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

# matrix-expression

The groupant beside models/matrix-expression.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:** 7
- **repository folder:** [`models/matrix-expression.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/matrix-expression.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) |
| `layout-transport` | representation_transport | partial source derived model | [layout-transport](#layout-transport) |
| `syntax-context` | context_partition | partial source derived model | [syntax-context](#syntax-context) |
| `validation-order` | failure_precedence | partial source derived model | [validation-order](#validation-order) |
| `effects` | effect_boundary | partial source derived model | [effects](#effects) |

## Model text


### descriptant

#### matrix-expression: wave30

lexer space_before distinguishes [1 -2] from [1 - 2]; Caret and DotCaret are both left-folded by the parser, retaining distinct Pow and EPow tags. Interp resolves End to dimensions and dispatches index/ops/core. value column-major layout must survive index gather and core reshape; transpose permutes it. ops short-circuit logic belongs to interp/vm; core callbacks, files, RNG and timer effects cross group and remain unexecuted here.

This source-bound partial group organizes existing Mova code. Native evidence and excluded effects are recorded in source sidecars and the root wave30 report. Registration is not a universal proof or whole-system runtime claim.

### model

## matrix-expression

### forward

text --lexer(context,space,line)--> tokens --parser(precedence,index_depth)--> AST --interp/vm caller--> column-major Value; index selects/mutates k=j*r+i; ops broadcasts or multiplies values; core creates/reshapes and delegates range/concat. Shape is part of output: vector selection, colon columnization, reshape and transpose differ.

### invariant

On bounded well-formed matrices len(re)=r*c and optional im same length; transpose is a permutation, reshape retains flattened data, ordinary bounded assignment validation errors precede mutation. No universal validity from public fields, no finite arithmetic guarantee, and AST representation is distinct from evaluation.

### cost

Lexing O(chars+tokens); ordinary parsing O(tokens) with speculative reparsing and unbounded nesting caveat. Matrix storage/transforms O(cells); indexing O(indices+output/growth), deletion may sort; broadcast O(output), multiplication O(mnk) or delegated faer; callbacks, allocation and effects add unbounded costs. No speed measurements.

### composition

lexer space_before distinguishes [1 -2] from [1 - 2]; Caret and DotCaret are both left-folded by the parser, retaining distinct Pow and EPow tags. Interp resolves End to dimensions and dispatches index/ops/core. value column-major layout must survive index gather and core reshape; transpose permutes it. ops short-circuit logic belongs to interp/vm; core callbacks, files, RNG and timer effects cross group and remain unexecuted here.

### domain

CPU synthetic bounded strings and well-formed matrices with finite modest indices/dimensions/range spans; no GPU, datasets, external API or live filesystem effects.

### limitations

Source-derived relations; caller enforces valid buffers and resources. f64 NaNs, infinities, casts and zero behavior follow source branches, not mathematical ideal arithmetic. Seven tests observe specific contracts, not all source branches.

### checks

- ast::wave30::representation
- lexer::wave30::context
- parser::wave30::precedence
- value::wave30::layout
- index::wave30::gather_update
- ops::wave30::arithmetic
- builtins::core::wave30::constructors

### catalog

### behavior-complement

Accepted bounded composition excludes erased matrix whitespace, right-associated unparenthesized powers, row-major reinterpretation, broadcast of incompatible non-singleton dimensions and successful shape-changing reshape with unequal numel. It does not exclude public malformed values, nonfinite arithmetic or core side effects.

### reverse-reconstruction

For observation y, compatible antecedents are text/AST/state triples whose parse/evaluation gives y. Comments and spellings, overwritten/deleted cells, broadcast operand factorizations and reshape dimension syntax cause ambiguity. Transpose is uniquely invertible only on valid recorded Mat; reshape requires original shape; indexing fixes selected cells only.

### layout-transport

Mat index k=j*r+i is preserved by reshape buffers, permuted to i*c+j by transpose and gathered by index; substituting row-major storage breaks all three joins.

### syntax-context

Lexer preserves whitespace and newline observations; parser contextual sign boundary and index_depth transform them into Matrix/Unary/End versus subtraction/identifier branches.

### validation-order

Whole lex precedes parse; index validates selected shape before growth; core reshape computes its unchecked known-dimension product before hole counting, then on bounded arithmetic checks hole count before divisibility/rank/product; error order cannot be commuted across adapters.

### effects

Most value/lexer/parser paths allocate only; index mutates target after bounded checks; ops linalg may warn; core can mutate interpreter/RNG and inspect files/time or invoke callbacks. Pure helper test evidence never certifies those effects.