(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 11 months ago
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Edward Kmett  Logic Programming à la Carte
Edward KmettChair of the Haskell Core Libraries Committee, Research EngineerMachine Intelligence Research Instituteschedule 11 months ago
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Philip Wadler  Programming Language Foundations in Agda
Philip WadlerProfessor of Theoretical Computer ScienceUniversity of Edinburghschedule 8 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

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Ken Scambler  Applied Category Theory  The Emerging Science of Compositionality
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