---
title: "mlab-numerics-reduce-folds — Mova code model"
description: "Mova code model of mlab/src/builtins/reduce.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/mlab/src/builtins/reduce.rs.groupant/reduce-folds.groupant/"
---
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# mlab-numerics-reduce-folds

The groupant beside mlab/src/builtins/reduce.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:** [`mlab/src/builtins/reduce.rs`](https://github.com/ElamurAI/mova-free/blob/main/mlab/src/builtins/reduce.rs)
- **source SHA-256:** `0f9cbbd92e1b1868…`
- **covers:** slices(dim1) lists column indices j*rows+i, dim2 row indices, else singleton. reduce_c folds (init,0) with complex operation and returns shaped result; absent dim on0x0 yields scalar init. cumulative uses same slices but real-only running accumulation. (bytes 3864–5763)
- **part of:** [mlab-numerics-reduce](https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/reduce.rs.groupant/)
- **repository folder:** [`mlab/src/builtins/reduce.rs.groupant/reduce-folds.groupant`](https://github.com/ElamurAI/mova-free/tree/main/mlab/src/builtins/reduce.rs.groupant/reduce-folds.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` |
| **cost** | symbolic source derived | [invariant](#invariant) |
| **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) |
| `column_fixture` | column_fixture | partial source derived model | [column_fixture](#column-fixture) |
| `identity` | identity | partial source derived model | [identity](#identity) |
| `explicit_empty` | explicit_empty | partial source derived model | [explicit_empty](#explicit-empty) |
| `real_scan` | real_scan | partial source derived model | [real_scan](#real-scan) |

## Model text


### descriptant

#### mlab-numerics-reduce-folds

slices(dim1) lists column indices j*rows+i, dim2 row indices, else singleton. reduce_c folds (init,0) with complex operation and returns shaped result; absent dim on0x0 yields scalar init. cumulative uses same slices but real-only running accumulation.

##### Modeling epoch 2026-10-31

Prospective source reading preceded inline tests. This node records implementation behavior, not a complete MATLAB compatibility contract. Models retain limits discovered in source reading, including real-only projections and warning-only result gates. Synthetic CPU fixtures are independent of frozen suites. No external effects, teacher, corpora or benchmark main are executed.

### approximant

#### Forward relation

slices(dim1) lists column indices j*rows+i, dim2 row indices, else singleton. reduce_c folds (init,0) with complex operation and returns shaped result; absent dim on0x0 yields scalar init. cumulative uses same slices but real-only running accumulation.

Executable Rust surrogate gap: no calibrated replacement is attached. Exact test calls are evidence for the reference, not a fast approximant. Numerical approximants would need a named domain, zero convention and metric at supported caps 1/2/5/10%; categorical errors/effects have no percent surrogate here.

### invariant

#### Invariants and cost

Output shape dim1=1xcols,dim2=rowsx1,else original. Complex storage narrows via Mat::complex only for reduce_c.

##### Cost

O(N+S) fold, slice-index/vector-header allocation and output storage; cumulative O(N+S) plus cloned real cells. For0xM at dim1, N0 but S=M identity outputs.

Allocation failure, unchecked usize dimension arithmetic and IEEE nonfinite propagation are outside finite fixture guarantees. No measured throughput or global accuracy claim.

### models

## Typed source models: mlab-numerics-reduce-folds

### behavior_complement

No default empty fold calls f. Singleton higher dimensions exclude cross-cell accumulation. cumulative excludes imaginary dependence.

### reverse_reconstruction

Given sum result, compatible inputs have the requested shape and per-slice sum; product fibers depend on zeros and scaling pairs. Cumulative real sum can be differenced along same dimension absent rounding, but cannot recover imaginary input.

### column_fixture

2x2 re[1,3,2,4] summed dim1→1x2[4,6].

### identity

0x0 with no dim and init1 returns scalar1 before slicing.

### explicit_empty

Explicit dim changes empty handling, producing shape derived from slices rather than scalar shortcut.

### real_scan

cumulative output is new real Mat even for input with im; no complex prefix-product claim.


### tests

#### Evidence and limits

Selected wave30_tests exercise this source; fragment-specific limits are stated in its operators.

Native command specifications, numeric exits, profile-paired logs, compiled controls and exact-restoration receipts are retained externally in the wave30 numerics run. Tests exercise actual source, not a copied model. The selected finite fixtures do not prove full convergence, backend accuracy on all matrices, resource exhaustion or side-effectful callback behavior.