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:
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