Abstract
We give an overview of Agda, the latest in a series of dependently typed programming languages developed in Gothenburg. Agda is based on Martin-Löf’s intuitionistic type theory but extends it with numerous programming language features. It supports a wide range of inductive data types, including inductive families and inductive-recursive types, with associated flexible pattern-matching. Unlike other proof assistants, Agda is not tactic-based. Instead it has an Emacs-based interface which allows programming by gradual refinement of incomplete type-correct terms.
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Agda wiki page, http://wiki.portal.chalmers.se/agda/
Bertot, Y., Castéran, P.: Interactive Theorem Proving and Program Development. In: Coq’Art: The Calculus of Inductive Constructions. Springer, Heidelberg (2004)
Bove, A., Dybjer, P.: Dependent types at work. In: Barbosa, L., Bove, A., Pardo, A., Pinto, J.S. (eds.) LerNet ALFA Summer School 2008. LNCS, vol. 5520, pp. 57–99. Springer, Heidelberg (to appear, 2009)
Coquand, T., Huet, G.: The calculus of constructions. Information and Computation 76, 95–120 (1988)
Dybjer, P.: Inductive families. Formal Aspects of Computing 6, 440–465 (1994)
Dybjer, P.: A general formulation of simultaneous inductive-recursive definitions in type theory. Journal of Symbolic Logic 65(2) (June 2000)
Dybjer, P., Setzer, A.: Indexed induction-recursion. Journal of Logic and Algebraic Programming 66(1), 1–49 (2006)
Epigram homepage, http://www.e-pig.org
Gonthier, G.: The four colour theorem: Engineering of a formal proof. In: Kapur, D. (ed.) ASCM 2007. LNCS, vol. 5081, p. 333. Springer, Heidelberg (2008)
Gordon, M., Milner, R., Wadsworth, C.: Edinburgh LCF. In: Kahn, G. (ed.) Semantics of Concurrent Computation. LNCS, vol. 70. Springer, Heidelberg (1979)
Martin-Löf, P.: Constructive mathematics and computer programming. In: Logic, Methodology and Philosophy of Science, VI, 1979, pp. 153–175. North-Holland, Amsterdam (1982)
Martin-Löf, P.: Intuitionistic Type Theory. Bibliopolis, Napoli (1984)
Nordström, B., Petersson, K., Smith, J.M.: Programming in Martin-Löf’s Type Theory. An Introduction. Oxford University Press, Oxford (1990)
Norell, U.: Towards a practical programming language based on dependent type theory. PhD thesis, Chalmers University of Technology (2007)
Norell, U.: Dependently typed programming in Agda. In: Lecture Notes from the Summer School in Advanced Functional Programming (2008) (to appear)
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Bove, A., Dybjer, P., Norell, U. (2009). A Brief Overview of Agda – A Functional Language with Dependent Types. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03359-9_6
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DOI: https://doi.org/10.1007/978-3-642-03359-9_6
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