Print what the parser reads

[Rafael-SOWNet]

Stringize's contract is that parsing what it prints gives back what was printed. Four kinds of expression broke it, and all four broke it silently — a wrong reading is still a valid expression, so nothing threw.

The one that changes a value

var e = MathS.FromString("(2 ^ 3) ^ 2");
e.Evaled                          // 64
e.Stringize()                     // "2 ^ 3 ^ 2"
e.Stringize().ToEntity().Evaled    // 512

Powers group to the right, so it is the base that needs bracketing when it is a power of its own — the mirror of the rule the left-associative operators use (Divf already does < on the left and <= on the right; Powf needs the opposite). Latexise had it right all along, which is how I knew where to look.

The three that come back as a different node

	printed as	came back as
lambda(x, x + 1)	x -> x + 1	x implies x + 1 — -> is the implication operator
apply(lambda(x, x + 1), 2)	(x -> x + 1) 2	(x implies x + 1) ^ 2
piecewise(1 provided x > 0)	(1 if x > 0)	1 * if * x > 0 — if read as an undeclared variable
piecewise(1 provided x > 0, 2 provided x < 0)	(1 if x > 0, 2 if x < 0)	parse error

None of -> for lambda, juxtaposition for application, or if for piecewise is in the grammar. They now print as the function call the parser does have: lambda(x, x + 1), apply(f, 2), piecewise(a provided p, b provided q). The piecewise one is the same class of defect as #687 — a printed form that comes back as an implicit product of undeclared variables.

Latexise is untouched. Nothing parses LaTeX, so it is under no such obligation.

Tests

A round-trip test over 98 expressions covering every node kind — arithmetic and grouping, all the trigonometric and hyperbolic families, calculus nodes, booleans and comparisons, sets and intervals, matrices, numbers, and the four above. It went from 88/98 to 98/98.

Worth recording what the ten failures were, since two of them are not bugs: the hyperbolic and inverse-hyperbolic functions, cbrt and sqr are rewritten as they are parsed — sinh(x) is (e^x - e^(-x))/2 and arsinh(x) is ln(x + sqrt(x^2+1)) — so they never print back as themselves. What round-trips is the expression, not the spelling, and the test asserts that.

Also: a syntax reference

Sources/AngouriMath/Docs/Usage/Syntax.md. There was none, and the grammar was the only statement of what the language accepts — which is ANTLR source, and not something a user reads. It covers the precedence table, the round-trip contract, the function names, and a short list of the things that catch people out (^ groups right; an unknown name is a silent product; intervals use ; where vectors use ,; -> is implication). Every claim in it was checked against the parser rather than read off the grammar.

Suite: Failed: 0, Passed: 4461, Skipped: 14, Total: 4475 — no existing test had pinned the wrong output, so nothing needed its expectation changed.

Independent of #703 and #705.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 81.79%. Comparing base (90c00a8) to head (b578dc7).
⚠️ Report is 79 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #706      +/-   ##
==========================================
+ Coverage   80.99%   81.79%   +0.80%     
==========================================
  Files         155      159       +4     
  Lines       13687    13795     +108     
  Branches     1957     2329     +372     
==========================================
+ Hits        11086    11284     +198     
+ Misses       1990     1858     -132     
- Partials      611      653      +42     

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