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For IRM backquote documentation, you can MAN BQUOTE to get the entry in DInfo, or search for backquote in the IRM

As for which LAMBDA is used, that's not something that's determined by backquote processing, it was determined when the form was read.

The ` readmacro, just expands as the form wrapped in IL:BQUOTE, with the , , ,@ , etc. converted to a slightly different IL: litatom.
I.e., your example, entered into the XCL-EXEC:

(QUOTE `(lambda () (frobulate ,FOO-INSTANCE )))

expands to:

(IL:BQUOTE (LAMBDA NIL (FROBULATE (IL:\\\, FOO-INSTANCE))))

(In an Interlisp EXEC, the IL:\\\, is just \,. The extra \ are just for XCL readtable special character quoting in the litatom's p-name.)

That ulti…

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