---
title: "latex-ast — Mova code model"
description: "Mova code model of latex/src/ast.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/latex/src/ast.rs.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

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# latex-ast

The groupant beside latex/src/ast.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant
- **status:** partial source bound model
- **source:** [`latex/src/ast.rs`](https://github.com/ElamurAI/mova-free/blob/main/latex/src/ast.rs)
- **source SHA-256:** `88786b90964d7ee3…`
- **repository folder:** [`latex/src/ast.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/latex/src/ast.rs.groupant)
- **repository commit:** `48f2e6f74146`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **composition** | partial | [composition](#composition) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#tests) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `span_quotient` | span_quotient | partial source derived model | [span_quotient](#span-quotient) |
| `normalization` | normalization | partial source derived model | [normalization](#normalization) |
| `traversal_order` | traversal_order | partial source derived model | [traversal_order](#traversal-order) |
| `unknown_projection` | unknown_projection | partial source derived model | [unknown_projection](#unknown-projection) |

## Parts

- [latex-ast-stage0](https://md.groupants.elamur.ai/free/en/mova/latex/src/ast.rs.groupant/stage0.groupant/)
- [latex-ast-stage1](https://md.groupants.elamur.ai/free/en/mova/latex/src/ast.rs.groupant/stage1.groupant/)
- [latex-ast-stage2](https://md.groupants.elamur.ai/free/en/mova/latex/src/ast.rs.groupant/stage2.groupant/)

## Model text


### descriptant

#### latex-ast

norm collapses exactly one atom; empty is Row([]). walk is preorder and preserves row/cell order; Scripts visits base, sub, sup, optional roots visit index before body. unknowns collects names and actual stored spans; has_unknown traverses all nodes.

Epoch2026-10-31: full source reviewed before edits; prospective models retained externally. No optimization.

### approximant

#### Forward relation

norm collapses exactly one atom; empty is Row([]). walk is preorder and preserves row/cell order; Scripts visits base, sub, sup, optional roots visit index before body. unknowns collects names and actual stored spans; has_unknown traverses all nodes.

No useful approximate executable metric for exact categorical syntax; future caps1/2/5/10% only.

### invariant

#### Domain, invariant and cost

norm collapses exactly one atom; empty is Row([]). walk is preorder and preserves row/cell order; Scripts visits base, sub, sup, optional roots visit index before body. unknowns collects names and actual stored spans; has_unknown traverses all nodes.

Public Node permits non-normal forms; no validation enforces singleton Row absence. Span u32 represents byte coordinates but equality deliberately ignores them.

walk/size/has_unknown O(N), O(D) recursion; unknowns adds name bytes and K outputs; usize size overflow not separately guarded.

### composition

#### Composition

norm collapses exactly one atom; empty is Row([]). walk is preorder and preserves row/cell order; Scripts visits base, sub, sup, optional roots visit index before body. unknowns collects names and actual stored spans; has_unknown traverses all nodes.

Build generates table enums consumed by parser dispatch and printers. Lexer tokens feed macros and parser; parser returns AST whose equality ignores spans. Printers and gate compare that quotient, not original bytes. Shared parent syntax backs scoped stages; stages are byte-bound projections, not independent Rust modules.

### models

### behavior_complement

Span equality cannot distinguish coordinates; traversal cannot silently omit Unknown arguments or script children.

### reverse_reconstruction

A structural equality class admits arbitrary span assignments. norm inverse of atom n includes [n], and when n is Row(v), v subject to normalization; original grouping/positions cannot be uniquely inferred.

### span_quotient

Eq(Span a,Span b)=true independently of start/end.

### normalization

norm([])=Row([]), norm([a])=a, norm(v)=Row(v) when len differs from1.

### traversal_order

Root precedes children; scripts base/sub/sup and env row-major.

### unknown_projection

unknowns preserves traversal order and stored offsets; has_unknown agrees with nonempty unknowns for finite valid trees.

### tests

#### Evidence — 2026-10-31

ast::wave28_tests::normalization_and_span_quotient; ast::wave28_tests::traversal_preserves_script_and_unknown_order

Selected library filters ast:: lex:: macros:: parse:: print:: table:: and integration gate excluding document_extraction_with_preamble_macros and random_token_soup_never_panics_and_roundtrips. Direct rustc --test latex/build.rs exercises private helpers. All selected tests twice debug/release with identical sorted names. Four compiled mutants at build/AST/parser/printer boundaries fail assertions then exact restoration passes. These do not individually cover every source. Build-main failure effects, allocation failures and universal roundtrip are unproved. Strict Clippy reports existing lints. No corpus/live VMM/API/GPU/full-school/held-out tests.