The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,
minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.

The isomorphism has many aspects, even at the syntactic level:
formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation,...

This book constitutes the refereed proceedings of the 31st International Symposium on Mathematical Foundations of Computer Science, MFCS 2006. The book presents 62 revised full papers together with the full papers or abstracts of 7 invited talks. All current aspects in theoretical computer science and its mathematical foundations are addressed, from algorithms and data structures, to complexity, automata, semantics, logic, formal specifications, models of computation, concurrency theory, computational geometry and more.

The 7th International Conference on Typed Lambda Calculi and Applications (TLCA 2005) was held in Nara (Japan) from 21 to 23 April 2005, as part of the Joint Conference on Rewriting, Deduction and Programming (RDP 2005). This book contains the contributed papers, and extended abstracts of two invited talks, given by Thierry Coquand and Susumu Hayashi. A short abstract of the joint RDP invited lecture by Amy Felty is also included. The 27 contributed papers were selected from 61 submissions of generally very high quality, and the Program Committee had a hard time making the selection. The...