---
title: "parsecmp-main-bracket-intersection — Mova code model"
description: "Mova code model of tools/parsecmp/src/main.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/tools/parsecmp/src/main.rs.groupant/bracket-intersection.groupant/"
---
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# parsecmp-main-bracket-intersection

The groupant beside tools/parsecmp/src/main.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_fragment
- **status:** partial source bound model
- **source:** [`tools/parsecmp/src/main.rs`](https://github.com/ElamurAI/mova-free/blob/main/tools/parsecmp/src/main.rs)
- **source SHA-256:** `8d5c1b3d4b13c46e…`
- **covers:** bracket-intersection (bytes 5663–6115)
- **part of:** [parsecmp-main](https://md.groupants.elamur.ai/free/en/mova/tools/parsecmp/src/main.rs.groupant/)
- **repository folder:** [`tools/parsecmp/src/main.rs.groupant/bracket-intersection.groupant`](https://github.com/ElamurAI/mova-free/tree/main/tools/parsecmp/src/main.rs.groupant/bracket-intersection.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 | `model.md` |
| **ast** | partial | `../syntax.json` |
| **composition** | partial | [Composition](#composition) |
| **cost** | partial | [invariant-and-cost](#invariant-and-cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant-and-cost](#invariant-and-cost) |
| **tests** | 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) |
| `multiplicity` | multiplicity | partial source derived model | [multiplicity](#multiplicity) |
| `symmetry` | symmetry | partial source derived model | [symmetry](#symmetry) |
| `empty_identity` | empty_identity | partial source derived model | [empty_identity](#empty-identity) |
| `order_invariance` | order_invariance | partial source derived model | [order_invariance](#order-invariance) |

## Model text


### descriptant

#### Descriptant

build counts of spans in a, scan b decrement positive stored counts and increment hit, return (hit,a.len,b.len).

##### Epoch 2026-10-31

Prospective source reading identified conditional input alignment, information loss and failure order before tests. Existing production code is retained; added tests use actual helpers. Finite results update this source-bound model, not all parser/corpus semantics.

No executable percentage surrogate has a justified observation metric for these categorical/effectful APIs. Future profiles require metric, domain and real-reference evidence at caps 1/2/5/10%; no higher cap. Syntax is partial lexical Rust projection without macro expansion or semantic resolution.

### approximant

## Forward approximant

build counts of spans in a, scan b decrement positive stored counts and increment hit, return (hit,a.len,b.len).

### Composition

This fragment is the exact byte-scoped helper identified in the manifest; its relation is restricted to the operations above.

The containing source wires this scoped relation to its callers. Treeagree proposal→gate→commit and treebanks parse→match→collect→render are actual joins; parsecmp is an independent diagnostic path. The external group model distinguishes these tags.

### catalog

## Typed models for parsecmp-main-bracket-intersection

Subject: source SHA-256 `8d5c1b3d4b13c46e7f0b31fad87b1197b29574d987a2ea1c89ed012961a9a9e7`; manifest supplies exact source/byte scope. Domain: admitted states in forward model, nonoverflow arithmetic and successful allocations. Observation: one terminating invocation, except explicitly described file trace. Source-derived partial relations; named finite tests constrain selected cases only. Each entry holds arguments and environment fixed except its stated intervention.

### behavior_complement

hit cannot exceed either input length and unmatched/exhausted spans cannot increase hit.

Operator: inner exclusion on admitted domain. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### reverse_reconstruction

Output counts identify cardinalities and overlap multiplicity only; many labeled-span multisets share the same triple.

Operator: compatible antecedent relation, retaining ambiguity. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### multiplicity

Two copies in b against one in a yield one hit, unlike set or unrestricted membership counting.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### symmetry

Swapping a,b preserves hit and swaps last two counts under nonoverflow arithmetic.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### empty_identity

Empty a or b yields zero hit with exact other length, including (0,0,0).

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### order_invariance

Permuting either multiset preserves triple; this function does not validate half-open span coordinates.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### tests

#### Scoped evidence

Parent native slice and exact names are in `../tests.md`.

Only named finite assertions cover selected inputs; other branches and invalid-domain behavior remain source-derived.

This fragment has no independent full-coverage claim. Its byte range and source hash bind the source-derived relation; parent test success is evidence only where that helper is actually reached.

### invariant-and-cost

#### Invariant and cost

O((a+b)*log distinct_a) comparisons, O(distinct_a) map memory; labels compare strings.

hit cannot exceed either input length and unmatched/exhausted spans cannot increase hit.

The complement and specialized catalog constrain preserved coordinates and effect boundaries. Empty/malformed domains are only guaranteed where explicitly admitted. No whole-program cost bound follows from a helper bound.