Schedule

EventDateDescriptionCourse Material

Lecture09/08/2021
WednesdayWe’ll talk about what Lean is and see what it can do, and also go over some organizational points about the course.
Takeaways: verified programming is fun and powerful, and this course is very experimental!

Lecture09/13/2021
MondayIn this lecture we’ll learn the basics of the Lean programming and specification language: types and terms, type inhabitation, and writing and evaluating very simple functional programs. No proving yet!
We covered HHG 1.1 and 1.2.

Assignment09/13/2021
MondayAssignment #1 released! 
Lecture09/15/2021
WednesdayThe basics of Lean syntax, continuedWe’ll finish Chapter 1 of the HHG, and get a head start on Chapter 2, where we’ll actually start proving some theorems. Today’s topics: inductive types (continued), function definition and evaluation, specifications, and basic tactics. We talked about
intro
andapply
, and how tactic mode is like a proving minigame.More on Chapter 2 next time!

Lecture09/20/2021
MondayBackward (tactic) proofsWe’ll dive into the meat of the HHG Ch. 2: what are some of the moves available to us in the tactic proving minigame, beyond
intro
andapply
? How do we deal with logical connectives:and
,or
,not
, and so on? 
Assignment09/20/2021
MondayAssignment #2 released! 
Lecture09/22/2021
WednesdayBackward (tactic) proofs, continuedWe’ll continue talking about tactic proofs. How do we deal with equality? What about the natural numbers?
We’ll also talk about classical vs constructive logic.

Due09/22/2021 15:00
WednesdayAssignment #1 due 
Lecture09/27/2021
MondayForward proofsWe’ll see another way to write proofs in Lean, incorporating forward reasoning.
Structured (“proofterm”) proofs are a little closer to the underlying logic. Surprise: proofs in Lean are, literally, just terms in the type theory.

Assignment09/27/2021
MondayAssignment #3 released! 
Lecture09/29/2021
WednesdayDependent typesThe type theory that Lean is based on, the Calculus of Inductive Constructions, is an instance of dependent type theory. In DTT, we follow the PAT principle: propositions as types, proofs as terms. (Buzzword: the CurryHoward correspondence!) We’ll look deeper today into these foundations.

Due09/29/2021 15:00
WednesdayAssignment #2 due 
Lecture10/04/2021
MondayFunctional programming: data structuresChapter 4 of the Hitchhiker’s Guide introduces some paradigms – inductive types, structures, recursive definitions, type classes – that might be familiar from other functional programming languages. The interesting thing for us is how these paradigms interact with writing proofs. For instance, how do we mix properties into data structures?

Assignment10/04/2021
MondayAssignment #4 released! 
Lecture10/06/2021
WednesdayFunctional programming: type classes, lists, treesType classes are a language feature inspired by Haskell with equivalents in Scala, ML, and other languages. They allow us a kind of ad hoc polymorphism: we can define functions on types that implement certain interfaces, and can declare that certain types implement these interfaces, without bundling the interfaces into the data type itself.
We’ll see how this interacts with some of the data structures we like to use, as we implement and specify functions on these types.

Due10/06/2021 15:00
WednesdayAssignment #3 due 
No Lecture10/11/2021
MondayIndigenous Peoples' Day 
Lecture10/13/2021
WednesdayInductive predicatesWe’ll cover ch. 5 of the Hitchhiker’s Guide today, on inductive predicates. This will complete what we need to know about foundations for now: inductive predicates give us a way to introduce new propositions and prove things about them.
Inductive predicates are also the source of most of the propositional symbols we’ve used so far –
and
,or
,exists
,eq
, …. 
Due10/13/2021 15:00
WednesdayAssignment #4 due 
Lecture10/18/2021
MondayBigstep operational semanticsWe’re jumping ahead to Chapter 8 today! Time to start putting what we’ve learned into practice. We’ll define the syntax of a toy programming language inside of Lean, discussing the difference between shallow and deep embeddings. Using inductive predicates, we’ll define a transition system and use this to prove things about the execution of programs in this toy language.

Assignment10/18/2021
MondayAssignment #5 released! 
Lecture10/20/2021
WednesdaySmallstep operational semanticsThe bigstep semantics we saw on Monday aren’t finegrained. We can’t reason about intermediate states. An alternative is using a smallstep semantics, where our program execution path is broken down much further. This comes with upsides and downsides.

Lecture10/25/2021
MondayLecture 
Lecture10/27/2021
WednesdayLecture 
Due10/27/2021 15:00
WednesdayAssignment #5 due 
Lecture11/01/2021
MondayLecture 
Lecture11/03/2021
WednesdayLecture 
Lecture11/08/2021
MondayLecture 
Lecture11/10/2021
WednesdayLecture 
Assignment11/14/2021
SundayFinal project released! 
Lecture11/15/2021
MondayLecture 
Lecture11/17/2021
WednesdayLecture 
Lecture11/22/2021
MondayLecture 
No Lecture11/24/2021
WednesdayThanksgiving break 
Lecture11/29/2021
MondayLecture 
Lecture12/01/2021
WednesdayLecture 
Lecture12/06/2021
MondayLecture 
Due12/12/2021 23:59
SundayFinal project due