This repository contains a simple implementation of a stratified picture language written in Scheme. It is heavily inspired by the papers Functional Geometry by Peter Henderson, and Lisp: A Language for Stratified Design by Harold Abelson and Gerald Jay Sussman. A more expansive discussion of these ideas can be found in chapter 2.2.4 of SICP.
The code uses raylib to abstract away context creation and rendering onto a context to focus on the geometry language itself. Gambit Scheme is used as a compiler. Consider everything in this repository experimental( aka, ready to break/explode at any moment).
Consider this code to be "the busy work already done", so that you can experiment with the picture language at your leisure.
This repository is purposefully kept very basic and simple. It is meant to be a starting point for your own experiments, not as some kind of "reference implementation".
This repository comes with raylib already integrated as a git submodule. This reflects my personal preferences, if you prefer to use CMake's FetchPackage, it should be easy enough to modify the main CMakeLists.txt to do that (I haven't tested it, though).
It comes with a simply CMake-based language configuration for Gambit Scheme. These are the tools you need to use the code in this repository:
- CMake
- make (or any build system you prefer, like Ninja, etc.)
- Gambit Scheme
- Optional: Raylib (if you want to use a system-wide installation instead of the submodule provided here)
To start writing code, clone this repository and make sure all submodules are downloaded too:
git clone --recursive https://github.com/georgjz/functional-geometry-gambit-scheme.git functionalgeometryTo build the example code found in src/main.scm, just execute:
cd functionalgeometry
cmake -S . -B build
cmake --build build
./build/functional-geometry-fishBuilding raylib for the first time may take a minute or two, but it only needs to be done once. If you wish to change the name of the output binary, just edit line 8 of CMakeLists.txt.
Because I'm using Arch Linux, there's a bit of a naming conflict when installing Gambit Scheme. So the Gambit compiler gsc is called gambitc on my system (this avoids a naming clash with GhostScript). To avoid this problem, there are three options:
- If you already have Gambit Scheme compiler installed as
gscon your system, change all occurences ofgambitcintogscin all files in thecmakesubdirectory. - If you build Gambit Scheme from source, use the
--enable-interpreter-nameand--enable-compiler-nameoptions during the configuration step to renamegscintogambitc. $ alias gambitc=gsc
It's a bit annoying right now, but this will be fixed when I improve the CMake language definition.
This code tries to follow the ideas presented in Lisp: A Language for Stratified Design. For that purpose, I'm going to describe the layers used in this repository and my reasoning behind my design decisions. I do not claim that this is the best way to execute layered/stratified design, this is just my attempt at it with code written from scratch. The layers/strata are presented from buttom to top.
The ultimate goal is to provide a picture language based on simple procedures that operate under closure over pictures. That is, every procedure takes (a) picture(s), and returns a picture. This allows to you build complex pictures from a handful of simple manipulators and combinators, and lets you define your own easily.
I name this stratum "-1" because these procedures aren't strictly part of the picture language in my understanding. The procedures in src/raylib.scm bind Scheme procedures to their raylib counterparts. For the most part, they take care of creating and destroying an OpenGL context with GLFW for the code to render onto. Some simple rendering procedures are bound too. Keep in mind that I only bind a very small handful of procedures found in raylib, check the documentation for a full list. It may be useful to bind additional raylib prodecures for your own experiments.
src/vector.scm contains a few simple procedures for 2D vector arithmetics. I debated myself if this procedures should rather be in stratum 0, but I reasoned that procedures of one stratum should (ideally) rely exclusively on procedures provided by the stratum directly below it (as you'll see, I wasn't always able to adher to this rule). A proper list of (at least) two floating-point numbers is considered a vector in this code.
(define vec1 '(2.0 3.5)) ; valid vector
(define vec2 (list 6.1 3.33)) ; valid vector
(define vec3 '(4.5 . 7.6)) ; invalid vector, improper list
(define vec4 '(8.1 6.9 5.2)) ; while invalid in a logical sense, would still work with this codeI considered adding helper procedures for boxes, but decided against it for brevity. If you wish to add them, it's trivial to do:
(define offset (lambda (box) (car box)))
(define horiz (lambda (box) (cadr box)))
(define vert (lambda (box) (caddr box)))This is the lowest stratum of the picture language. A picture is a function that takes a box as argument and transforms its list of vectors with the help of the procedure mapper. To create a picture, use the procedure primitive-picture which takes a list of vectors as argument.
These procedures take one or more pictures as argument and return a transformed picture. A picture is worth a thousand words (see what I did there?):
;;; Define actual data to draw
(define triangle (primitive-picture '((0.85 0.15)
(0.85 0.85)
(0.15 0.85)
(0.85 0.15))))
;;; Assume a rendering context with an origin at (0, 0) and a size of 600 by 600 pixels
(define base-box '((0.0 0.0)
(600.0 0.0)
(0.0 600.0)))(triangle base-box)
((rot triangle) base-box)
((flip triangle) base-box)
((above triangle triangle) base-box)
((beside triangle triangle) base-box)
((rot45 triangle) base-box)
((over triangle
(rot (rot triangle)))
base-box)
Caveat: When reading the code in src/primitives.scm and comparing it to Functional Geometry, keep in mind that in Peter Henderson's paper, the origin of the coordinate system is in the lower left corner, while most computer graphic libraries (including raylib) put the origin at the upper left corner. This results in slightly different implementations (i.e., some of the vectors are calculated differently). But the basic idea of manipulating the vectors of an enclosing box to transform pictures remains the same.
This is the real meat of the code. The procedures in this file are probably your best starting point for your own experiments. They all are built on top of the procedures bound in src/primitives.scm to build complexity step by step.
((nonet fish fish fish fish fish fish fish fish) base-box)
Read Functional Geometry. No, seriously.
Read. The. Paper.
- Colors! Line thickess! Use your imagination
- Rewrite the primitives
beside,above, andoveras variadic functions (aka, pass as many images as you want; warning, this is not trivial! May need to rethink how to represent a shape) - Add curves
- There's a lot of duplicate code in
src/primitives.scm, lots of potential for abstraction/flex your functional muscle. - THE THIRD DIMENSION O_O
- In the build commands above, I explicitly tell CMake to use
gcc; I have used bothgccandclangsuccessfully to build all code in this repository. But since Gambit Scheme itself is built withgcc, I prefer to keep it consistent. - This code is not tested on Windows and OSX. I have only tested this code as well as the CMake files on Arch Linux.
- I'd want to add some CEPL-like environment.
Here's a few links with related material that might be helpful:
- The paper Functional Geometry by Peter Henderson
- An implementation based on Henderson's ideas found in Structure and Interpretation of Computer Programs
- A Jupyter notebook implementing square-limit in Julia
- Another LISP implementation by Frank Buß
- A JavaScript/HTML port of Frank Buß' implementation
- Notebook that uses Python
- A very interesting presentation on how the principles presented by Henderson can be used in concatenative languages like PostScript (aka, stack-based languages)
- Very detailed PhD thesis by Ian Mackie, uses geometry to implement programming languages
- A Scala implementation
- Blog post describing the geometric properties of Escher's square limit and how to construct them
Contributions are highly encouraged and welcomed! I'll probably need some help by porting to Windows and OSX; my experience on developing on these platforms is very limited.
Everything in this repository is released under the MIT License (see LICENSE). For the raylib license, go here.