Highly-Assured PLDI using Dependent Types.

In this first lecture we will look at how we can represent abstract syntax using dependent types. Specifically, we will show how dependent types support embedding of a language’s type-system directly within the term representation itself.

By the end of this lecture you will be able to:

1. understand that term representation using algebraic datatypes can lead to ill-typed terms being constructed;
2. explain how intrinsically-typed terms support construction of well-typed terms;
3. be able to construct intrinsically-typed terms for expressions, statements, and programs;
4. explain how dependent-types and quantitative type-theory make nameless representations runtime efficient;

The lecture is split into the following sections:

• The Problem with ASTs and ADTs
• Typing Expressions
• Nameless Representations
• Efficiently Nameless
• Typing Statements
• Typing Memory
• Typing Imperative Programs
• Summary
• Exercises