We use types in programming, often without realizing how deeply rooted they are in the foundations of mathematics. There is a constant flow of ideas from type theory to programming (and back). We are familiar with algebraic data types; inductive types, like lists or trees; we've heard of dependent types and, in the future, we might encounter identity types and possibly get familiar with elements of homotopy type theory. I can't possibly talk about all of this, but I'll try to give you a little taste.

PARTICIPANT PREPARATION:

Clone the repository at

https://github.com/plfa/plfa.github.io/

This is the textbook for the course.

Install Agda, the Agda standard library, and configure the plfa library. This can be done by following the instructions under the heading

Getting Started with PLFA

at

https://plfa.github.io/GettingStarted/

Outline:

This course is an introduction to formal methods in Agda, covering datatypes, recursion, structural induction, indexed datatypes, dependent functions, and induction over evidence; with focus on formal definitions of naturals, addition, and inequality, and their properties.

The textbook is freely available online:

• Programming Language Foundations in Agda
  plfa.inf.ed.ac.uk
  github.com/plfa/plfa.github.io/

The book has been used for teaching by me at:

• University of Edinburgh (Sep-Dec 2018)
• Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio) (Mar-Jul 2019)
• University of Padova (Jun 2019)

and by others at

• University of Vermont
• Google Seattle.

The book is described in a paper (of the same title) at the XXI
Brazilian Symposium on Formal Methods, 28--30 Nov 2018, which is
available here:

http://homepages.inf.ed.ac.uk/wadler/topics/agda.html#sbmf

The paper won the SBMF 2018 Best Paper Award, 1st Place.

The Yoneda lemma is not the first thing to learn in category theory, but sooner or later it appears in studying the field. Unfortunately, there is quite a gap between the intuitive idea, "tell me your friends, and I will know who you are" , and its precise formulation. This talk aims to bridge this gap by introducing algebraic results in the middle, namely Cayley's theorem for groups and its generalization to semigroups. These are elementary enough, but at the same time they exhibit the conceptual step of representability, and the idea of studying all different things in a familiar form.

The conventional wisdom in functional programming communities is that lambda calculus was "discovered". Extending the logic of the statement to its extreme, we might propose that an alien would recognize lambda calculus as a computational model. But would we be able to recognize an alien lambda calculus?

This talk is part gedankenexperiment, part speculative fiction, part practical advice on compiler design. We begin by imagining ourselves to be creatures in a universe which is very different from the one we're in, except the notion of consciousness and intelligence are preserved from our current universe. From there, we shall explore the physics and alternate philosophies that would yield an alien lambda calculus.

Of course, being from an alien conception, there are some questions that must be answered - in the name of practicality, is there perhaps even a weak notion of a functor from the alien lambda calculus to that of the one we know today? Is there anything from the alien lambda calculus that we may yield and put into practice? And what is this pesky business with state? Isn't the point of functional programming to hide states from the programmer by abstracting over them? Or was it to make clear the states? And what of names? Isn't lambda purely anonymous?

A quine is a program that outputs its own source code, but can you create a 2 quine, a pair of programs that output each other with an A->B->A->B cycle? What about between different languages? Can you gzip your own source code? Is there a structured way to do this with theory? All these questions will be somewhat answered, in ways that will make your head hurt... math-a-magical demos and over 9000 layers of meta-ness await!

What do programming, quantum physics, chemistry, neuroscience, systems biology, natural language parsing, causality, network theory, game theory, dynamical systems and database theory have in common?

As functional programmers, we know how useful category theory can be for our work - or perhaps how abstruse and distant it can seem. What is less well known is that applying category theory to the real world is an exciting field of study that has really taken off in just the last few years. It turns out that we share something big with other fields and industries - we want to make big things out of little things without everything going to hell! The key is compositionality, the central idea of category theory.

This talk will introduce the emerging field of applied category theory, with the aims of:

• Giving attendees a broad overview of cutting-edge applications of category theory
• Building an understanding of a small number of the most important core concepts
• Getting attendees excited, inspired to learn more, and equipped to apply some basic concepts to their work

In the post-AlphaGo era there is no need for introducing the game of Go. It is one of the most complex games with very simple rules. But wait a minute, how simple are they exactly? ... different solutions for a problem with clashing requirements, leading to endless debates; edge cases where specifications offer no help; complexity hopeless to tame... Are we still talking about the game, or about software development?!? Well, both. This may come as a surprise, but there is no agreement on the rules of Go. The different rule sets are compatible most of the time, but when they disagree, they do it in a big way in deciding who is the winner. Can we fix the rules then? There are researchers working on the problem, but the perfect rule set is as elusive as the perfect software application.

This talk is a cautionary tale about the power and limits of formalization, and how humans relate to formal specifications. We will discuss the different rule sets, analyze their differences. The `simple' case of Go will serve as an analogue for software specifications and foundations of Mathematics.

Type System plays an important role in building type-safe applications which reduce immense runtime exceptions and developer mistakes. This sophisticated system is leverage by Scala’s most famous functional libraries like Scala-Cats and ScalaZ. This feature-rich system allows implementing pure Functional programming on JVM. It is a beast due to its complex syntax as it prevents developers to explore its beautiful aspects like partial types in Scala. In this talk, we’d be taming the beast and use its beauty to solve real-life issues faced during coding

This is a hands-on workshop to show how Typed Spreadsheet Programming library Owlet and Cats typeclasses can help making Reactive UI functional and simple just like how you'd get thing done in spreadsheet.

Functional Programming in practice always end up in question of how to properly abstract effects from pure, testable, rationale business.

Some believe ReaderT is all you need to abstract your effects, some believe that MTL has enough transformers to transform your effects, some believe IO can do all these jobs and much performant, others believe it's best to be able to freely abstract what ever effects they can imagine

But in the real world, when you create a practical industry project that need to scale, as the code base get lager, more effects we will have/need, and much clearer that different cake layers of these 3 technique will fell into

So, eventually we need all of these approaches to server different layer of abstractions, and hence the reason I'm working on luci(鸕鶿) recently.