C.29.2:4.2 - Choose represented state and operations together

Choose data in which the relevant next operation can be expressed. Explain what each stored value means, how an input initializes it, and how a returned value will be interpreted. The same mathematical quantity may be represented by an integer, an interval, a symbolic expression or another subject-appropriate object; the operations must match that choice.

Construct the state from what the continuation needs. In a sequential procedure this often includes a control position and intermediate values. For each proposed next step, ask what it reads, changes and preserves. If two histories reach the same stored state but require different continuations, recover the omitted condition or summary. Use A.3.3 for the underlying state-and-continuation construction; keeping every past observation is only one possible repair.

Specify the meaning of an elementary operation at the level used by the argument. An exact integer addition is different from modular word addition. A comparison of exact rational numbers is different from comparing rounded observations. If an operation is available only through another procedure, expose that dependency when its conditions or cost can change this computation.

A formulation can specify equations or constraints without choosing an evaluation order. Identify the supplied quantities or boundary conditions, admissible solutions and the output the receiver needs. An applicable solver or modeled computational process must connect those relations to obtaining a result; its execution order may remain an implementation choice. When restructuring the equations, preserve the required solutions under the stated conditions and retain expressions that recover requested quantities removed from the computational state. If no such construction is available, the equations still characterize answers and the missing way remains a task under :4.3.

The available operations can also be the starting contribution. A collaborator working under C.29.3 may supply preparable inputs, controllable changes, readable outputs and their limits for a candidate system. Use those capabilities to propose computational states and operations that can answer a useful question; do not force them into an unsuitable instruction set. Keep the physical model and the experimental or conditional basis of that contribution visible. A new computational model or language needs meanings for its expressions as well as formation rules. A.6.3.RT helps construct expressions under available notation rules; designing missing rules is separate notation or language-design work.