The PL Junior Seminar is for beginning PhD and interested undergrad and masters students to understand the foundations of programming languages research. It serves to fill in background knowledge and get up to speed with different areas of PL research.

For the spring 2017 instance of PL Junior we chose program synthesis, the sequent calculus, and logic programming as topics we wanted to learn more about. We also did two group paper readings for Luca Cardelli’s Typeful Programming and Alan Kay’s Early History of Smalltalk. At the same time, we changed up the format from the previous semester.

The Programming Language Seminar, Junior (or “PL Junior”), is a seminar for junior students to learn and discuss topics at a pace more suitable to our background. This semester, we decided to study dependent types. We chose this topic because

1. working from the TAPL presentation of type systems, dependent types are a step up in difficulty (excepting F-omega-sub), and
2. they represent a significant increase in the reasoning power of types over programs.

The λ-calculus is often introduced by showing how to build a real programming language from it’s simple syntactic forms. In this series of post, I attempt to introduce it as a tool for modeling semantics. So if you’re opening Barendregt for the first time, trying to understand a lecture from a programming languages or functional programming class, or just starting to become involved in PL research, I hope this post will help you understand evaluation by substitution (β-reduction).