NOT.2:11 - SoTA-Echoing
| Source and contribution | Adoption and limit |
|---|---|
| Gheri and Popescu, A Formalized General Theory of Syntax with Bindings, §2 | Constructors alone leave binding positions undecided. Sections :4.1/.3 add the required binding rules; :5.1 works the sum and capture contrast. The source’s alpha-equivalence, freshness and substitution theory supports formal development when needed. Its full mechanization adds no necessary step to the local notation example. |
| Piedeleu and Zanasi, An Introduction to String Diagrams for Computer Scientists, §2 | Sections :4.2/.4 use typed, ordered interfaces and drawing equivalence under stated equations; :5.2 shows why equal input types alone lose a needed role distinction. Symmetric monoidal categories supply one mathematical class of schemes, not every notation’s composition law. |
| Wehmeier, Binding in classical and dynamic predicate logic, 2026, introduction and §2 | Shared surface syntax can have different semantic binding behaviour. Section :4.3 therefore selects a resolution policy that fits the interpretation instead of treating nearest lexical binding as universal. The paper’s proposed general binding schema is not imported into every notation. |
| Dutilh Novaes, Formal Languages in Logic, 2012, pp. 53-54 and §5.2.1, historical foundation | Keep diagrammatic formation and work with external inscriptions among the available choices in :4.2/.6. This counters selecting textual syntax merely because it has explicit rules. The resulting convention still has to support the reader’s operation; explicitness alone establishes no learning advantage. |
| Zwaan and van Antwerpen, Scope Graphs: The Story so Far, 2023, §§1–2 and 5 | Scopes, references and declarations can be related by paths with visibility and precedence policies. This is a developed alternative when static name resolution crosses nonlexical boundaries. Its expressiveness and execution costs remain relevant; the method is not a universal account of physical references or component composition. |
Choosing the rule design. Retain familiar conventions when they already determine the needed grouping, reference and connection. A constructor list or an implicit layout is cheaper to state, but the sum and ratio cases show the price when it leaves two consequential readings. For that local difficulty, add the missing scope, delimiter or operand role and try the changed expression. This costs more signs or conventions to learn, while preserving a first use through a legend and worked construction.
When static references cross imports or other boundaries that simple nested environments do not handle conveniently, a scope-graph model can make the resolution policy explicit and reusable. It requires constructing those scopes, paths and priorities, and assessing the available implementation. Use that richer account when the reference problem calls for it, rather than adding it to the elementary sum. Likewise, choose a formal binding theory or diagram calculus when its laws are needed for repeated transformation or reasoning.
Revisit the retained choice when a needed expression cannot recover its references or composition, the interpreted operation changes, or a less costly available scheme preserves the same needed distinction. The synthesis is a way to construct and revise those rules; it does not select one notation or one binding policy for every practice.