... And a pdf version is also available at the arxiv, ... Agda is a dependently-typed functional programming language. 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. The methodology is implemented in the ooAgda library. Accordingly, I have written a new textbook, Programming Language Foundations in Agda (PLFA). I'm a programming language enthusiast and a hobby designer, so obviously, I got interested. Lecture notes on Interactive Theorem Proving. I would expect from this the study of programming languages in general. gramming language, Agda, based on type theory. Dan Licata, Ian Voysey, Programming and proving in Agda. TaPL - Types and Programming Languages - Benjamin C. Pierce; PROT Proofs and Types - Jean-Yves Girard, Yves Lafont and Paul Taylor - 1987-90 pdf References. 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's type system is expressive enough to support full functional verification of programs, in two styles. Programming Language Foundations in Agda by Philip Wadler and Wen Kokke.. From the preface: The most profound connection between logic and computation is a pun. 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. Note that this README is only about Agda, not its standard library. 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. 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 A variety of programming language features What did I learn from writing PLFA? Some other loosely related languages are Coq, Epigram, and Idris. The soundness of a language design—the absence of ill-defined programs—follows naturally. 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. ICFP 2019 is the 24th ACM SIGPLAN International Conference on Functional Programming. 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. This year, ICFP is also co-located with BOBKonf, which will take place on August 21 at the same venue. Prerequisites ##### # # 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. Programming Language Foundations in Agda (plfa.github.io) 71 points by blewboarwastake 10 hours ago | hide | past | favorite | 4 comments: samvher 7 hours ago. 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. What is Agda?¶ Agda is a dependently typed 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. Introduction to Agda. # # Note 1: use the eev command (defined in eev.el) and the # ee alias (in my .zshrc) to execute parts of this file. The book is broken into two parts. Is this in any way related to Software Foundations Volume 2: Programming Language Foundations [0] (in Coq)? Programming Language Foundations in Agda. group or topological space), formulating constructions to be performed (e.g. 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). The original Agda system was developed at Chalmers by Catarina Coquand in 1999. I think Practical Foundations for Programming Languages [0] does a good job on that front. General information on Agda is at. We develop a methodology for writing interactive and object-based programs (in the sense of Wegner) in dependently typed functional programming languages. On the Agda Language (in Japanese) Slides (English) Slides (Japanese) Anton Setzer. 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. In addition, … This document is called "programming language theory". Agda 2. Programming Languages Foundations in Agda is an introduction to programming language theory using the proof assistant Agda. PLFA - Programming Language Foundations in Agda - Philip Wadler, Wen Kokke; SF - Software Foundations - Benjamin C. Pierce et al. The main conference will take place during August 19-21, 2019 at the Hotel Scandic Berlin Potsdamer Platz. Accordingly, I have written a new textbook, Programming Language Foundations in Agda (PLFA), based on the proof assistant Agda. User manual (per-commit pdf can be downloaded from the github actions page); CHANGELOG; Getting Started. One of the leading textbooks for formal methods is Software Foundations (SF), written by Benjamin Pierce in collaboration with others, and based on Coq. Roosta, Foundations of Programming Languages Foundations of Programming Languages Seyed H. Roosta Chapter Four Syntax Specification. Daniel Peebles. CubicalAgda 87:3 inparticularwedescribehowsomeprimitivenotionsofcubicaltypetheoryareinternalizedaspre … Meanwhile, dependent type theory is rich enough to express various correctness properties to be verified by the type checker. # Executing this file as a whole makes no sense. Science of Computer Programming, volume 194, 2020. Introduction to Univalent Foundations of Mathematics with Agda. The program thus obtained is correct by construction. So I was kinda expecting the same from Raku, but boy was I mistaken. First, that it is possible. 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. This course is an introduction to programming language principles and theory. Use of a proof assistant in teaching provides immediate feedback to students. Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types. Programming Language Foundations in Agda – Table of Contents Source • Table of Contents This book is an introduction to programming language theory using the proof assistant Agda. 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 learn-you-an-agda (and achieve enlightment) Ulf Norell, James Chapman, Dependently Typed Programming in Agda (). Its current version (Agda 2) is a complete rewrite instigated by Ulf A one-semester course can expect to cover Logical Foundations plus most of Programming Language Foundations or Verified Functional Algorithms, or selections from both. It is written as a literate script in Agda, and available at the above URLs. Programming Language Foundations in Agda (SCP) Wen Kokke, Jeremy G. Siek, Philip Wadler. Other languages in this tradition are Alf, Alfa, Agda 1, Cayenne. Co-located workshops and tutorials will take place on August 18 and 22-23. Agda Wiki ‘Hello World!’ in Adga. PLFA covers much of the same ground as SF, although it is not a slavish imitation. Documentation. 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 Volume 1: Logical Foundations is the entry-point to the series. See the Agda Wiki for information about the library.. 2 Agda Basics Agda is a dependently typed language based on intuitionistic type the-ory[4]. Agda is a language for defining mathematical notions (e.g. Agda is an advanced programming language based on Type Theory. Much more impressive examples have been done by others, showing that the ideas developed in this thesis are viable in practise. We have developed a library, AoPA (Algebra of Programming in Agda), to encode relational derivations in the dependently typed programming language Agda. 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. 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 purpose of this book is to explain this remark. Swansea University. Perl has a bad rap of being unreadable, messy, and so on. 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. 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. 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. 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. 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. This book offers good coverage of logical foundations and programming language foundations. The first part, Logical Foundations, develops the needed formalisms. 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. Ulf Norell, Towards a practical programming. 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