent alternative to Fay or Haste for creating Javascript code! So I thought I would give it a try and implement something similar to the above Wolfram demonstration! So this is the result I accomplished after one day’s work on a PureScript clone:

PureScript learning resources

First of all these are the best resources on PureScript development that I found:

24 days of PureScript gives a very good overview of the PureScript library landscape. Above all, running code for every introduced library is given which is crucial to getting quickly started. In addition, there is a project called Pursuit which provides a search engine for functions of PureScript packages. It is still far from being as useful as Hoogle or Hayoo for Haskell development, though.

PureScript libraries and building process

PureScript libraries are managed by bower which has worked surprisingly well for me. However, at the beginning I had problems getting the interpreter psci running with all dependencies as I’m not used to grunt (and npm) which are typically needed in the whole building process. Anyway, when I decided to use certain PureScript libraries for my implementation their integration worked like a charm!

HTML5 Canvas bindings

PureScript has very decent wrappers of the HTML5 Canvas API in form of purescript-canvas and purescript-free-canvas. Obviously, I made heavy use of those to get the circle and the polygon drawn.

center = { x : 210, y : 210 }
drawCircle = do
  arc { x: center.x, y: center.y, r: radius, start: 0, end: Math.pi * 2 }
  setFillStyle "#000000"

As an argument to arc we actually have an example of the Object syntax of PureScript which is just like native JavaScript.

Angular, React or something else?

PureScript does have bindings to AngularJS and React (find PureScript libraries by searching bower), however, they are both still experimental and alpha. So I somehow didn’t want to commit to something half-working which could be very hard to understand for a PureScript newbie like me. Anyway, I decided that the JQuery binding of purescript-jquery should be enough for my Pi approximation application; in the end, I also used purescript-rx (also mentioned on 24 days of PureScript) but I only scratched the surface of reactive PureScript UI modelling.

What about the slider?

I definitely wanted a fancy slider for setting the number of vertices of the polygon like in the Wolfram demo – without too much ado, I immediately decided on using the vanilla JQuery-UI slider. Copy-Paste. That however means that my PureScript has to somehow interact with the native slider JavaScript.

The main function

The first few lines are about getting representations of the HTML elements with purescript-jquery. Then I define event handlers for changing the number of vertices and for toggling the checkbox to show/hide the triangles. onAsObservable actually is from the purescript-rx binding to the reactive RxJS libraries which could be used to define complex event handling.

main = do
  canvas <- getCanvasElementById "canvas"
  context <- getContext2D canvas
  verticesInput <- select "#vertices"
  polygonArea <- select "#polygonArea"
  pi <- select "#pi"
  triangles <- select "#triangles"

  let updateUI num showTriangles = do
          { pArea : polygonAreaPercent, pi : piApprox } <- showPolygon canvas context num showTriangles
          setText (show polygonAreaPercent <> "%") polygonArea
          setText (show piApprox) pi
  let updateUI' = do
              showTriangles <- ((== "true") <<< stringify) <$> getProp "checked" triangles
              num <- (stringify >>> readInt 10) <$> getValue verticesInput
              updateUI num showTriangles

  trianglesChange <- "click" `onAsObservable` triangles
  trianglesChange `subscribe` \_ -> void updateUI'

  verticesChange <- "focus" `onAsObservable` verticesInput
  verticesChange `subscribe` \_ -> void updateUI'

  updateUI defaultVertices defaultShowTriangles

The Foreign Function Interface

In the above code I accessed the current value of the checkbox and the slider value with the purescript-jquery functions getValue and getProp. However, it was surprisingly difficult to use those values as they were not of type String but Foreign and I got those dragged into the field of the Foreign Function Interface for communicating with JavaScript code. Anyway, after some digging in I ended up writing the function stringify which trivially transforms the incoming Javascript value to a String.

foreign import stringify
  "function stringify(x) {\
 \  return x+\"\";\
 \}" :: Foreign -> String

That’s an example of how you can integrate JavaScript functions in PureScript. It is a little bit of a joke as of now sice you need to add all those backslashes, however, things might get easier in case PureScript gets a meta programming facility like TemplateHaskell in the Haskell world in the future.


All in all, PureScript really makes a nice impression. There is already a surprising number of libraries available; decent, mature bindings to Angular or React would be crucial for getting easy web development adoption, though. Meta programming integration of JavaScript code would also prove very nice as would be Source Map support… anyway, I’m looking forward to using it again and might get into improving it myself.

PS: You find the code for the PureScript application on my GitHub.