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3-LISP WORKING GUIDE#7: Back-quote

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Issue #7:Nested backquotes

Description:What do nested back-quotes mean? E.g., what should ‘@@[A ,B ,,C]’ expand to?

Status:Resolved, I think — see discussion.

Last Edited:September 20, 1982 (Jim des Rivières)

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The back-quote principle: "A lexical expression E1 preceded by a back-quote will notate a structure S1 that designates a structure S2 that would be notated by E1 with the exception that those fragments of S2 that would be notated by portions of E1 that are preceded by a comma will in fact be designated by the structures that those portions notate, rather than notated by them directly." (thesis 4.d.v, page 334).

Consider the following four expressions: ‘’’[A]’, ‘@’[A]’, ‘’@[A]’, and ‘@@[A]’. The first of these involves no back-quotes; thus, it notates the structure ’’[A]. The second one involves a single back-quote preceding a notated handle; it too will notate the structure ’’[A]. The third expression, ‘’@[A]’, has a back-quote on the inside. By itself, ‘̀@[A]’ notates the pair (RCONS ’A). Since the handle notation is supposed to be strictly compositional, we conclude that ‘’@[A]’ notates ’(RCONS ’A). Which leaves us with ‘@@[A]’. But this one is easy — it is equivalent to ‘@’(RCONS ’A).

Following this line of reasoning, the expression ‘@@[A ,B ,,C]’ notates the structure (PCONS ’RCONS (RCONS ’’A ’B C)), which could also be written (PCONS ’RCONS @[’A B ,C]). If C designates ’3, then this expression will normalize to ’(RCONS ’A B ’3), which could also be written ’@[A ,B 3]. In other words, nested back-quotes appear to be expanded from inside to the outside. (Am I making any sense?)