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PODCAST

Iowa Type Theory Commute

Aaron Stump talks about type theory, computational logic, and related topics in Computer Science on his short commute.

technology mathematics

All Episodes

16:18

Nominal Isabelle/HOL

Iowa Type Theory Commute ·

2025/01/31

In this episode, I discuss the paper Nominal Techniques in Isabelle/HOL, by Christian Urban. This paper shows how to reason with terms modulo alpha-equivalence, using ideas from nominal logic. The basic idea is that instead of renamings, one works with permutations of names.

en-us

19:54

The Locally Nameless Representation

Iowa Type Theory Commute ·

2025/01/03

I discuss what is called the locally nameless representation of syntax with binders, following the first couple of sections of the very nicely written paper "The Locally Nameless Representation," by Charguéraud. I complain due to the statement in the paper that "the theory of λ-calculus identifies terms that are α-equivalent," which is simply not true if one is considering lambda calculus as defined by Church, where renaming is an explicit reduction step, on a par with beta-reduction.&n...

en-us

15:14

POPLmark Reloaded, Part 1

Iowa Type Theory Commute ·

2024/12/23

I discuss the paper POPLmark Reloaded: Mechanizing Proofs by Logical Relations, which proposes a benchmark problem for mechanizing Programming Language theory.

en-us

13:59

POPLmark Reloaded, Part 2

Iowa Type Theory Commute ·

2024/12/23

I continue the discussion of POPLmark Reloaded , discussing the solutions proposed to the benchmark problem. The solutions are in the Beluga, Coq (recently renamed Rocq), and Agda provers.

en-us

12:20

Introduction to Formalizing Programming Languages Theory

Iowa Type Theory Commute ·

2024/11/25

In this episode, I begin discussing the question and history of formalizing results in Programming Languages Theory using interactive theorem provers like Rocq (formerly Coq) and Agda.

en-us

17:39

Turing's proof of normalization for STLC

Iowa Type Theory Commute ·

2024/05/21

In this episode, I describe the first proof of normalization for STLC, written by Alan Turing in the 1940s. See this short note for Turing's original proof and some historical comments.

en-us

9:39

Introduction to normalization for STLC

Iowa Type Theory Commute ·

2024/05/14

In this episode, after a quick review of the preceding couple, I discuss the property of normalization for STLC, and talk a bit about proof methods. We will look at proofs in more detail in the coming episodes. Feel free to join the Telegram group for the podcast if you want to discuss anything (or just email me at aaron.stump@gmail.com).

en-us

7:29

The curious case of exponentiation in simply typed...

Iowa Type Theory Commute ·

2024/05/04

en-us

9:56

Arithmetic operations in simply typed lambda calculus

Iowa Type Theory Commute ·

2024/05/04

en-us

15:45

More on basics of simple types

Iowa Type Theory Commute ·

2024/04/29

en-us

15:41

Begin Chapter on Simple Type Theory

Iowa Type Theory Commute ·

2024/04/19

en-us

23:16

Some advanced examples in DCS

Iowa Type Theory Commute ·

2023/09/25

en-us

19:45

DCS compared to termination checkers for type theories

Iowa Type Theory Commute ·

2023/09/19

en-us

17:23

Getting started with DCS

Iowa Type Theory Commute ·

2023/09/10

en-us

11:36

Introduction to DCS

Iowa Type Theory Commute ·

2023/09/04

en-us

15:20

Semantics of subtyping

Iowa Type Theory Commute ·

2023/07/24

en-us

9:06

More on type inference for simple subtypes

Iowa Type Theory Commute ·

2023/07/16

en-us

9:13

Subtyping, the golden key

Iowa Type Theory Commute ·

2023/07/09

en-us

13:27

Type inference with simple subtypes

Iowa Type Theory Commute ·

2023/06/30

en-us

8:05

Basics of subtyping

Iowa Type Theory Commute ·

2023/06/21

en-us

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