The Progress theorem states that if a program is well-typed (
The Progress theorem states that if a program is well-typed, it is either already a value (fully evaluated) or it can take an execution step. In short, a well-typed program never gets "stuck" in an undefined state. 2. Preservation
Instead of teaching you how to use a specific language like Python or Java, 15-312 teaches you how to design and reason about languages themselves. The course relies heavily on mathematical logic and type theory to prove that a language behaves exactly as intended. Core Pillars of the Curriculum
Enables code reuse while maintaining strict compile-time type safety. Dynamic classification 15312 foundations of programming languages
ABTs build scope directly into the syntax representation. They mechanically handle alpha-equivalence and (ensuring that substituting a variable into a new scope doesn't accidentally change its meaning because of a name collision). By mastering ABTs, language designers avoid the common pitfalls of scope confusion that plague early language implementations. 3. Statics vs. Dynamics
The rules of type systems that predict program behavior before execution.
Through intensive programming assignments, students build interpreters, type checkers, and compiler phases for various experimental languages, putting theoretical models into working code. 5. Why Study 15-312? The Progress theorem states that if a program
The gold standard of a well-designed language is . In the framework of 15-312, type safety is proven using two fundamental theorems established by computer scientist Robin Milner: Progress: If a program is well-typed (
As the course progresses, students use these foundational tools to analyze complex language paradigms, including:
Type systems catch errors before the program runs. They are the mathematical armor against entire classes of bugs. Preservation Instead of teaching you how to use
As the course progresses, it moves beyond basic arithmetic and functions into complex computational paradigms:
Together, these theorems provide a mathematical guarantee of type safety, ensuring that "well-typed programs cannot go wrong." Higher-Order Features and Abstraction