He is known in unification theory for having shown the non-existence of minimal sets of unifiers in some equational theories (conjecture of Plotkin, 1972),[5]
and the decidability of associative-commutative unification[6] in presence of several function symbols (conjecture of Stickel, 1981[7]).
In rule-based modelling, he is known for having created in 1988 a reactive rule-based language at Thomson-CSF (now Thalès group), which was later industrialized by ILOG (now IBM-Ilog) and became ILOG-Rules in 1996.
In 2010 Fages co-ordinated a project to use mathematics to improve the packing of light bulbs and other oddly shaped products.[11]
In 2014 Fages works in computationalsystems biology,
coordinates the development of the Biochemical Abstract Machine (BIOCHAM) rule-based modeling and logical analysis software and studies biochemical processes in the cell cycle and in cell signaling.
^Erdem, Esra; Lifschitz, Vladimir; (2001) "Fages' Theorem for Programs with Nested Expressions". Proc. ICLP 2001:242-254, MIT Press.
^Betz, Hariolf; Frühwirth, Thom (2005). "A Linear-Logic Semantics for Constraint Handling Rules". Proc. Principles and Practice of Constraint Programming - CP 2005:137-151, Springer-Verlag.
^Palamidessi, Catuscia; Saraswat, Vijay; Valencia, Franck (2006). "On the Expressiveness of Linearity vs Persistence in the Asychronous Pi-Calculus". Proc. Logic in Computer Science - LICS 2006:59-68.