Editing Random-access machine (section)

===Creating "convenience instructions" from the base sets===
The three base sets 1, 2, or 3 above are equivalent in the sense that one can create the instructions of one set using the instructions of another set (an interesting exercise: a hint from Minsky (1967){{spaced ndash}}declare a reserved register e.g. call it "0" (or Z for "zero" or E for "erase") to contain the number 0). The choice of model will depend on which an author finds easiest to use in a demonstration, or a proof, etc.

Moreover, from base sets 1, 2, or 3 we can create ''any'' of the [[primitive recursive function]]s ( cf Minsky (1967), Boolos-Burgess-Jeffrey (2002) ). (How to cast the net wider to capture the ''total'' and ''partial'' [[mu recursive function]]s will be discussed in context of indirect addressing). However, building the primitive recursive functions is difficult because the instruction sets are so ... primitive (tiny). One solution is to expand a particular set with "convenience instructions" from another set:
:''These will not be subroutines in the conventional sense but rather ''blocks'' of instructions created from the base set and given a mnemonic. In a formal sense, to use these blocks we need to either (i) "expand" them into their base-instruction equivalents{{spaced ndash}}they will require the use of temporary or "auxiliary" registers so the model must take this into account, or (ii) design our machines/models with the instructions 'built in'.''
:Example: Base set 1. To create CLR (r) use the block of instructions to count down register r to zero. Observe the use of the hint mentioned above:
:* CLR (r) =<sub>equiv</sub>
:* ''loop'': JZ (r, ''exit'')
::* DEC (r)
::* JZ (0, ''loop'')
:* ''exit'': etc.

Again, all of this is for convenience only; none of this increases the model's intrinsic power.

For example: the most expanded set would include each unique instruction from the three sets, plus unconditional jump J (z) i.e.:
* { CLR (r), DEC (r), INC (r), CPY ( r<sub>s</sub>, r<sub>d</sub> ), JZ (r, z), JE ( r<sub>j</sub>, r<sub>k</sub>, z ), J(z) }

Most authors pick one or the other of the conditional jumps, e.g. Shepherdson-Sturgis (1963) use the above set minus JE (to be perfectly accurate they use JNZ{{spaced ndash}}Jump if ''Not'' Zero in place of JZ; yet another possible convenience instruction).