Higher-Order Algebra, Logic, and Term Rewriting

Gilles Dowek is Director of Research at INRIA and heads the LOGICAL project-team. He is also a Professor at the École Polytechnique and a researcher at the École Polytechnique's Computer Science Laboratory (LIX). He is an advisor to the National Institute of Aerospace, a NASA Langley research centre laboratory. His research focuses on formalising mathematics, on demonstration processing systems related to quantum programming language design and on safety for aerospace systems. He has written several works aimed at explaining maths and science theory in layman's terms.

Term graph rewriting.- Approximation and normalization results for typeable term rewriting systems.- Modular properties of algebraic type systems.- Collapsing partial combinatory algebras.- A complete proof system for Nested Term Graphs.- R n - and G n -logics.- The variable containment problem.- Higher-order equational logic for specification, simulation and testing.- The correctness of a higher-order lazy functional language implementation: An exercise in mechanical theorem proving.- Assertions and recursions.- Development closed critical pairs.- Two different strong normalization proofs?.- Third-order matching in the polymorphic lambda calculus.- Higher-order algebra with transfinite types.- Abstraction of hardware construction.