15-312 is famous for using Standard ML (SML) as its implementation language. Why SML?
Furthermore, advanced sections use Twelf (a logical framework) to encode programming language definitions as logic programs. In Twelf, you declare rules, and the system checks if your type safety proof is valid. It’s like a proof assistant for language designers.
A student who finishes 15312 sees code differently. A loop is not just a loop—it’s a fixed point. A variable is not just a name—it’s a reference cell in a store. A function call is not just a jump—it’s a β-reduction in lambda calculus.
They can look at a new language and ask:
The foundations of programming languages are the grammar, logic, and mathematics of computation itself. And once you learn them, every language becomes a dialect of a single, universal tongue—the language of thought made formal.
End of story.
Since "15-312 Foundations of Programming Languages" is the specific course number for Carnegie Mellon University (CMU), this guide is tailored to that curriculum. The course is famous for its rigorous, mathematically grounded approach to programming languages, primarily based on the book "Practical Foundations for Programming Languages" (PFPL) by Robert Harper.
This is not a "learn to code in Python" course; it is a "learn how and why programming languages work" course. It deals with type theory, logic, and the mathematical structure of computation.
Here is a comprehensive guide to navigating 15-312.
Primary Resource: Practical Foundations for Programming Languages (PFPL) by Robert Harper.
Our type inference algorithm is based on the Hindley-Milner algorithm. We'll extend it to support parametric polymorphism.
Algorithm Steps:
Modern engineering relies on DSLs (SQL, Regex, configuration languages like YAML, even Terraform HCL). 15-312 gives you a blueprint for defining your own language: syntax, semantics, and a type checker.
