MMP.22:4.2 - Recover the mathematical operations and their working meaning

Represent the contribution to be changed at the detail the transformation uses. Recover each operation’s input, result and relevant state, including information available when it is performed. If an operation alters its input or the surroundings, include that effect in the account used for the transformation.

MATH.17 lets operations themselves be constructed and transformed; MATH.18 compares what different accounts preserve. MMP.21 constructs the comparison with actual work requirements.

Distinguish several transformations that can look alike on a diagram. Copying a value can differ from obtaining a second observation. Commuting two pure functions can differ from interchanging actions on a shared object. Parallel branches in a mathematical representation do not provide two available performers.

Choose a richer account only when the omitted distinction can change the candidate or its use. A deterministic function can be sufficient for transforming a fixed-data calculation. Stochastic observations need their dependence; shared-state actions need their effects.