(Programming Languages) in Agda = Programming (Languages in Agda)
The most profound connection between logic and computation is a pun. The doctrine of Propositions as Types asserts that propositions correspond to types, proofs to programs, and simplification of proofs to evaluation of programs. The proof of a conjunction is a pair, the proof of a disjunction is a case expression, and the proof of an implication is a lambda expression. Proof by induction is just programming by recursion.
Dependentlytyped programming languages, such as Agda, exploit this pun. To prove properties of programming languages in Agda, all we need do is program a description of those languages Agda. Finding an abstruse mathematical proof becomes as simple and as fun as hacking a program. This talk introduces *Programming Language Foundations in Agda*, a new textbook that is also an executable Agda scriptand also explains the role Agda is playing in IOHK's new cryptocurrency.
Target Audience
Programmers
Links
schedule Submitted 7 months ago
People who liked this proposal, also liked:

keyboard_arrow_down
Bartosz Milewski  A Taste of Type Theory
60 Mins
Keynote
Beginner
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.

keyboard_arrow_down
Edward Kmett  Logic Programming à la Carte
Edward KmettChair of the Haskell Core Libraries Committee, Research EngineerMachine Intelligence Research Instituteschedule 7 months ago
30 Mins
Invited Talk
Beginner
I've been working on a logic programming framework in Haskell, called guanxi (關係) with an eye towards scalability. To build it I leaned heavily on my previous work on propagators and a bunch of other little bits and pieces of algebra and category theory in the design process. A number of patterns have arisen repeatedly throughout the process of building this library. I'll give a tour through the current state of guanxi and try to extract some of the more reusable bits of its design for your inspection. 
keyboard_arrow_down
Philip Wadler  Programming Language Foundations in Agda
Philip WadlerProfessor of Theoretical Computer ScienceUniversity of Edinburghschedule 4 months ago
90 Mins
Code Jam
Advanced
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 (SepDec 2018)
 Pontifícia Universidade Católica do Rio de Janeiro (PUCRio) (MarJul 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, 2830 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.
 Programming Language Foundations in Agda

keyboard_arrow_down
Edward Kmett / Tony Morris  Let's Lens
Edward KmettChair of the Haskell Core Libraries Committee, Research EngineerMachine Intelligence Research InstituteTony MorrisSr. Software EngineerQueensland FP Lab, Data61schedule 7 months ago
480 Mins
Introductory Workshop
Beginner
Let's Lens presents a series of exercises, in a similar format to the Data61 functional programming course material. The subject of the exercises is around the concept of lenses, initially proposed by Foster et al., to solve the viewupdate problem of relational databases.
The theories around lenses have been advanced significantly in recent years, resulting in a library, implemented in Haskell, called lens.
This workshop will take you through the basic definition of the lens data structure and its related structures such as traversals and prisms. Following this we implement some of the lowlevel lens library, then go on to discuss and solve a practical problem that uses all of these structures.

keyboard_arrow_down
Attila EgriNagy  Approaching the Yoneda Lemma
Attila EgriNagyAssociate Professor of MathematicsAkita International Universityschedule 6 months ago
30 Mins
Talk
Intermediate
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.

keyboard_arrow_down
Xuanyi Chew  An Alien Lambda Calculus
30 Mins
Talk
Beginner
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?

keyboard_arrow_down
Andy Kitchen  Metaquines
30 Mins
Talk
Beginner
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... mathamagical demos and over 9000 layers of metaness await!

keyboard_arrow_down
Ken Scambler  Applied Category Theory  The Emerging Science of Compositionality
30 Mins
Talk
Intermediate
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 cuttingedge 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

keyboard_arrow_down
Attila EgriNagy  The rules of the game
Attila EgriNagyAssociate Professor of MathematicsAkita International Universityschedule 6 months ago
30 Mins
Talk
Beginner
In the postAlphaGo 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.

keyboard_arrow_down
Harmeet Singh  Type System: The Beauty And The Beast
30 Mins
Talk
Intermediate
Type System plays an important role in building typesafe applications which reduce immense runtime exceptions and developer mistakes. This sophisticated system is leverage by Scala’s most famous functional libraries like ScalaCats and ScalaZ. This featurerich 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 reallife issues faced during coding

keyboard_arrow_down
Harmeet Singh  Simplified Scala Monads And Transformation
30 Mins
Talk
Beginner
Keeping the functional paradigm intact while using complicated monad structure in your code could be quite a tedious task. Especially, when your business logic needs to be structured in a flow, suddenly you realize that your code is moving away from the functional paradigm. Well, definitely Monads composition is the savior in this kind of situations, however, composing them practically is again a cumbersome task. We will be jumping into some coding examples in this talk, which would hopefully make you sit back and relax when you face this kind of situation again. We will create custom monads, right usage of monadic operator and resolution of monad composition problems and monads transformation with some reallife scenarios and examples.

keyboard_arrow_down
Jichao Ouyang  Building blocks reactive UI with <&> <+> flatMap ... in Scala.js

keyboard_arrow_down
Jichao Ouyang  Functional "Design Pattern"? ReaderT, MTL or Free Monad? Why not all?
30 Mins
Talk
Intermediate
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.