I assume you've already read my page on The Concept.
During the literature search for my Master's thesis, the classification of grammars into "adaptive" and "nonadaptive" was always so clear that it took me six months to notice —when I finished gathering my data and started organizing it into a survey— that I didn't know what an adaptive grammar is. Eventually I settled on the following semi-formal definition.
ADAPTIVE GRAMMAR MODEL: A grammatical formalism that allows rule sets (aka sets of production rules) to be explicitly manipulated within a grammar.(By "grammatical formalism", or "grammar model", I mean the common formal structure of a class of grammars, such as Chomsky Grammars, or Knuth's Attribute Grammars.)
Existing adaptive grammar models fall neatly into two distinct families, depending on whether the manipulation of rule sets is supported by imperative or declarative means. The wording of the above definition was chosen to cover both families. Excluded by the wording of the definition is the family of conventional two-level grammars.
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Imperative adaptive grammars
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Adaptive Grammars