---
title: "formula-syntax — Mova code model"
description: "Mova code model of models/formula-syntax.groupant: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/models/formula-syntax.groupant/"
---
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# formula-syntax

The groupant beside models/formula-syntax.groupant 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_group
- **status:** partial descriptive instance
- **bound sources:** 8
- **repository folder:** [`models/formula-syntax.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/formula-syntax.groupant)
- **repository commit:** `855da7bd4a7b`

> **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 | [forward](#forward) |
| **ast** | not materialized |  |
| **composition** | partial | [composition](#composition) |
| **cost** | symbolic source derived | [cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | see source local evidence | [checks](#checks) |

## 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) |
| `table-transport` | representation_transport | partial source derived model | [table-transport](#table-transport) |
| `marker-discipline` | substream_boundary | partial source derived model | [marker-discipline](#marker-discipline) |
| `canonical-adapters` | roundtrip_adapter | partial source derived model | [canonical-adapters](#canonical-adapters) |
| `resource-guards` | resource_boundary | partial source derived model | [resource-guards](#resource-guards) |

## Model text


### descriptant

#### formula-syntax: wave28

Generated enum order must match canonical arrays. Stack reversal preserves expansion order. Printer relax adapters prevent unknown swallowing groups and aligned swallowing brackets; optional rbrack and trailing-row compensation preserve parser structure. Span quotient cannot validate original coordinates.

This source-bound partial group organizes existing Mova code. Native evidence and excluded effects are recorded in source sidecars and the root wave28 report. Registration is not a universal proof or whole-system runtime claim.

### model

## formula-syntax

### forward

Ordered command rows compile to enums/lookups. Lex(source)->positioned tokens; scan(preamble)->macro map; parse_with(tokens,map)->Result<Node,Error>; print(Node)->canonical bytes; gate compares reparsed Node modulo Span. Text is a separate lossy projection.

### invariant

Local macros shadow document definitions, CmdRaw preserves captured built-ins. Normalized parser trees retain unknown names and presentation structure; coordinates are outside equality.

### cost

Build O(B+V²+E) expected hash work; lex O(B); parse cost depends on expanded tokens and substitution copies, not input bytes alone. LaTeX O(nodes+output); text nested temporary copies conservatively O(depth*output+nodes). No speed claim.

### composition

Generated enum order must match canonical arrays. Stack reversal preserves expansion order. Printer relax adapters prevent unknown swallowing groups and aligned swallowing brackets; optional rbrack and trailing-row compensation preserve parser structure. Span quotient cannot validate original coordinates.

### domain

Finite valid UTF-8, representable u32 positions, available memory/filesystem. Roundtrip restricted to normalized supported parser trees, not arbitrary public AST.

### limitations

Generated include matches command table. No semantic TeX engine, precedence inference or live effects. Build compile evidence does not inject write/read failures.

### checks

- Selected library/gate/build tests twice debug/release, matching sorted outcomes
- Four compiled assertion-failing mutants and restored positives
- Eight paired syntax projections

### catalog

### behavior-complement

Exclude tuples violating byte coordinates, local-first expansion, stop errors and supported fixture canonicalization; no universal arbitrary-AST contract.

### reverse-reconstruction

Canonical tree preimages contain aliases, whitespace/comments, dropped styles and macro programs. Original coordinates/definitions are not uniquely recoverable.

### table-transport

Ordered build rows induce discriminants/arrays and lookup Entry joins parser dispatch.

### marker-discipline

End markers delimit parser substreams. Stream group_tokens/opt_tokens and macros collect_until explicitly restore End on their failure paths. Macro match_pattern literal matching consumes the next token before comparison and can consume End on mismatch; read_let can likewise consume an invalid End target. No universal scan-failure preservation law is claimed.

### canonical-adapters

relax, rbrack and row compensation preserve parsing boundaries.

### resource-guards

Depth and expansion thresholds are local; pre-expansion token check does not bound peak substituted vector.