NOT.Preface:3 - The methods and their connections

NOT.Preface:3.1 - Design what can be expressed and done

NOT.1 derives a design requirement from the operation and from cases that need different treatment. NOT.2 constructs formation, grouping, scope and reference rules. NOT.3 gives the resulting expressions a meaning and a route by which a prepared reader obtains a consequence. These contributions connect what the work needs, what can be written and what the reader can do with it.

NOT.4 constructs changes to expressions, with their applicability conditions and preserved observations. A mathematical argument may justify a rewrite. A computational procedure may apply it. A surrounding physical or organizational use determines whether the preserved observation is sufficient. The same marks can therefore admit one transformation in a pure calculation and require another treatment when each occurrence performs an interaction.

NOT.Preface:3.2 - Translate, combine and improve notations

NOT.5 constructs a translation with the receiving question in view. It identifies losses, needed supplements and the limits of returning to the source. NOT.6 keeps several useful forms in joint use: it connects their referents and dependencies, then interprets an edit before propagating its consequences. A derived display value and an independently observed value can require different treatment even when they occupy similar cells.

NOT.7 locates an actual reading or editing burden, changes the expression or editing arrangement there, and compares both the intended improvement and effort moved elsewhere. NOT.8 adds the origins, frames, segmentation and available replay or enactment operations needed when signs unfold in time or bodily action. A temporal score can need the same formation, interpretation, translation and redesign methods as a static diagram.

There is no compulsory eight-stage process. Enter where the difficulty occurs. A translation loss can return to the original design requirement. An inconsistent update can expose a reference problem. A reading difficulty can require teaching a missing operation rather than another symbol. The working reminder for a longer combination is: Recover the operation; make references and interpretation usable; carry the intended change; retain useful differences; repair the remaining burden. The relevant bodies supply the conditions under which each continuation is needed.

NOT.Preface:3.3 - Constituent actions in ongoing work

Defining an operator’s binding rule can be part of constructing an expression grammar while a notation for working calculations is being designed. If users must transform an expression without changing its meaning, visually convenient grouping is insufficient: the interpretation of the transformed expression must remain recoverable. Symbol recognition and subject knowledge can both be present while the intermediate ability to follow binding and transformation rules is absent. The notation design must provide those rules and support their use; a successful reading of one expression does not establish the whole notation’s suitability.

FPF B.1.5.EW helps recover these constituent–whole connections; B.1.5.RS examines a proposed replacement. Use the parts of the vertical that can change the present result. A Method described here can require additional capability, available support and compatible resources at other grains.