Write down what the grammar accepts, and correct three statements that were not true (#746 items 8, 74)

[Rafael-SOWNet]

Docs/Usage/Syntax.md is the only statement of this language other than the grammar itself, so what it omits is undiscoverable and what it gets wrong is worse than nothing. #746 item 8 asks for the omissions and item 74 for the wrong statements.

How the list was derived

Not taken from the roadmap's count. Every function-open literal in Sources/AngouriMath/Core/Antlr/AngouriMath.g — 102 of them — checked by name against the page, plus the non-function productions of atom, the lexer rules (NUMBER, BOOLEAN, VARIABLE, COMMENT, NEWLINE) and the token insertion in Core/Parser.cs. That left 20 function names and 15 features undocumented.

Added

sum, product	the operators that declare a name over a range — the headline of item 8
exp, log10, log2	and log with one argument, which is base 10
inverse hyperbolics	the a- spellings of all six, and the five refusals beyond arcsinh
(|x|)	absolute-value brackets
True, False	which is what Stringize prints
//, /* */, newlines	skipped by the lexer
.5, 1., 3i, 1.5e3i	number literal forms
ExplicitParsingOnly	the setting that turns implicit operators off
Cyrillic	a letter in a name, as much as Greek

sum and product get their own section, since getting the argument order wrong is the difference between 55 and something else, and since the declared name shadows what it would otherwise mean: sum(i, i, 1, 10) is 55, sum(sqrt(-1) * i, i, 1, 10) is 55i, product(pi, pi, 1, 4) is 24, and a name that outlives its operator comes back as pi_1.

Corrected

The variable-name rule, which said "a letter or _ followed by letters, digits or _". The grammar is letter+ ('_' (letter|digit)+)? and disagrees four ways:

"_x".ToEntity();     // lexer error -- a name cannot begin with _
"x_".ToEntity();     // lexer error -- nor end with one
"x_1_2".ToEntity();  // lexer error -- at most one _ (#524)
"x1".ToEntity();     // x ^ 1, not a name: a digit is not a letter
"альфа".ToEntity();  // a name -- Cyrillic, which the page did not mention

sinx is s * i * n * x — a third wrong statement, not in the roadmap's count. It is false: the lexer takes the longest match, so sinx is one variable named sinx. Nothing in this language produces a product of one-letter names.

"Juxtaposition is multiplication" is half of it, and the missing half is the surprising one. A number, name or ) followed by a number inserts ^:

"x2".ToEntity();   // x ^ 2
"x(2)".ToEntity(); // x * 2
"x i".ToEntity();  // x ^ i  -- i is a number token
"3 2".ToEntity();  // 3 ^ 2

Already fixed, so left alone: item 74's other statement — everything but ^ groups to the left — was corrected by #1009 when the printer was fixed. The roadmap entry predates that merge.

Recorded rather than fixed

• Stringize drops a codomain, so domain(x, ZZ) prints as x (Stringize drops a node's Codomain, so domain(x, ZZ) prints as x and does not round trip #1022).
• A // comment that ends the input is a parse error, because COMMENT requires the newline. Filed as A // comment that ends the input is a parse error, because the lexer rule requires the newline #1039 from this work — a grammar change means regenerating the ANTLR parser and is its own change.
• [] reaches MathS.Vector's IndexOutOfRangeException through the parser and not only through the API; noted on SumAll, MultiplyAll and ToVector throw an internal bug exception on an empty sequence, where ToSet and ToPiecewise answer #1028 rather than filed again.

Measured

Sources/Tests/UnitTests/Convenience/SyntaxDocumentedTest.cs runs every example the page prints — the precedence table row by row against explicitly bracketed forms, the four shapes that are not names, both juxtaposition rules, ExplicitParsingOnly, the number and boolean spellings, comments, the inverse hyperbolic table, and sum/product including what the declared name shadows. It compares entities, never printed forms.

7930 passed, 0 failed, 14 skipped   (7825 / 0 / 14 before; the 105 are this file)

No library code is touched, so no answer changes and BREAKING-CHANGES.md is owed nothing. The new test file carries the default 2019-2022 header — Sources/.editorconfig pins it and belongs to other pull requests this cycle, so no 2026 scope was added there.

🤖 Generated with Claude Code

https://claude.ai/code/session_01Bjumi5K7fg8yx6UK1mZTQd