Graph Rewriting and Relabeling with PBPO$$^{+}$$

Abstract

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From Linear Term Rewriting to Graph Rewriting with Preservation of Termination

“…First, PBPO + is expressive: for Graph in particular, and assuming monic matching, we conjecture [17] that PBPO + is able to faithfully model DPO, SPO [13], SqPO [5], AGREE [3] and PBPO. More precisely, for any rule in such a formalism, there exists a PBPO + rule that generates exactly the same rewrite relation.…”

“…Third, we have defined a non-adhesive category called Graph (L,≤) [17] that combines very nicely with PBPO + , allowing graph rewrite rules to easily model notions of relabeling, type systems, wildcards and variables. These notions have been significantly more challenging to define for DPO.…”

“…Definition 10 (PBPO + Rewriting [17]). A PBPO + rewrite rule ρ (left) and adherence morphism α : G L → L induce a rewrite step G L ⇒ α ρ G R on arbitrary G L and G R if the properties indicated by the commuting diagram on the right hold Lemma 11].…”

“…Building on PBPO by Corradini et al [4] and our own patch graph rewriting formalism [16], we recently proposed the PBPO + algebraic graph rewriting approach [17], in which rules employ a type graph to specify transformations and control rule applicability. In the present paper we give an embedding of linear term rewrite systems into PBPO + that preserves global termination, despite being applicable to graphs that are not encodings of terms.…”

“…In Section 2, we summarize the relevant categorical and TRS preliminaries. In Section 3, we give a self-contained introduction to PBPO + and to Graph (L,≤) [17], a special category that combines well with PBPO + . In Section 4, we define an embedding of linear term rewriting into PBPO + rewriting over category Graph (L,≤) .…”