Agda (theorem prover)

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Usual file extensions .agda, .lagda
Paradigm Functional
Stable release 2.2.4 (July 7, 2009; 145556543 ago)
Influenced by Epigram, Haskell
OS Cross-platform
Website Agda wiki
File:Agda proof.jpg
Excerpt of a proof in agda2

Agda is a proof assistant, i.e. a computer program that can check mathematical proofs. More specifically, it is an interactive system for developing constructive proofs in a variant of Per Martin-Löf's Type Theory. It can also be seen as a functional programming language with dependent types and was developed by Ulf Norell, a post-doc at Chalmers University of Technology.

Agda is based on the idea of direct manipulation of proof-term and not on tactics. The proof is a term, not a script. The language has ordinary programming constructs such as data-types and case-expressions, signatures and records, let-expressions and modules. The system has an Emacs interface and a graphical interface, Alfa.


The current version of Agda, Agda 2, has been developed at Chalmers by Ulf Norell. The syntax has changed from Agda 1 (though some conversion tools are being developed as well), introducing for instance implicit variables, that can be omitted when deducible from the context. Agda 2 also makes extensive use of Unicode as a way to obtain easily-readable proofs.

Agda 2 provides either a commandline tool or a powerful Emacs mode, developed by Makoto Takeyama and Nils Anders Danielsson.

The 10th Agda Implementor's Meeting was held in Gothenburg in September 2009. AIM11 is scheduled for March in Japan.

Agda 2 is similar to Epigram.


  • C. Coquand et al. An Emacs interface for type directed support constructing proofs and programs. ENTCS 2006.
  • A. Abel, et al. Verifying Haskell Programs Using Constructive Type Theory, ACM SIGPLAN Workshop Haskell'05, Tallinn, Estonia, 30 September 2005
  • M. Benke et al. Universes for generic programs and proofs in dependent type theory. Nordic Journal of Computing, 10(4):265-289, 2003.
  • T. Coquand et al. Connecting a Logical Framework to a First-Order Logic Prover. FroCos 2005, pp. 285-301.

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