M / Mlang

In short: Mlang is the compiler the French tax administration’s own programs pass through; Arxo models what the code article says. The comparison is administration-versus-text fidelity on fixed inputs. This page is for readers who compute French income tax and need the exact semantic seams: undefined values, number representation, and yearly editions.

Key differencesChoosing and combiningEvidence & limitations

What Mlang is for

Mlang compiles DGFiP’s legacy tax language M: yearly administration sources plus a fixed-format test language with year fields, several backends (interpreter, C, Python) from one codebase, reproducible binary releases with asset hashes, and validation claimed against the administration’s private suite. Its core carries a mechanically checked semantics with verbatim undefined-value rules instead of ad hoc nulls — the strongest formal claim in this section.

Where it meets Arxo

Both sides compute French income tax on fixed inputs — the administration’s program against a model written from the code article text — with sums compared after the statute’s rounding rule. The studied fragment is one marginal bracket with family quotient and rounding; deontics, presumptions, article-level provenance, and judgment requests are out of this calculator language’s purpose, and out of the comparison.

Key differences

• Undefined is a language property with fixed rules. Addition and subtraction absorb it, multiplication and comparisons propagate it, min-max treat it as zero, division by zero yields zero, branching on it yields it. Arxo refuses on missing facts. Fixed semantic pairs, not matches — the contract lists them before any run.
• Numbers are administration fidelity. Binary floating point by default, “what the administration uses”, with precision flags; rounding primitives are identity stubs in the formalization. Arxo money is exact decimal. Compare after the statute’s rounding, never before.
• Each year is a separate source drop, not a language revision construct. Edition comparison here means swapping yearly drops and drivers, and one edit case tests driver invariance rather than law.
• The administration thesis is currently untestable in public. The yearly administration sources have no public project and their license is undetermined; the private validation suite is author-stated, not verified here. The page narrows every dependent claim accordingly.

A concrete scenario

Twelve fragment cases — mid-bracket, exact thresholds plus and minus one euro, zero, negative, and missing income, split family parts, half-euro rounding, a zero-parts control — plus three edits: a scale-year change, a discount on and off, a driver-generation swap. Totals compare side by side; the upper bracket is honestly outside the micro-model.

Choosing and combining

Choose Mlang when the deliverable must match the administration’s own computation bit for bit, with a checked core behind it. Look to Arxo when the question is what the article text supports — including refusal where the text is silent — with dated editions and reviewable grounds. Combined, the compiler holds administration fidelity while Arxo holds textual fidelity, and their divergence points are exactly where a reviewer should look.

Evidence and open questions

• Sources checked: September 2026, second pass (repository, formal semantics file, release assets with hashes, the semantics paper, and administration brochures).
• Studied profile: the compiler at its release pin; the yearly administration sources are not publicly available and unfrozen.
• Basis: confirmed by documentation plus a prepared protocol; comparative run not performed, with no subject-package on the Arxo side beyond the unexecuted stand.
• Open: source availability and licensing, production-transition and private-suite claims, and the run itself.

Sources and reproducible materials

• Compiler project: github.com/MLanguage/mlang
• Formal semantics paper: arxiv.org/abs/2011.07966