personal/egparedes: connectivities as types — Cartesian axis dimensions, and UGRID/SGRID alignment

content/index.md

@@ -44,8 +44,8 @@ Work-in-progress proposals, organized by contributor.
 
 - [[personal/egparedes/layered-architecture|A layered architecture for gt4py with enforced public/internal decoupling]] — keywords: architecture, layering, tach, modularity, public-api, semi-public, internal, packaging, dependencies, refactoring, infrastructure, over-engineering, otf, workflow, dsl, config, allocators, caching, fingerprint, compiled-program, process-pool, factory-boy, instrumentation, adr, jax, decoupling, migration, tech-debt
 - [[personal/egparedes/otf-toolchain-split|Dissolving gt4py.next.otf into a toolchain core and DSL-agnostic build infrastructure]] — keywords: otf, toolchain, workflow, pipeline, refactoring, architecture, layering, modularity, backend, bindings, build-system, caching, runners, compiled-program, factory-boy, naming, observability, stage-inspection, adr, tach, tech-debt
-- [[personal/egparedes/connectivities-as-types/connectivities-as-types|Connectivities as types: one declaration for offset, local dimension and provider key]] — keywords: type-system, type-checking, dimensions, local-dimensions, connectivities, offset-provider, unstructured, neighbor-sum, reduction, frontend, foast, gtir, embedded, gtfn, dace, nominal-types, dependent-types, metaclass, serialization, fingerprint, staggering, migration, adr, tech-debt, shared-local-dimensions, implemented
-- [[personal/egparedes/discretization-independent-fd-syntax|A discretization-independent surface syntax for finite-difference computations]] — keywords: finite-difference, finite-volume, mesh-invariant, structured, unstructured, exterior-calculus, dec, mimetic, de-rham, location-typing, stencil, weight-generation, rbf-fd, gfdm, moment-matching, conservation, field-operators, icon, pace, pmap, fv3, ifs-fvm, arakawa-staggering, c-grid, d-grid, a-grid, dynamical-core, hevi, vertical-solve, elliptic-solve, mpdata, semi-implicit, miura, atlas, prior-art, dsl-design
+- [[personal/egparedes/connectivities-as-types/connectivities-as-types|Connectivities as types: one declaration for offset, local dimension and provider key]] — keywords: type-system, type-checking, dimensions, local-dimensions, connectivities, offset-provider, unstructured, neighbor-sum, reduction, frontend, foast, gtir, embedded, gtfn, dace, nominal-types, dependent-types, metaclass, serialization, fingerprint, staggering, axis-dimensions, cw-complex, exterior-calculus, domain, dimension-kind, ugrid, sgrid, migration, adr, tech-debt, shared-local-dimensions, implemented
+- [[personal/egparedes/discretization-independent-fd-syntax|A discretization-independent surface syntax for finite-difference computations]] — keywords: finite-difference, finite-volume, mesh-invariant, structured, unstructured, exterior-calculus, dec, mimetic, de-rham, cw-complex, location-typing, stencil, weight-generation, rbf-fd, gfdm, moment-matching, conservation, field-operators, icon, pace, pmap, fv3, ifs-fvm, arakawa-staggering, c-grid, d-grid, a-grid, dynamical-core, hevi, vertical-solve, elliptic-solve, mpdata, semi-implicit, miura, atlas, prior-art, dsl-design
 
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content/personal/egparedes/connectivities-as-types/connectivities-as-types_alternatives.md

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+---
+title: "Connectivities as types — alternatives considered"
+author: egparedes
+tags: [type-system, connectivities, local-dimensions, offset-provider, nominal-types]
+created: 2026-10-01
+status: draft
+---
+
+> **Appendix** to [[personal/egparedes/connectivities-as-types/connectivities-as-types|Connectivities as types]].
+> The alternatives rejected on grounds other than the axis levels, which are in the
+> [[personal/egparedes/connectivities-as-types/connectivities-as-types_staggering|staggering appendix]]. Each entry states the alternative, then why
+> it loses.
+
+## Alternatives
+
+**Keep every concept; fix only which string wins.** Emit `FieldOffset.value`
+instead of `foast.Name.id` in `foast_to_gtir`, validate `value == target[-1].value`
+eagerly, extend the #1789 regression test. Two PRs, low risk — and the
+`foast_to_gtir` part is a real bug, fixed regardless, in GridTools/gt4py#2898.
+But it *enforces* the tangle rather than removing it; no concept goes away.
+
+**A declaration object with a derived local dimension, keeping `Dimension`
+instances.** Same shape as this proposal minus static typing and minus type
+identity: `local_dim.value == name` by construction, provider keyed by the
+declaration object. Superseded by building on dimensions as types instead:
+once dimensions are classes, the nested-class form is both simpler and
+statically meaningful.
+
+**`(name, kind)` value equality with an interning registry** (the design of
+[[shared/dimensions-as-types|dimensions as types]] and GridTools/gt4py#2844).
+Keeps independently declared same-named dimensions interchangeable and
+avoids the importability rule. Rejected because it decouples the Python
+type's identity from the IR's, needs a registry plus `copyreg` plus a custom
+fingerprint deconstructor to paper over that gap, and cannot give a nested
+`V2E.Local` a unique name without further convention. See [[personal/egparedes/connectivities-as-types/connectivities-as-types#identity-is-the-qualified-python-name|Identity]].
+
+**Integer type parameters for `max_neighbors`** (`LocalDimensionIndex[F: int, M: int]`).
+Would need `Literal[6]` type arguments and `Final[F]` over a `TypeVar`;
+checkers gain nothing. Class keywords instead.
+
+**Data on the class** (`data: ConnectivityField | Unbound`). Process-global
+mutable state; tests bind several meshes per process, and the compile cache
+assumes the table travels separately from the type. Binding per call, keyed by
+the class, keeps the invariant structural.
+
+**`axis=V2E` as sugar.** Rejected for now; keep the local axis explicit.
+
+**Static-only `max_neighbors` / `min_neighbors`.** Simplest, and correct for
+fixed-arity meshes. Rejected as the *only* mode because it binds DSL source
+to one mesh family (`fvm_nabla_setup.py` sizes `V2E` from the atlas mesh) and
+because skip-value presence is configuration-dependent in ICON, so a static
+`min_neighbors` forces either duplicate classes or always-on skip handling.
+Declared counts stay available as a constraint; see [[personal/egparedes/connectivities-as-types/connectivities-as-types#binding-model|Binding model]].
+
+**Owner-less local axes as non-LOCAL dimensions.** Rejected: they would
+become domain dimensions with a range in every program domain and lose the
+sparse storage treatment, changing ICON4Py's layout for `LsqUnkDim` fields.