Algorithmic Equality in Heyting Arithmetic Modulo -- CoqJVM: An Executable Specification of the Java Virtual Machine Using Dependent Types -- Dependently Sorted Logic -- Finiteness in a Minimalist Foundation -- A Declarative Language for the Coq Proof Assistant -- Characterising Strongly Normalising Intuitionistic Sequent Terms -- Intuitionistic vs. Classical Tautologies, Quantitative Comparison -- In the Search of a Naive Type Theory -- Verification of the Redecoration Algorithm for Triangular Matrices -- A Logic for Parametric Polymorphism with Effects -- Working with Mathematical Structures in Type Theory -- On Normalization by Evaluation for Object Calculi -- Attributive Types for Proof Erasure.

This book constitutes the thoroughly refereed post-conference proceedings of TYPES 2007, the concluding conference of the Types project, held in Cividale del Friuli, Italy, in May 2007. The 13 revised full papers presented were carefully reviewed and selected from 22 submissions. The topic of this last annual workshop of the Types Working Group was formal reasoning and computer programming based on type theory. Great importance was attached to languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalization of mathematics and mathematics education.