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- André Luiz Galdino, César A. Muñoz, Mauricio Ayala-Rincón
- WoLLIC
- 2007

Highly accurate positioning systems and new broadcasting technology have enabled air traffic management concepts where the responsibility for aircraft separation resides on pilots rather than on air traffic controllers. The Formal Methods Group at the National Institute of Aerospace and NASA Langley Research Center has proposed and formally verified an… (More)

- André Luiz Galdino, Mauricio Ayala-Rincón
- Journal of Automated Reasoning
- 2010

A mechanical proof of the Knuth–Bendix Critical Pair Theorem in the higher-order language of the theorem prover PVS is described. This well-known theorem states that a Term Rewriting System is locally confluent if and only if all its critical pairs are joinable. The formalization of this theorem follows Huet’s well-known structure of proof in which the… (More)

- André Luiz Galdino, Mauricio Ayala-Rincón
- J. Formalized Reasoning
- 2008

- André Luiz Galdino, Mauricio Ayala-Rincón
- Electr. Notes Theor. Comput. Sci.
- 2009

A theory, called trs, for Term Rewriting Systems in the theorem Prover PVS is described. This theory is built on the PVS libraries for finite sequences and sets and a previously developed PVS theory named ars for Abstract Reduction Systems which was built on the PVS libraries for sets. Theories for dealing with the structure of terms, for replacements and… (More)

This paper shows how a previously specified theory for Abstract Reduction Systems (ARSs) in which noetherianity was defined by the notion of wellfoundness over binary relations is used in order to prove results such as the wellknown Newman’s Lemma and the Yokouchi’s Lemma. The former one known as the diamond lemma and the later which states a property of… (More)

This work presents a general methodology for verification of the completeness of firstorder unification algorithms à la Robinson developed in the higher-order proof assistant PVS. The methodology is based on a previously developed formalization of the theorem of existence of most general unifiers for unifiable terms over first-order signatures. Termination… (More)

- Andréia B. Avelar, André Luiz Galdino, Flávio L. C. de Moura, Mauricio Ayala-Rincón
- Logic Journal of the IGPL
- 2014

- André Luiz Galdino, Mauricio Ayala-Rincón
- CLEI Electron. J.
- 2008

A theory for Abstract Reduction Systems (ARS) in the proof assistant PVS (Prototype Verification System) is described. Adequate specifications of basic definitions and notions such as reduction, confluence, normal form are given and well-known results proved, which includes non trivial ones such as Noetherian Induction, Newman’s Lemma and its… (More)

We point out the importance of the use of the refined dependent types available in the proof assistant PVS for the correct specification of a geometrical approach to solve the problem of air traffic conflict detection and resolution (between two aircrafts in mid air). A correct PVS specification which completely solves this problem giving a triplet which… (More)

- Ana Cristina Rocha Oliveira, André Luiz Galdino, Mauricio Ayala-Rincón
- Journal of Automated Reasoning
- 2016

Orthogonality is a discipline of programming which syntactically guarantees determinism of functional specifications. Essentially, orthogonality avoids critical forks in term rewriting systems (TRSs) twofold: avoiding overlappings between left-hand sides of the rules (non-ambiguity) prohibiting rules in the definitions of functions that may apply… (More)