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 (Consistent with this, our particular interpreter has no explicit code in LOOKUP which specifies copying.) The other place in Puzzle #3 where copying might occur is in the binding of U and v. Examining the text of our particular meta-circular interpreter shows that BIND also has no explicit code for copying. There remains the possibility that binding does implicitly copy in the text of the meta-circular interpreter; this would consistently cause copying in the bindings of the interpreted code, because ENV would be copied whenever bound in the text of the interpreter. This, however, would cause the answer to Puzzle #1 to be A, because ENV is bound at other places which would cause incorrect copying. We therefore conclude that no implicit copying can occur, and so the answer to Puzzle #3 is Z.

We emphasize that this result rests on our acceptance of a particular class of meta-circular interpreters. (These interpreters, however, closely model what real LISP systems do.) There are other languages which do implicitly copy structured values when binding variables, such as Algol 60 when using call-by-value. For such a language, the answer to Puzzle #3 would be A (if we represented the list (A B C) as an Algol 60 array, for example), even though the answer to Puzzle #1 would still be Z.

One can argue both for and against copying during binding on the basis of modularity. Copying isolates the caller from the called routine by preventing the called routine from performing under-the-table side-effects on the caller's data objects. Not copying allows data objects to encapsulate independent pieces of state which can be operated on by low-level routines whose details need not be understood by their caller (an example of such a data object is the symbol table of an assembler, with its insertion and lookup routines).

We now consider Puzzle #2. If we accept that binding and variable referencing do not makes copies, then Puzzle #2 is a question about the nature of CONS: if CONS is called twice with arguments which are the same, are the two results the same? (Note that this is the inverse of Postulate 4 for S-expressions in {Note S-expression Postulates and Notation}.) If the answer is consistently A (as in most real LISP systems), then CONS must generate a new object every time it is called. (It must produce different results if the two sets of arguments differ, and an answer of A to Puzzle #2 requires different results if the two sets of arguments are the same.) CONS perforce contains a side effect. Calls to it are not referentially transparent.

The other possibility, given that variable binding and variable referencing do not make copies, is that the answer to Puzzle #2 is Z. In this case, CONS of the same arguments must always produce the same result. This choice leads to galloping non-modularity of data structures without compensation. Suppose, for example, we represent arrays as lists of numbers (a reasonable LISP representation), and want to alter the last element of one such array (using RPLACA). Under this scheme, all arrays whatsoever with the same last element would be magically altered! A language with such characteristics would be extremely difficult to control.

Supposing now that binding does make copies as in Algol 60, the answer to Puzzle #2 must be A. Here it does not matter whether CONS of the