The 9th Italian Conference on Theoretical Computer Science (ICTCS 2005)was held at the Certosa di Pontignano, Siena, Italy, on October 12 14 2005. The Certosa di Pontignano is the conference center of the University of Siena; it is located 8 km away from the town and it is in the Chianti region. The Certosa is a place full of history (founded in the 15th century, it was set on ?re a century later and reconstructed) and of valuable artworks, like frescoes of the Scuola Senese. Previous conferences took place in Pisa (1972), Mantova (1974 and 1989), L Aquila(1992), Ravello(1995), Prato(1998), Turin(2001)andBertinoro(2003). Theconferenceaimsatbringingtogethercomputerscientists, especiallyyoung researchers, to foster cooperation, exchange of ideas and results. Great e?orts have been made to attract researchers from all over the world. The main t- ics of the conference cover all the ?elds of theoretical computer science and include analysis and design of algorithms, computability, computational c- plexity, cryptography, formal languages and automata, foundations of progr- ming languages and program analysis, foundations of arti?cial intelligence and knowledge representation, foundations of web programming, natural computing paradigms (quantum computing, bioinformatics), parallel and distributed c- putation, program speci?cation and veri?cation, term rewriting, theory of c- currency, theory of data bases, theory of logical design and layout, type theory, security, and symbolic and algebraic computation."

These proceedings contain a selection of refereed papers presented at or related to the 3rd Annual Workshop of the Types Working Group (Computer-Assisted Reasoning Based on Type Theory, EU IST project 29001), which was held d- ing April 30 to May 4, 2003, in Villa Gualino, Turin, Italy. The workshop was attended by about 100 researchers. Out of 37 submitted papers, 25 were selected after a refereeing process. The ?nal choices were made by the editors. Two previous workshops of the Types Working Group under EU IST project 29001 were held in 2000 in Durham, UK, and in 2002 in Berg en Dal (close to Nijmegen), The Netherlands. These workshops followed a series of meetings organized in the period 1993-2002 within previous Types projects (ESPRIT BRA 6435 and ESPRIT Working Group 21900). The proceedings of these e- lier workshops were also published in the LNCS series, as volumes 806, 996, 1158, 1512, 1657, 2277, and 2646. ESPRIT BRA 6453 was a continuation of ESPRIT Action 3245, Logical Frameworks: Design, Implementation and Ex- riments. Proceedings for annual meetings under that action were published by Cambridge University Press in the books "Logical Frameworks", and "Logical Environments", edited by G. Huet and G. Plotkin. We are very grateful to the members of the research group "Semantics and Logics of Computation" of the Computer Science Department of the University of Turin, who helped organize the Types 2003 meeting in Torino.

This volume contains a refereed selection of revised full papers chosen from the contributions presented during the Third Annual Workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs. The workshop took place in Torino, Italy, in June 1995.
Type theory is a formalism in which theorems and proofs, specifications and programs can be represented in a uniform way. The 19 papers included in the book deal with foundations of type theory, logical frameworks, and implementations and applications; all in all they constitute a state-of-the-art survey for the area of type theory.