From Hertzsprung’s problem to pattern-rewriting systems

Tree Pattern Rewriting Systems

Classical verification often uses abstraction when dealing with data. On the other hand, dynamic XML-based applications have become pervasive, for instance with the ever growing importance of web services. We define here Tree Pattern Rewriting Systems (TPRS) as an abstract model of dynamic XML-based documents. TPRS systems generate infinite transition systems, where states are unranked and unor...

ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti

The programming environment FoCaLiZe allows the user to specify, implement, and prove programs. It produces as output OCaml executable programs along with proof hints that help the first-order theorem prover Zenon to find proofs. In the actual version, those proofs found by Zenon are verified by Coq. In this paper we propose to extend the FoCaLiZe compiler by a backend to the Dedukti language –...

From Abstract Rewriting Systems to Abstract Proof Systems

Some personal recollections on the introduction of ‘abstract proof systems’ as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel de Vrijer: the analogy with abstract

Universit a Di Pisa from String Rewriting to Logical Metabolic Systems from String Rewriting to Logical Metabolic Systems

From the Calculus of Structures to Term Rewriting Systems

The calculus of structures is a recently developed proof theoretical formalism that extends one-sided sequent calculus, with the gain of interesting proof theoretical properties. In contrast to sequent calculus, it does not rely on the notion of main connective and, like in term rewriting, permits the application of inference rules anywhere deep inside a formula. In this paper, exploiting this ...