We develop logic and combinatorial methods for automating the generation of sorting
algorithms for binary trees, starting from input-output specifications and producing …

CLKID^ ω ω is a sequent-based cyclic inference system able to reason on first-order logic
with inductive definitions. The current approach for verifying the soundness of CLKID^ ω ω …

Cyclic pre-proofs can be represented as sets of finite tree derivations with back-links. In the
frame of the first-order logic with inductive definitions, the nodes of the tree derivations are …

SPIKE, an induction-based theorem prover built to reason on conditional theories with
equality, is one of the few formal tools able to perform automatically mutual and lazy …

In the present paper, we address the following general question in the framework of
classical first-order logic. Assume that a certain mathematical principle can be formalized in …

Structural and (Noetherian) cyclic induction are two instances of the Noetherian induction
principle adapted to reason on first-order logic. From a theoretical point of view, every …

Checking the soundness of cyclic induction reasoning for first-order logic with inductive
definitions (FOLID) is decidable but the standard checking method is based on an …

We develop various proof techniques for the synthesis of sorting algorithms on binary trees,
by extending our previous work on the synthesis of algorithms on lists. Appropriate induction …

Cyclic induction is a powerful reasoning technique that consists in blocking the proof
development of certain subgoals already encountered during the proof process. In the …

The object of research is the theory of the design of technological machines and devices.
The main idea of this theory is the possibility of a priori quantitative evaluation of the design …