IO and OI. I

Second-Order Abstract Categorial Grammars as Hyperedge Replacement Grammars

“…Since in this case the abstract language is a local tree language, second-order ACGs belong to a long list of grammar formalisms that have "context-free" derivations. De Groote and Pogodalla (2004) showed that such well-known "context-free" grammar formalisms as linear context-free rewriting systems (Weir 1988), or non-erasing multiple context-free grammars (Seki et al 1991), and linear and non-deleting contextfree tree grammars (Rounds 1970, Engelfriet andSchmidt 1977) can be faithfully encoded by second-order ACGs. Subsequently, Salvati (2007) showed that the string generating power of second-order ACGs exactly matches that of LCFRSs using the fact that the latter coincides with the class of output languages of deterministic tree-walking transducers (Weir 1992).…”

A Generalization of Linear Indexed Grammars Equivalent to Simple Context-Free Tree Grammars

“…(This makes it easier to relate them to indexed grammars, but is not essential.) A context-free tree grammar [23,2] is a quadruple G = (N, Σ, P, S), where…”

A Grammar-Based Approach to Invertible Programs

“…Inside-out (IO) context-free tree grammar (CFTG) [9] enables us to investigate accumulation parameters (parameters that are never pattern-matched in evaluation) in parsing. For example, the following IO CFTG can be obtained for reverse.…”

“…For example, to invert double and snoc, regular tree grammars (RTG) [6] is sufficient. To invert reverse, however, we need grammar beyond regular, such as (inside-out) context-free tree grammar [9]. While a more general grammar covers more programs, it also implies higher worst-case time complexity of parsing and, therefore, a less-efficient inverse.…”