arXiv:2601.14252 · v7
Semantic Completeness for Correct Maintenance: A Strict Hierarchy of Typing and Inheritance
摘要
Removing nominal types or inheritance is defended as reducing burden; cited Java and Go rationales measure no comparison. Correct maintenance minimizes outside answers and repair obligations, preserving required answers and excluding invalid states. Answers identify meanings, memberships, and required implementations. Five capacities form a strict chain. With nominal identities fixed, only multiple contract and implementation parents attain the answer-and-repair optimum on every finite declared history. Incomplete mechanisms force slop: answers restated in code or tooling. In 20 pinned multiple-inheritance Python projects, recovered implementation-class pairs grouped by source class would need outside supply: 12,880 without inheritance, 8,792 under first parents, 739 under sound one-parent optima (checked), zero with multiple parents. With provider and state carriers fixed, state-bearing rows alone force 236 outside pairs. Java and C# interface defaults supply no instance state. At least 24 of 65 size-qualified wheels among the top 150 pure-Python downloads have positive recovered gap (36.9%, 34 unscored). For distinct, independently changing implementations, the ancestry gap is the exact outside-pair minimum with one parent supplying only required pairs, even with reparenting, infinite helpers, delegation, or generators. Zero gap and one-parent contract coverage hold iff class sets nest or are disjoint. Identical records with distinct answers need the confusability graph's chromatic number of keys. Every tree-shaped growth step inserting an off-path provider strictly between ancestors forces one-parent repair. Every snapshot in our constructed history has gap zero, yet repair obligations recur each step; multiple parents add one edge per step. At fixed design costs, bans never lower optima; savings imply suboptimal unrestricted choices.
作者备注：Main PDF: 36 pages, 9 figures, 4 tables. Supplementary: 119 pages, 2 figures, 9 tables. Lean 4 artifact available at https://zenodo.org/records/23393039