How do we write one function that works for many types? 15-312 distinguishes between:
The study of programming languages is a fundamental aspect of computer science, and 15312 Foundations of Programming Languages provides a comprehensive introduction to the design, implementation, and analysis of programming languages. In this post, we will explore the key concepts, principles, and techniques that underlie programming languages.
You might ask: "I build web apps. Do I really need to understand the simply typed lambda calculus?" 15312 foundations of programming languages
Yes. Here is why the foundations of programming languages makes you a better engineer:
You will extend the basic calculus with powerful features: How do we write one function that works for many types
Before diving into the specifics of the 15-312 syllabus, we must understand the three pillars that support the entire discipline: Syntax, Semantics, and Type Systems.
Syntax is the surface. In formal foundations, we don't use regular expressions; we use Context-Free Grammars (CFGs) and Abstract Syntax Trees (ASTs) . 15-312 emphasizes the difference between concrete syntax (what the programmer types) and abstract syntax (what the compiler understands). You learn to define languages using BNF (Backus-Naur Form) with a rigor that erases ambiguity. You might ask: "I build web apps
Type theory is the jewel in the crown of 15-312. A type system is a logical discipline for classifying values and expressions. The famous Curry-Howard Correspondence (a central topic) reveals that a program is a proof, and a type is a logical formula. If your program type-checks, it is provably free of certain classes of errors (like adding a string to an integer).