NOT.4:1 - Problem frame

Use this when an expression is difficult to read, derive from or change, and you need a rule for turning it into a more useful expression without losing the consequence on which the work relies. Examples include naming a repeated construction, exposing a hidden intermediate step, regrouping a diagram, or replacing a long sequence by an expandable abbreviation.

Start with the reader operation that is difficult. Construct a proposed manipulation from the expression’s formation and interpretation rules. State where the manipulation applies, explain what it preserves, then obtain and use a transformed expression. The result can instead be a located condition that prevents the proposed transformation.

The reader needs the notation’s interpretation and the subject laws used in the manipulation. NOT.2 supplies grouping and reference rules; NOT.3 supplies interpretation and reading operations. Elementary arithmetic and ordered sequences suffice for the worked cases. More specialized laws can be supplied by a collaborator.

Apply an existing transformation directly when its rule and conditions already answer the question. Use this method when that rule must be constructed, extended or repaired. A change of notation calls for NOT.5’s translation and recovery work. Constructing an effective interpreter or compiler calls for CMP.12. Choosing a different physical process or working method requires the corresponding subject methods as well as a way to express the change.