Abstract
Tree languages are powerful tools for the representation and schematization of infinite sets of terms for various purposes (unification theory, verification and specification ...). In order to extend the regular tree language framework, more complex formalisms have been developed. In this paper, we focus on Tree Synchronized Grammars and Primal Grammars which introduce specific control structures to represent non regular sets of terms. We propose a common unified framework in order to achieve the membership test for these particular languages. Thanks to a proof system, we provide a full operational framework, that allows us to transform tree grammars into Prolog programs (as it already exists for word grammars with DCG) whose goal is to recognize terms of the corresponding language.
Highlights
Tree languages [3, 6] have been extensively studied and have many applications in various areas such as term rewriting, term schematization, specification and verification
We focus on two particular non regular classes of tree languages defined by their associated notion of tree grammars: Tree Synchronized Grammars and Primal Grammars
There is no more need to distinguish Tree Synchronized Grammars (TSG) and Primal Grammars (PG) since they have been embedded into the same formalism
Summary
Tree languages [3, 6] have been extensively studied and have many applications in various areas such as term rewriting, term schematization, specification and verification. E-unification [17] is known to be undecidable in general, but, as explained in [14], some decidable classes can be characterized by using such tree languages Due to their specific definitions introducing control in the derivation process, a notion of automata can not be derived for these two classes of tree languages. Due to these two specific control mechanisms (synchronization and counter variables), the standard notion of automata does not appear clearly. The membership test, for a language described by a grammar, just consists in proving a particular formula in a sequent calculus using a proof system This approach provides a uniform framework for the definition and use of both type of grammars.
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