YAML

L[yaml] is every text that is one YAML document, read as YAML 1.2, the current version of the spec. Membership is decided by ruamel.yaml's safe loader, installed with pip install "mathema-language[yaml]".

What makes YAML worth a language of its own is the gap between what someone writes and what a loader returns. PyYAML, the loader most Python code uses, reads by the older YAML 1.1 rules, and several plain-looking values change meaning there:

Written	YAML 1.2 (L[yaml])	PyYAML (yaml.safe_load)
country: no	'no'	False
on: push	key 'on'	key True
mode: 012	12	10
t: 1:20	'1:20'	80
x: 1e3	1000.0	'1e3'
python: 3.10	3.1	3.1
released: 2026-10-10	a date	a date

These are the language's hazards, visited before any random document, with the others a config file meets in practice: a comment after a value, a byte-order mark, Windows line endings, an empty document, deep nesting. Outside the language are the texts no YAML reader accepts: a tab in the indentation, a key given twice, a: b: c, an unclosed bracket, two documents in one text.

A worked claim

The shop's deploy tool reads its configuration with PyYAML, from examples/shop/deploy.py:

def read_config(text: str) -> object:
    """A deploy configuration as the deploy tool reads it."""
    return yaml.safe_load(text)


def replicas(text: str) -> int:
    """How many copies of the service a configuration asks for, 1 when
    it does not say."""
    return int(yaml.safe_load(text).get("replicas", 1))

Comparing the tool's reading with YAML 1.2's, wherever the tool reads the text at all:

f = read_config
let reference = mathema_language.text.yaml_language.load, for text in L[yaml], assuming is_defined(f), f(text) == reference(text)
    falsified   text = '1:0': 60 vs '1:0'

1:0 is the text '1:0' in YAML 1.2, and sixty to PyYAML, which reads it as a base-sixty number; the same holds for a time written 1:20. A deploy tool reading country: no gets False the same way.

A loader that assumes a mapping fails on documents that are not one:

f = replicas
for text in L[yaml], is_language_defined(text)
    falsified   text = '' (inside L[yaml]) raised AttributeError…

An empty file is a YAML document, and it loads as None, which has no .get.