# # Note 1: use the eev command (defined in eev.el) and the # ee alias (in my .zshrc) to execute parts of this file. As an illustrating example we show how to program a simple certified prover for equations in a commu-tative monoid, which can be used internally in Agda. The methodology is implemented in the ooAgda library. Programming Language Foundations in Agda (SCP) Wen Kokke, Jeremy G. Siek, Philip Wadler. On the Agda Language (in Japanese) Slides (English) Slides (Japanese) Anton Setzer. Accordingly, I have written a new textbook, Programming Language Foundations in Agda (PLFA), based on the proof assistant Agda. I'm a programming language enthusiast and a hobby designer, so obviously, I got interested. The doctrine of Propositions as Types asserts that a certain kind of formal structure may be read in two ways: either as a proposition in logic or as a type in computing. We introduce Voevodsky's univalent foundations and univalent mathematics, and explain how to develop them with the computer system Agda, which is based on Martin-Löf type theory. Ulf Norell, Towards a practical programming. Philip Wadler is an ACM Fellow and a Fellow of the Royal Society of Edinburgh, past chair of ACM SIGPLAN, past holder of a Royal Society-Wolfson Research Merit Fellowship, winner of the SIGPLAN Distinguished Service Award, and a winner of the POPL Most Influential Paper Award. The original Agda system was developed at Chalmers by Catarina Coquand in 1999. It is written as a literate script in Agda, and available at the above URLs. General information on Agda is at. Use of a proof assistant in teaching provides immediate feedback to students. Programming Language Foundations in Agda (plfa.github.io) 71 points by blewboarwastake 10 hours ago | hide | past | favorite | 4 comments: samvher 7 hours ago. In addition, … One of the leading textbooks for formal methods is Software Foundations (SF), written by Benjamin Pierce in collaboration with others, and based on Coq. Co-located workshops and tutorials will take place on August 18 and 22-23. The soundness of a language design—the absence of ill-defined programs—follows naturally. A variety of programming language features User manual (per-commit pdf can be downloaded from the github actions page); CHANGELOG; Getting Started. Daniel Peebles. gramming language, Agda, based on type theory. I'll focus on the Lambda Calculus, the Agda dependently-typed programming language and proof assistant, and Type theory Here is how to get Agda: I'm working on getting Agda installed on the department linux machines, but I expect you will want it on your own machine. Programming Languages Foundations in Agda is an introduction to programming language theory using the proof assistant Agda. The program thus obtained is correct by construction. The syntax of a language is governed by the constructs that define its types, and its semantics is determined by the interactions among those constructs. After five years using the leading textbook Software Foundations in the classroom, which is based on the proof assistant Coq, I have come to the conclusion that Coq is not the best vehicle for this purpose. Agda Wiki ‘Hello World!’ in Adga. The purpose of this book is to explain this remark. Other languages in this tradition are Alf, Alfa, Agda 1, Cayenne. Introduction to Agda. A one-semester course can expect to cover Logical Foundations plus most of Programming Language Foundations or Verified Functional Algorithms, or selections from both. This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of higher inductive types. ##### # # E-scripts on Agda. ooAgda provides a syntax similar to the one used in object-oriented programming languages, thanks to Agda's copattern matching facility. ... And a pdf version is also available at the arxiv, ... Agda is a dependently-typed functional programming language. A professor at my uni has recommended Raku (formerly Perl 6) to me as an interesting language with a bunch of cool design choices. Agda is a dependently typed functional programming language: It has inductive families, which are similar to Haskell's GADTs, but they can be indexed by values and not just types. This year, ICFP is also co-located with BOBKonf, which will take place on August 21 at the same venue. Dan Licata, Ian Voysey, Programming and proving in Agda. It is an extension of Martin-Löf’s type theory, and is the latest in the tradition of languages developed in the programming logic group at Chalmers. # Executing this file as a whole makes no sense. Science of Computer Programming, volume 194, 2020. 2 Agda Basics Agda is a dependently typed language based on intuitionistic type the-ory[4]. Formal specification of a programming language Help language comprehension Supports language standardization Guides language design Aids compiler and language system writing Supports program correctness verification So I was kinda expecting the same from Raku, but boy was I mistaken. Swansea University. The book is broken into two parts. In the second half, we change gears, and start studying the foundations of programming languages, using the Agda tools and concepts that we have learned and developed. I think Practical Foundations for Programming Languages [0] does a good job on that front. The first part, Logical Foundations, develops the needed formalisms. We have developed a library, AoPA (Algebra of Programming in Agda), to encode relational derivations in the dependently typed programming language Agda. It also has parameterised modules, mixfix operators, Unicode characters, and an interactive Emacs interface (the type checker can assist in the development of your code). Volume 1: Logical Foundations is the entry-point to the series. See the Agda Wiki for information about the library.. These lecture notes are based on Agda and contain an introduction of Agda for students with a very basic background in logic and functional programming. Introduction to Univalent Foundations of Mathematics with Agda. References. Documentation. This book offers good coverage of logical foundations and programming language foundations. First, that it is possible. group or topological space), formulating constructions to be performed (e.g. Agda's type system is expressive enough to support full functional verification of programs, in two styles. Roosta, Foundations of Programming Languages Foundations of Programming Languages Seyed H. Roosta Chapter Four Syntax Specification. Book Name: Foundations of Programming Languages Author: Kent D. Lee ISBN-10: 3319133136 Year: 2014 Pages: 368 Language: English File size: 21.36 MB File format: PDF Some other loosely related languages are Coq, Epigram, and Idris. What did I learn from writing PLFA? Agda is an advanced programming language based on Type Theory. 13 Lambda Alonzo Church’s lambda calculus was the first formal model of general computation defined, and enabled the first proof of uncomputability in 1936. Much more impressive examples have been done by others, showing that the ideas developed in this thesis are viable in practise. TaPL - Types and Programming Languages - Benjamin C. Pierce; PROT Proofs and Types - Jean-Yves Girard, Yves Lafont and Paul Taylor - 1987-90 pdf But we can assume the axiom of choice or the principle of excluded middle for pieces of mathematics that require them, at the cost of losing the implicit programming-language PLFA - Programming Language Foundations in Agda - Philip Wadler, Wen Kokke; SF - Software Foundations - Benjamin C. Pierce et al. Meanwhile, dependent type theory is rich enough to express various correctness properties to be verified by the type checker. I would expect from this the study of programming languages in general. Its current version (Agda 2) is a complete rewrite instigated by Ulf It covers functional programming, basic concepts of logic, computer-assisted theorem proving, and Coq. In external verification, we write pure functional programs and then write proofs of properties about them. Agda is a constructive mathematical system by default, which amounts to saying that it can also be considered as a programming language for manipulating mathematical objects. Agda is a dependently typed functional programming language originally developed by Ulf Norell at Chalmers University of Technology with implementation described in his PhD thesis. CubicalAgda 87:3 inparticularwedescribehowsomeprimitivenotionsofcubicaltypetheoryareinternalizedaspre … What is Agda?¶ Agda is a dependently typed programming language. Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types. Prerequisites ICFP 2019 is the 24th ACM SIGPLAN International Conference on Functional Programming. Agda 2. the dependently typed language Agda and its basic features, and Sec-tion 3 explains a couple of programming techniques made possible by the introduction of dependent types.