The goals of the PROTHEO project are the design and implementation of tools for integrating program developments and proofs of properties, while taking advantage of the complementary nature of automated deduction, logics for programming and constraint solving.

We are interested in three research areas which strongly contribute to the previous objectives : first the problems of constraint satisfaction and solving, second the study of logics for programming or proving including the constraint paradigm, and third the proof of program properties. We are thus working on the following topics : Constraint solving, Automated deduction with constraints, Proofs by induction, Proofs of program properties, Parallelization of deduction processes.

We are developing several systems, in particular UNIF (a library of symbolic constraint solving algorithms), SPIKE (an inductive theorem prover), ELAN (a logical framework based on the rewriting logic).

Some of our main advances in these domains during 1995 are :

- The extension and distribution of the theorem prover SPIKE.
- The distribution of the logical framework ELAN V1.17.
- The introduction of SOUR graphs, a structure allowing to represent subterms, orientation, unification and rewriting, all at the object level.
- The use of SOUR graphs for designing goal directed theorem proving procedures and concurrent deduction processes.
- The design of a new higher order unification algorithm and its specialisation to patterns.
- The conception of a new specification formalism allowing the combination of abstract data types and set theory.