---
title: "algorithm-quickselect-tests — Mova code model"
description: "Mova code model of algorithms/src/quickselect/tests.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/quickselect/tests.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**

This page as HTML: <https://groupants.elamur.ai/free/en/mova/algorithms/src/quickselect/tests.rs.groupant/>

# algorithm-quickselect-tests

The groupant beside algorithms/src/quickselect/tests.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 descriptive instance
- **source:** [`algorithms/src/quickselect/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/quickselect/tests.rs)
- **source SHA-256:** `2783d36987154cf7…`
- **repository folder:** [`algorithms/src/quickselect/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/quickselect/tests.rs.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 | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [approximant](#approximant) |
| **tests** | existing checks referenced | [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) |
| `independent_oracle` | independent_oracle | partial source derived model | [independent_oracle](#independent-oracle) |
| `property_assumptions` | property_assumptions | partial source derived model | [property_assumptions](#property-assumptions) |
| `bounded_coverage_cost` | bounded_coverage_cost | partial source derived model | [bounded_coverage_cost](#bounded-coverage-cost) |

## Model text


### descriptant

#### quickselect tests groupant

Epoch 2026-10-29: prospective predictions saved outside repository before
implementation. Original std-only code/fixtures; four algorithm tests pass
twice. Compiled red control: reverse strict partition comparison.

Combiner: source identity, recurrence, invariant and checks constrain a
conditional model. Complement and converse answer different questions; no
additive inverse identity. Syntax is partial with opaque macros and no type
or name resolution. Finite evidence is not proof of all inputs or parent wiring.
Lawful Ord and successful execution are assumed; trait panics and allocation
failures are outside successful-call semantics. Preserve these observations
in future epochs. No runtime speedup claim.

### approximant

#### Forward, invariant and cost

Generate bounded fixtures, compute independent references, assert agreement
and separate structural properties. References do not consult production
outputs. Compare every rank with fully sorted copy; separately assert partition and multiset.

Assumptions: Invalid rank preserves exact input; valid prefix<=selected<=suffix; lawful Reverse wrapper.

Coverage: 3280 ternary arrays length 0..7, 24604 rank attempts including invalid endpoints; seeded 516 full-width entries and sorted/reverse/equal vectors.
Test oracle costs are described in models.md; production cost: O(n²) worst time, O(1) auxiliary space; invalid rank O(1).

### models

## quickselect test models

Subject/revision: tests.rs at manifest SHA. Observe one test invocation under
lawful Ord and ordinary allocation. Partial source-derived models have bounded
evidence; no universal proof or arbitrary panic behavior is modeled.

### behavior_complement

U=(fixture, candidate result, verdict). Pass with violated oracle equality
or explicit property assertion is absent from the assertion graph. This exact
complement slice does not exclude implementations overfit to tested fixtures.
The compiled mutation (reverse strict partition comparison) is rejected by one exact filtered test.

### reverse_reconstruction

Passing fixtures constrain implementation outputs/properties only on this
finite domain; all agreeing functions remain compatible. Failure identifies
a counterexample, not a unique bug or source. The mutant is one member of
a failure fiber. Complete source reconstruction is not implemented.

### independent_oracle

Compare every rank with fully sorted copy; separately assert partition and multiset.
Independent control flow can still share contract misunderstandings; bounded
correspondence is evidence rather than a proof of all inputs.

### property_assumptions

Invalid rank preserves exact input; valid prefix<=selected<=suffix; lawful Reverse wrapper.
Dropping lawful order or changing strictness invalidates these targets.
Witnesses and custom-order tests exercise only the declared bounded projection.

### bounded_coverage_cost

3280 ternary arrays length 0..7, 24604 rank attempts including invalid endpoints; seeded 516 full-width entries and sorted/reverse/equal vectors.
Seeds use wrapping arithmetic. Generation is exponential in a fixed small
bound. Reference vectors add O(n) space; reference sorting work is separate
from the algorithm under test. Production cost: O(n²) worst time, O(1) auxiliary space; invalid rank O(1).

### checks

#### Evidence, 2026-10-29

Four tests for this algorithm passed twice with temporary local crate exports:
66 total tests, identical normalized outcomes. Strict all-target Clippy and
rustfmt passed. Temporary exports are not committed.

Coverage: 3280 ternary arrays length 0..7, 24604 rank attempts including invalid endpoints; seeded 516 full-width entries and sorted/reverse/equal vectors.

External mutant (reverse strict partition comparison) compiled; exactly one filtered new exhaustive test
failed an assertion with exit 101. No mutant committed. One red control is not
mutation completeness. Parent owns final exports, registry and source bindings.