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Arithmetic and logical expressions elegantly modeled and visualized using protocol-oriented binary trees. 🌳
Swift Objective-C
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Expression.playground Simplification of operator protocols Dec 29, 2017
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Twitter: @pangburnout

Arithmetic and logical expressions elegantly modeled and visualized using protocol-oriented binary trees with value semantics.


  • Model arithmetic and logical expressions using binary trees.
  • Write expressions in code in the same manner as they would be written for evaluation, i.e. making full use of literals and both unary and binary operators.
  • Visualize expressions by rendering image representations, which can be easily seen using the Xcode Playground QuickLook feature.
  • Animate the evaluation of expressions using UIViews, and observe these animations using the Xcode Playground Live View feature.
  • Demonstrate the power of protocol-oriented programming by creating other simple tree structures, such as binary search trees, which gain QuickLook visualization for free.


The principal focus of this project is to demonstrate the structure and evaluation of arithmetic and logical expressions in an elegant, expressive way. Thanks to Swift's powerful ExpressibleBy*Literal protocols and operator overloading, we can write code like this:

let expression: ArithmeticExpression<Int> = 2*(1+3)-8/4

and in doing so create the full tree representing this expression, which in turn can be visualized in an Xcode Playground via QuickLook:

Furthermore, we can animate the evaluation of this expression by calling animateEvaluation(of:) in a Playground page. We can observe this animation in the Playground's Live View:

In addition to arithmetic expressions, logical expressions can be similarly created, viewed, and animated.

let expression: LogicalExpression = !(true || false) && false || !true

As a simple demonstration of the power of protocol-oriented programming, I've also implemented a couple of other tree structures, including a traditional binary search tree and a red-black tree, which can be visualized with QuickLook.

Getting Started

While a brief outline of the project's contents is provided in the section above, this is a Playground-based project and ultimately better demonstrated than explained:

  1. Clone the project.
  2. Open Expression.xcworkspace.
  3. Build the project.
  4. Within the Expression Playground, navigate to the ArithmeticExpression page to begin.
  5. See the magic through Xcode Playground's QuickLook and Live View features. Each Playground Page demonstrates a type of expression or other tree-based structure.


Expressions is released under the MIT license. See LICENSE for details.

If you find this project to be a useful tool in learning or teaching expressions or binary trees, please reach out to me on Twitter--I'd love to hear from you.

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