Token-Sensitive Enclosure Semantics for Measurement-Bearing Expressions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913074918719488 |
|---|---|
| author | Hulak, David B. Ramos, Arthur F. de Queiroz, Ruy J. G. B. |
| author_facet | Hulak, David B. Ramos, Arthur F. de Queiroz, Ruy J. G. B. |
| contents | Token identity is semantic information for measurement-bearing expressions. Intervals, dimension tags, and token-erased syntax can say what values a measured leaf may take, but they cannot say whether two occurrences name the same observation or two fresh observations. We give a small formal semantics in which each measured leaf carries an interval of possible exact values and an opaque observation-event token. Here "token" means an identity for a measurement event, not a lexical token of the source syntax. The denotation of an expression is its warranted enclosure: the set of exact values still justified by hidden-value environments that assign one value to each observation token and respect the declared intervals. Over this semantics, e -> e' is a claim-tightening judgment, equivalently enclosure containment Encl(e') subseteq Encl(e), while interchangeability is equality of enclosures. The distinction is visible in cancellation, background subtraction, and self-division: reusing one token gives interchangeability with the expected simplified expression, while using distinct tokens gives only one-way containment. We prove that provenance-blind summaries of the kind studied here, preserving intervals, dimension tags, and token-erased syntax, are insufficient to recover the correct rewrite class. The formal results are mechanized in Lean 4 with no sorry or admit placeholders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Token-Sensitive Enclosure Semantics for Measurement-Bearing Expressions Hulak, David B. Ramos, Arthur F. de Queiroz, Ruy J. G. B. Logic in Computer Science Programming Languages Token identity is semantic information for measurement-bearing expressions. Intervals, dimension tags, and token-erased syntax can say what values a measured leaf may take, but they cannot say whether two occurrences name the same observation or two fresh observations. We give a small formal semantics in which each measured leaf carries an interval of possible exact values and an opaque observation-event token. Here "token" means an identity for a measurement event, not a lexical token of the source syntax. The denotation of an expression is its warranted enclosure: the set of exact values still justified by hidden-value environments that assign one value to each observation token and respect the declared intervals. Over this semantics, e -> e' is a claim-tightening judgment, equivalently enclosure containment Encl(e') subseteq Encl(e), while interchangeability is equality of enclosures. The distinction is visible in cancellation, background subtraction, and self-division: reusing one token gives interchangeability with the expected simplified expression, while using distinct tokens gives only one-way containment. We prove that provenance-blind summaries of the kind studied here, preserving intervals, dimension tags, and token-erased syntax, are insufficient to recover the correct rewrite class. The formal results are mechanized in Lean 4 with no sorry or admit placeholders. |
| title | Token-Sensitive Enclosure Semantics for Measurement-Bearing Expressions |
| topic | Logic in Computer Science Programming Languages |
| url | https://arxiv.org/abs/2604.07626 |