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Pushdown element is a term used in CGEL, by Quirk. et al. I don't understand how this term is made up. Does it mean the element was pushed down.?

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In the context of grammars, it refers to the recursive nature of most natural languages, specifically the types of grammar elements that cause be used recursively (e.g. a noun phrase can be used in a prepositional phrase, which can be part of a larger noun phrase, and these can be nested indefinitely). Scientists and computer programmers generally use stacks to model recursive structures. The real-world analogy is a spring-loaded plate stack, as you might find in a restaurant buffet.

spring-loaded plate stack

Adding and removing things from a stack usually use the terms "push" and "pop". And as you can see, when you add plates to the stack the weight causes the platform to go down. As a result, "pushdown" is the word used in some disciplines to describe elements that obey this property (in computer science, another term for a stack is a "pushdown list", but it has become obsolete).

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