References for further reading for the Lernet summer school

General References

• H. Barendregt and H. Geuvers,
  Proof Assistants using Dependent Type Systems, Chapter 18 of the Handbook of Automated Reasoning (Vol 2), eds. A. Robinson and A. Voronkov, Elsevier 2001, pp. 1149 -- 1238.
• Henk Barendregt
  Lambda Calculi with Types (1992), Handbook of Logic in Computer Science, Volumes 1, Abramsky, Gabbay, Maibaum (Eds.), Clarendon
• Pawel Urzyczyn and Morten Sorensen
  Lectures on the Curry-Howard Isomorphism, Volume 149 of Studies in Logic and the Foundations of Mathematics, Elsevier
• Jean-Yves Girard, Paul Taylor, and Yves Lafont
  Proofs and types. Cambridge tracts in theoretical computer science, no. 7. Cambridge University Press.
• Robert Harper, Furio Honsell, Gordon Plotkin
  A Framework for Defining Logics (1987) Proceedings 2nd Annual IEEE Symp. on Logic in Computer Science, LICS'87, Ithaca, NY, USA, 22--25 June 1987
• Bengt Nordstrom, Kent Petersson, Jan M. Smith
  Programming in Martin-Lof's Type Theory An Introduction, Oxford University Press in 1990
• Per Martin-Lof. Intuitionistic type theory. Napoli, Bibliopolis, 1984.

On the Proof Assistant Coq

Coq web page.
• Yves Bertot and Pierre Castéran
  Interactive Theorem Proving and Program Development Coq'Art: The Calculus of Inductive Constructions EATCS Series: Texts in Theoretical Computer Science. 2004, 469 pp.

Older material that is interesting to read (and well accessible)

• A. Church (1940), A formulation of the simple theory of types. The Journal of Symbolic Logic 5(2):56-68.
• W. Howard. The formulas-as-types notion of construction. In JP Seldin and JR Hindley, editors, To HB Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism, pages 479--490. Academic Press, NY, 1980.