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

# algorithm-prim-tests

The groupant beside algorithms/src/prim/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/prim/tests.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/prim/tests.rs)
- **source SHA-256:** `426c850115b00d94…`
- **repository folder:** [`algorithms/src/prim/tests.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/prim/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 | [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) |
| `oracle-independence` | reference_separation | partial source derived model | [oracle-independence](#oracle-independence) |
| `mutation-sensitivity` | falsification_boundary | partial source derived model | [mutation-sensitivity](#mutation-sensitivity) |

## Model text


### descriptant

#### prim tests.rs

Execute bounded fixtures and independent oracles, assert exact outputs and return harness pass/failure identities. 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling.

Epoch 2026-10-30: original implementation and finite independent witnesses. O(V+E log(E+1)) time and O(V+E) storage. Every edge is inserted at most twice; stale internal edges are charged. Limits precede allocations; allocator failures are not typed.

Composition: Uses existing Kruskal Edge and Forest records; algorithmic optimum is additionally compared with Kruskal. Tie trace need not coincide.

No executable percentage-error surrogate: the public operation remains exact, and no useful approximate observation metric is claimed. Allocation failure, timing and general semantic resolution remain outside these models.

### approximant

#### Forward and cost

Domain: Finite native test inputs, literal fixtures and oracle outcomes for prim; trusted Rust harness. Vertex count and ordered undirected kruskal::Edge records with u64 weights, at most one million vertices and edges. Return kruskal::Forest with original indices in Prim acceptance order.

Execute bounded fixtures and independent oracles, assert exact outputs and return harness pass/failure identities. 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling.

Cost: Finite enumeration cost includes independent oracle; no production timing or unbounded correctness inferred.

### invariant

#### Invariant

Every passing comparison uses the same generated input for implementation and oracle. Named assertion failure rejects a mismatching observation; all domain coverage is finite.

### catalog

## Typed model family

### behavior-complement

Type: behavior_complement. Subject/revision: tests.rs sha256 426c850115b00d94b2c07a051fde0e4531ac009b793d92e1035e740061a40d16.
Domain: Finite native test inputs, literal fixtures and oracle outcomes for prim; trusted Rust harness. Vertex count and ordered undirected kruskal::Edge records with u64 weights, at most one million vertices and edges. Return kruskal::Forest with original indices in Prim acceptance order.
Observation: complete one-call return; tests observe named pass/failure.
Operator: Let U be declared inputs crossed with returned observations and R the forward relation in approximant.md. C=U minus R includes wrong first errors, wrong values and forbidden results. This is an exact specification complement and partial source-derived model, not a measured global Rust complement. For this test file, false acceptance of a mismatching finite fixture is excluded by assertions; passing unseen implementations remains possible. 
Approximation: exact specification under stated assumptions; partial source correspondence.
Assumptions: standard Rust integer semantics, trusted compiler and successful allocation; limits and order as documented.
Evidence: 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling. See tests.md for execution and controls.
Status: partial_source_derived_model. No semantic AST or general proof.

### reverse-reconstruction

Type: reverse_reconstruction. Subject/revision: tests.rs sha256 426c850115b00d94b2c07a051fde0e4531ac009b793d92e1035e740061a40d16.
Domain: Finite native test inputs, literal fixtures and oracle outcomes for prim; trusted Rust harness. Vertex count and ordered undirected kruskal::Edge records with u64 weights, at most one million vertices and edges. Return kruskal::Forest with original indices in Prim acceptance order.
Observation: complete one-call return; tests observe named pass/failure.
Operator: Pre(y)={x in domain | R(x,y)} retains all compatible inputs. A passing harness observation has many compatible implementations agreeing on tested cases; failure identities retain every implementation/oracle pair producing that failure. No unique recovery or inverse executor is claimed.
Approximation: exact specification under stated assumptions; partial source correspondence.
Assumptions: standard Rust integer semantics, trusted compiler and successful allocation; limits and order as documented.
Evidence: 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling. See tests.md for execution and controls.
Status: partial_source_derived_model. No semantic AST or general proof.

### oracle-independence

Type: reference_separation. Subject/revision: tests.rs sha256 426c850115b00d94b2c07a051fde0e4531ac009b793d92e1035e740061a40d16.
Domain: Finite native test inputs, literal fixtures and oracle outcomes for prim; trusted Rust harness. Vertex count and ordered undirected kruskal::Edge records with u64 weights, at most one million vertices and edges. Return kruskal::Forest with original indices in Prim acceptance order.
Observation: complete one-call return; tests observe named pass/failure.
Operator: Hold generated input fixed and compare different recurrences or exhaustive subsets rather than a production wrapper. 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling. The extra cross-algorithm check for Prim does not replace its independent subset optimum.
Approximation: exact specification under stated assumptions; partial source correspondence.
Assumptions: standard Rust integer semantics, trusted compiler and successful allocation; limits and order as documented.
Evidence: 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling. See tests.md for execution and controls.
Status: partial_source_derived_model. No semantic AST or general proof.

### mutation-sensitivity

Type: falsification_boundary. Subject/revision: tests.rs sha256 426c850115b00d94b2c07a051fde0e4531ac009b793d92e1035e740061a40d16.
Domain: Finite native test inputs, literal fixtures and oracle outcomes for prim; trusted Rust harness. Vertex count and ordered undirected kruskal::Edge records with u64 weights, at most one million vertices and edges. Return kruskal::Forest with original indices in Prim acceptance order.
Observation: complete one-call return; tests observe named pass/failure.
Operator: One compiled implementation mutant and one purpose-specific false oracle/literal per family fail a selected named assertion. Passing restored tests certifies only these finite observations; failure does not identify a unique cause.
Approximation: exact specification under stated assumptions; partial source correspondence.
Assumptions: standard Rust integer semantics, trusted compiler and successful allocation; limits and order as documented.
Evidence: 4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling. See tests.md for execution and controls.
Status: partial_source_derived_model. No semantic AST or general proof.

### tests

#### Finite evidence

4 tests: 761 weighted simple graphs on 0..4 vertices, each possible edge absent/0/3, compared with independent subset spanning optimum and traversed components; Kruskal weight/component agreement; deterministic ties, parallel edges, loops, isolates, wide sum, limits, orientation and scaling.

2026-10-30: 310 unit tests pass twice debug and twice release, with identical normalized names/results (sha256 3f3c86b69fdc0e79e1f9d3e885301a424073b04198a1874f587647a2a6d07a4e). This file contributes four tests. Six compiled controls (one implementation and one test oracle per algorithm) fail named assertions; restored 310-test suite passes. Algorithm all-target strict Clippy and narrow rustfmt pass. Raw logs are external; no performance gain is claimed.

This source control log sha256: f107a209dfba0f4d1391e86f0fb12090c6cb3586fd92425f0f065e9b5f37f53f. False subset oracle reports best+1; exhaustive_forests fails.