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A language for describing animated pictures

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Octocat-spinner-32 examples
Octocat-spinner-32 src
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Octocat-spinner-32 LICENSE
Octocat-spinner-32 README.markdown
Octocat-spinner-32 Setup.lhs
Octocat-spinner-32 fdl.cabal
README.markdown

FDL

FDL (pronounced "Fiddle") stands for Functional Drawing Language. It is a language for describing animated pictures. It was originally implemented as an embedded DSL in Haskell, but is now a full language with a standalone evaluator which renders using OpenGL. I'm also considering compiling to Processing.js. It is an example of Functional Temporal Programming (sometime called Functional Reactive Programming or FRP)

History

I wanted a way to teach programming to my daughters. I needed a problem domain that would motivate them and a language that would allow them to:

  • do something immediately;

  • do simple things quickly;

  • compose simple ideas to produce impressive results.

I also wanted something that would stimulate ideas from the basic building blocks.

I felt that a language for drawing pictures would work well as it could produce nice visual results and adding the ability to animate would really bring programs to life. I considered Logo, but as a functional programmer, I was somewhat disturbed by the core stateful nature of Logo programming. FRP frameworks like Fran and Reactive seemed to have the right idea but I found them a little too sophisticated for young learners.

Concept

FDL allows you to describe pictures by composing simple pieces. Attributes such as color, size and position are set in contexts and only affect contained elements - side effects can never escape. Any attribute can be defined as a time-varying value giving rise to animation. Eventually I hope to add audio input too, so pictures can respond to music.

Examples

The simplest FDL program would be something like:

circle

which... draws a circle. It uses the default color and size, so it will be white with a radius of 1. 1 what? Well a circle of radius of 1 will fill the window. Want it red?

color red circle

What this means is, with the drawing color set to red, draw a circle. We can compose drawings by following one by another (note that line breaks and indentation are significant), so:

color red circle
star

draws a white star on a red circle. Note that the color only affects the contained drawing, the circle. If we wanted them both red (which would be stupid), we would use an indented block:

color red
  circle
  star

We can name drawings so that we can reuse them:

move (-1/2,0) logo
move (1/2,0) logo

logo =
  size (1/2)
    color red circle
    star

We can add parameters to named drawings to create functions:

move (-1/2,0) (logo red)
move (1/2,0) (logo blue)

logo c =
  size (1/2)
    color c circle
    star

By setting an attribute as a time varying value, we get animations.

size pulse
  color red circle
  star

"pulse" gives a value that oscillates between 0 and 1. It uses a sine wave with a period of 1 second, so this gives a rather nasty pulsating effect. If we slow it down it is not so horrid:

speed (1/5)
  size pulse
    color red circle
    star

For more examples see the examples folder.

Running the examples

To install the package, switch to the root directory of the package and run

cabal install

To run an example use the draw command:

draw examples/xxx.hs

where xxx.hs is whichever example you want to run.

Status

All the examples above should work now. The language supports the following primitives:

Shapes

  • circle - A circle of unit radius (fills the window)

  • star - A 5 pointed star of unit radius

  • square - A 2 x 2 square (fills the window)

Color

  • color Color Picture - draws the given picture in the given color

  • red, green, blue, yellow, cyan, magenta, white, black, pink, purple - colors

  • rgba Number Number Number Number - produces a color from the given proportions of red green and blue as numbers from 0 to 1 and an alpha value from 0 (transparent) to 1 (solid)

Transformation

  • size Number Picture - draws the given picture scaled by the given size - a positive number where 1 is original size

  • scale (Number, Number) Picture - draws the given picture scaled by the given sizes - a pair of numbers for the width and height

  • move (Number, Number) Picture - draws the given picture at the given position - a pair of coordinates where (-1,-1) is the bottom left and (1,1) is the top right

  • rotate Number Picture - draws the given picture rotated by the given amount - 1 is a full 360 degree rotation

Numbers

  • Number - numbers can be positive or negative (negative numbers may need to be put in brackets)

  • Number + Number - the sum of the two numbers

  • Number - Number - the second number subtracted from the first

  • Number * Number - the product of the two numbers

  • Number / Number - the first number divided by the second

Time

  • time - the number of seconds since the program started

  • pulse - a value that moves smoothly between 0 and 1 - a sine wave of time with period of 1 second

  • speed Number Picture - draws the given picture with time multiplied be the given number

  • delay Number Picture - draws the given picture with time delayed by the given number

See the examples folder for use of all the above.

The language is still likely to change a lot. I've done no optimization of either the expression tree or the GL actions produced.

Learning

Apart from this note, there's no documentation at the moment, but the examples should be pretty self explanatory. I've been implementing the language one feature at a time, so you might want to run through the commit history to see how it developed.

Implementation

I started off by creating an embedded DSL in Haskell.

The implementation really became interesting when I added support for lambdas. Prior to that, I had an abstract syntax tree for your program (this is a deep embedding) and did a fairly simple transformation into a chain of IO actions that get executed for each frame. There was some complexity in the transformation in order to support the time varying values - which I handled using a reader monad to build up the operations in the IO monad. This code was perhaps a little confusing, but not particularly complicated.

Adding lambdas to the language representation was pretty simple, but handling variables in the transform to IO operations was where the fun began. I firstly altered my language representation to applications on primitives rather than nested expressions. Extending this with lambdas and variables formed a lambda calculus. I then implemented a transform to combinatory logic (SKI) which eliminates variables. This transform was actually pretty easy except for the replacement of a variable with the I combinator. The compiler was unable to verify that the types were correct. The solution was to introduce a type equivalence witness. Following this the transformation to the IO chain was trivial.

After that I decided it was time to go for an standalone language. This was mostly driven by wanting simpler syntax and easier to understand error messages. The parser was easy with a combinator library, but the fun bit was type checking and transforming from the untyped parse tree to the original GADT representation. I got pretty stuck on handling functions. The only way I could get it to work was by removing polymorphism from the language.

To see this development take a look at the commit history.

Have fun.

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