-calculus serves as the mathematical bedrock for functional programming. 15-312 explores the untyped and typed variants (such as the Church and Curry formulations), demonstrating how functions alone can encode booleans, integers, and recursion. Polymorphism and Data Abstraction
(Deep dive into call-by-value vs. call-by-name)
Perfect for decomposing abstract syntax trees.
: If a well-typed program takes an execution step, the resulting program has the exact same type as before.
In 15312, concurrency is studied through like CSP (Communicating Sequential Processes) and π-calculus. These formalisms treat programs as interacting processes, allowing algebraic reasoning about communication and synchronization. 15312 foundations of programming languages
Whether you are an aspiring language designer, a compiler engineer, or a software developer looking to drastically level up your code reasoning, understanding the core tenets of 15-312 will transform the way you view software. 1. The Core Philosophy of 15-312
Students analyze the critical differences between eager evaluation (call-by-value, used in languages like C and Java) and lazy evaluation (call-by-name/need, used in Haskell). 4. Type Safety: Progress and Preservation
How does a program decide what to do next? The usual answer: sequential execution, loops, conditionals, function calls.
The curriculum evolves from basic structural concepts to advanced language features: 15-312: Foundations of Programming Languages (Fall 2023) -calculus serves as the mathematical bedrock for functional
), the meaning of the function does not change. This is called (alpha-equivalence).
, which involves proving that "well-typed programs do not go wrong" through theorems like Preservation Structural Induction: Most properties in the course are proven using structural induction
If you want to delve deeper into a specific area of programming language theory, let me know. I can provide detailed , walk through a progress and preservation proof , or explain System F polymorphism . Which of these topics Share public link
Parametric polymorphism enables developers to write reusable code that works with multiple data types. However, manually specifying type parameters can be cumbersome and error-prone. By adding type inference, we can alleviate this burden and make PolyLambda more expressive and user-friendly. It was precise
feat: Add type inference with parametric polymorphism
-calculus). This framework allows functions to abstract over types themselves. You learn the profound difference between (writing code that works universally for any type, like mapping an array) and ad-hoc polymorphism (operator overloading). Storage Effects and Continuations
In the early days of computing, programmers spoke directly to machines in raw binary—ones and zeros. It was precise, but painfully slow. As machines grew more powerful, humans built languages to bridge the gap between human thought and machine execution. But each language had its own rules, quirks, and limitations.