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Source changed 2026-10-02 23:06:08 UTC · snapshot created 2026-10-03 01:38:24 UTC · last check 2026-10-03 03:05:10 UTC

NT-CHANGE-TOGETHER - Carry a changed request through several representations

  • Situation: A group uses a formula, operation graph and table for different operations, and a local request changes what their users should read or do.
  • Question: What does the request change, and how can the useful forms remain connected?
  • First useful result or blocker: The request expressed as a constraint on the shared construction, followed by its affected expressions or a conflict between requirements.
  • Start with: NOT.6 - Coordinate Complementary Representations through Shared References when the forms are already interpreted; NOT.1 - Choose the Distinctions and Operations a Notation Must Support when the required operation is still unclear.
  • Stop or return: Keep unaffected interpretations. Return to the changed assumption, discarded distinction or incompatible requirement; an adequate existing representation needs no redesign.

Worked connection for NT-CHANGE-TOGETHER

  1. Give the forms something definite to express. A stipulated rule is r(q,b) = q + q + b over real numbers. Both q occurrences use one supplied input; b is one shared parameter. The work is to obtain outputs and revise b. If grouping or references are unclear, NOT.2 - Define Expression Rules for Recoverable Binding and Composition supplies those rules. Its result lets NOT.3 - Give Expressions an Operative Interpretation specify the reading: add q to itself, then add b. In the operation graph, q feeds both inputs of the first addition; that result and b feed the second. At b=1 and q=0, 1, 2, the outputs are 1, 3, 5.

  2. Use the interpretation to justify a useful change of expression. NOT.4 - Construct Transformations of Expressions That Preserve Their Use can replace the formula by 2*q + b. Real arithmetic establishes the same output for every admitted q and b. The graph exposes the dependence; the compact formula makes the shared parameter easy to locate. Their value comes from those operations, not from one form being universally simpler.

  3. Give a translation only the work it can support. NOT.5 - Translate between Notations while Tracking Lost Distinctions produces the table (0,1), (1,3), (2,5) at b=1. This supports lookup at the listed inputs. The table alone does not determine the output at q=3: 2*q + 1 and 2*q + 1 + q*(q-1)*(q-2) agree on all three rows but give 7 and 13 there. Keep the generating rule with the table when the receiver needs other inputs or a rule change. If only the three listed answers are required, stop with the table.

  4. Interpret the request before propagating it. The group asks for r(1,b)=4 while retaining the coefficient 2. NOT.6 uses the correspondence between that table row and the formula to obtain 2*1 + b = 4, hence b=2. This new parameter supplies the graph and regenerates the table as (0,2), (1,4), (2,6). The unedited old cells were derived values, not instructions to hold them fixed. If the request also keeps r(0,b)=1, it requires b=1 and conflicts with b=2. Return the two requirements to the group for a decision. If a separate record says that an output of 3 was observed at q=1, keep that observation beside the new prediction of 4. A parameter change does not revise the past event.

  5. Reopen the relevant rule when an occurrence changes meaning. Suppose each q occurrence now means a fresh sensor read. With successive readings 4 and 5 and b=1, read() + read() + b gives 10; 2*read() + b, using the first reading, gives 9. Return to NOT.3 for the meaning of an occurrence and NOT.4 for the transformation’s conditions. If one sample is intended, bind that sample once and reuse it. If two observations are intended, retain both. The measurement method supplies the meaning of a read; CMP.12 - Construct an Interpreter or a Meaning-Preserving Translation supplies an effective interpreter when software must execute the expression.

  6. Repair the remaining burden only if it matters. If common parameter changes are still laborious, NOT.7 - Redesign a Notation around the Reader’s Difficult Operations compares one accessible definition of b with repeated independent entries. The shared definition makes a common edit local but adds reference-following for individual readings. Keep the table for frequent lookup if that benefit warrants its maintenance. A later local exception returns to the sharing assumption: it cannot be expressed by a global parameter change alone.

The result can be the new expressions, a sufficient table, an exposed conflict or a missing interpretation. Applying the rule to a physical quantity requires the corresponding subject account; the arithmetic construction supplies no observation of that subject.