Agda is a dependently typed functional programming language based on intuitionistic type theory. Type theory is concerned both with programming and logic.
Agda 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. It has inductive families, i.e., data types which depend on values, such as the type of vectors of a given length. It also has parametrised modules, mixfix operators, Unicode characters, and an interactive Emacs interface which can assist the programmer in writing the program. Other languages in this tradition are Alf, Alfa, Agda 1, Cayenne. Some other loosely related languages are Coq, Epigram, and Idris.
This language is also a proof assistant based on the propositions-as-types paradigm, but has no separate tactics language, and proofs are written in a functional programming style.
Agda is open-source and enjoys contributions from many authors. The center of the Agda development is the Programming Logic group at Chalmers and Gothenburg University.
Here’s our recommended tutorials to learn Agda.
1. Dependently Typed Programming in Agda by Ulf Norell and James Chapman
This tutorial begins with an introduction to the basic features of Agda and how they can be employed in the construction of dependently typed programs. The authors then move on to describe and exemplify a couple of programming techniques which are made available in dependently typed languages: views and universe constructions.
The final part deals with the topic of getting Agda programs to interact with the real world.
2. Lectures by Thorsten Altenkirch
This is a computer aided formal reasoning course.
3. Dependent Types at Work by Ana Bove and Peter Dybjer
The authors give an introduction to functional programming with dependent types. They use the dependently typed programming language Agda which is an extension of Martin-L ̈of type theory. First they show how to do simply typed functional programming in the style of Haskell and ML. Some differences between Agda’s type system and the Hindley-Milner type system of Haskell and ML are also discussed.
Then they show how to use dependent types for programming and we explain the basic ideas behind type-checking dependent types. They go on to explain the Curry-Howard identification of propositions and types. This is what makes Agda a programming logic and not only a programming language. According to Curry-Howard, we identify programs and proofs, something which is possible only by requiring that all program terminate. However, at the end of these notes they present a method for encoding partial and general recursive functions as total functions using dependent types.
4. Interactive Theorem Proving for Agda Users by Anton Setzer
This material contains the slides of the module “Interactive Theorem Proving”, a third year/postgraduate course held at Swansea University, with a guide to material specifically directed at Agda.
5. Agda: Equality by Andreas Abel
Agda has an internal notion of program equality. In essence, two programs are equal ifthey compute the same value
6. Agda Tutorial by Péter Diviánszky
This tutorial covers general information, sets, functions, modules and records, applications, and coinduction.
7. Introduction to Dependent Types in Agda by Jan Malakhovski
This material does not aim to teach Agda, but to show how dependently typed languages work behind the scenes without actually going behind the scenes.
8. Dependently Typed Programming in Agda by Daniel Licata
The program consists of 80 minute lectures presented by internationally recognized leaders in programming languages and formal reasoning research.
All tutorials in this series:
|Free Programming Tutorials|
|Java||General-purpose, concurrent, class-based, object-oriented, high-level language|
|C||General-purpose, procedural, portable, high-level language|
|Python||General-purpose, structured, powerful language|
|C++||General-purpose, portable, free-form, multi-paradigm language|
|C#||Combines the power and flexibility of C++ with the simplicity of Visual Basic|
|PHP||PHP has been at the helm of the web for many years|
|Ruby||General purpose, scripting, structured, flexible, fully object-oriented language|
|Assembly||As close to writing machine code without writing in pure hexadecimal|
|Swift||Powerful and intuitive general-purpose programming language|
|Groovy||Powerful, optionally typed and dynamic language|
|Go||Compiled, statically typed programming language|
|Pascal||Imperative and procedural language designed in the late 1960s|
|Perl||High-level, general-purpose, interpreted, scripting, dynamic language|
|R||De facto standard among statisticians and data analysts|
|COBOL||Common Business-Oriented Language|
|Scala||Modern, object-functional, multi-paradigm, Java-based language|
|Fortran||The first high-level language, using the first compiler|
|Scratch||Visual programming language designed for 8-16 year-old children|
|Lua||Designed as an embeddable scripting language|
|Logo||Dialect of Lisp that features interactivity, modularity, extensibility|
|Rust||Ideal for systems, embedded, and other performance critical code|
|Lisp||Unique features - excellent to study programming constructs|
|Ada||ALGOL-like programming language, extended from Pascal and others|
|Haskell||Standardized, general-purpose, polymorphically, statically typed language|
|Scheme||General-purpose, functional, language descended from Lisp and Algol|
|Prolog||General purpose, declarative, logic programming language|
|Forth||Imperative stack-based programming language|
|Clojure||Dialect of the Lisp programming language|
|Julia||High-level, high-performance language for technical computing|
|SQL||Access and manipulate data held in a relational database management system|
|Erlang||General-purpose, concurrent, declarative, functional language|
|VimL||Powerful scripting language of the Vim editor|
|OCaml||General-purpose, powerful, high-level language|
|Awk||Versatile language designed for pattern scanning and processing|
|Racket||Platform for programming language design and implementation|
|BASIC||Family of general-purpose, high-level programming languages|
|LaTeX||Professional document preparation system and document markup language|
|Elixir||Relatively new functional language that runs on the Erlang virtual machine|
|Dart||Client-optimized programming language for fast apps|
|ABAP||Advanced Business Application Programming|
|F#||General purpose, strongly typed, multi-paradigm language. Part of ML|
|Chapel||Parallel-programming language in development at Cray Inc.|
|Dylan||Multi-paradigm language, supports functional & object-oriented programming|
|D||General-purpose systems programming language with a C-like syntax|
|Solidity||Object-oriented, high-level language for implementing smart contracts|
|XML||Set of rules for defining semantic tags that describe the structure and meaning|
|Vala||Object-oriented language with a self-hosting compiler that generates C code|
|ECMAScript||Best known as the language embedded in web browsers|
|Kotlin||Statically typed, general-purpose programming language with type inference|
|Markdown||Plain text formatting syntax designed to be easy-to-read and easy-to-write|
|Pike||Interpreted, general-purpose, high-level, cross-platform, dynamic language|
|HTML||HyperText Markup Language|
|Factor||Dynamic stack-based language|
|Objective-C||General purpose language which is a superset of C|
|Standard ML||One of the two main dialects of the ML language|
|Alice||Educational language with an integrated development environment|
|Agda||Dependently typed functional language based on intuitionistic type theory|
|Icon||High-level, general-purpose language|
|PureScript||Small strongly, statically typed language with expressive types|
|Tcl||Dynamic language based on concepts of Lisp, C, and Unix shells|
|QML||Hierarchical declarative language for user interface layout with a syntax to JSON|
|VHDL||Very High Speed Integrated Circuit Hardware Description Language|
|OpenCL||Open Computing Language|
|Haml||HTML Abstraction Markup Language|
|J||Array programming language based primarily on APL|
|LabVIEW||Designed to enable domain experts to build power systems quickly|
|Hack||For the HipHop Virtual Machine (HHVM), created as a dialect of PHP|
|V||Statically typed compiled language to build maintainable software|
|PostScript||Page description language in electronic and desktop publishing|
|Arduino||Inexpensive, flexible, open source microcontroller platform|