> ## Documentation Index
> Fetch the complete documentation index at: https://mehen.ophi.dev/llms.txt
> Use this file to discover all available pages before exploring further.

# Markdown Halstead

> Halstead vocabulary and volume measured over Markdown-native operators and operands.

**Markdown Halstead** measures token vocabulary and volume using Markdown-native operators and operands
instead of code operators. It uses the same shape as
[source-code Halstead](/metrics/code/halstead) but with a documentation-specific operator/operand
taxonomy.

## Operators

* Heading markers by level (`#`, `##`, …).
* List markers (`-`, `*`, `1.`, …).
* Table delimiters (`|`, alignment markers).
* Link / image operators (`[…](…)`, `![…](…)`).
* Code-fence openers by language (` ```python `).
* Inline code, blockquote (`>`), math delimiters (`$…$`, `$$…$$`).
* Emphasis markers (`*`, `_`, `**`).
* Footnote operators.
* Raw-HTML / MDX / directive operators.
* Punctuation classes.
* Diagram DSL statement classes.
* Embedded-code operators.

## Operands

* Word-like tokens.
* Numeric / version tokens.
* Identifier-like tokens.
* Path-like tokens.
* Link destinations.
* Table headers.
* Image destinations / alt hashes.
* Code identifiers from embedded analyzers.
* Diagram node / edge labels.
* Math symbols and commands.

## Formulas

Same shape as source-code Halstead:

```text theme={null}
MDH_vocab  = n1 + n2
MDH_length = N1 + N2
MDH_volume = MDH_length · log2(max(2, MDH_vocab))
MDH_diff   = (n1 / 2) · (N2 / max(1, n2))
MDH_effort = MDH_volume · MDH_diff
```

## Embedded-code adjustment

Embedded analyzers contribute:

```text theme={null}
0.20 · sqrt(code_halstead_volume)
+ 0.50 · code_cognitive
+ 0.10 · code_loc
```

per code block. Raw embedded volume is square-rooted because it can otherwise dwarf document-level
signals; cognitive complexity stays linear because a hard example genuinely requires review.

## References

* Halstead, M. H. (1977). *Elements of Software Science.* Elsevier — the operator/operand model
  this metric ports to Markdown's token taxonomy.
  [OSTI record](https://www.osti.gov/biblio/5685613).
* Kearney, J. K., et al. *Software Complexity Measurement* — MIT lecture notes summarizing the
  Halstead operator/operand formulation.
  [PDF (MIT OCW 16.355)](http://sunnyday.mit.edu/16.355/kearney.pdf).

## See also

* [Halstead metrics for code](/metrics/code/halstead) — same formulas, different operator set.
* [DMI](/metrics/markdown/dmi) — uses MDH volume as one of its inputs.