Expression Reduction Systems and Extensions: An Overview

A unified approach to fully lazy sharing

“…Moreover, the descendant of a → lft -redex is still a → lft -redex (thanks to the rule Inside). From this we easily derive the orthogonality of → lft in the sense of [GKK05], and deduce that → lft has the diamond property.…”

“…• (Context) If t While Reify is the main rule of λ-lifting, Inside allows to close confluence diagrams (see Example 16) and consider λ-lifting as an orthogonal rewriting system (in the sense of [GKK05], after the extension of the notion of descendants given below). An Inside reduction can be seen as a reduction Reify inside a symbol.…”

Union of Reducibility Candidates for Orthogonal Constructor Rewriting

“…5.2, this amounts to show that every strongly normalizing reducible neutral term has a strong principal reduct. We prove it by using a general theorem on external redexes [13] (see also [12]). This result applies to the framework of orthogonal CCERSs, of which our higher-order rewrite systems β ∪ R ∪ D are an instance.…”

“…We use the notions of descendants and of redex-arguments of [13,12]. The key notion is that of external redex [13,12]: a redex u in a term t is external if for any derivation P : t → * βRD v, no descendant of u along P appears inside redex-arguments.…”

“…The key notion is that of external redex [13,12]: a redex u in a term t is external if for any derivation P : t → * βRD v, no descendant of u along P appears inside redex-arguments. Hence every descendant of an external redex is external.…”