Structural arithmetic implementation record

NoteHistorical planning and delivery record

This page preserves earlier plans and completion notes; proposed APIs and remaining-work statements below are not the current implementation contract. Use the history index for links to current guides.

All items from the first backtick-parser follow-up are implemented. This page remains as the completion record and as a compact index to the supported surface.

Parser surface

• Add comments inside .SArith bodies.
• Add the remaining RiX exact literal spellings, including mixed numbers, continued fractions, explicit bases, and intervals.
• Extend the initial ambiguity diagnostics (-x^2, -x!, 1/2!, and 1/2^3) as new prefix and postfix forms are added.
• Add explicit function parameter declarations, such as .SArith.Fun(y,x):body, when parameter order or unused parameters must be supplied rather than inferred.

Structural algebra

• Add configurable constructor/operation tables for custom operator glyphs, fixity, precedence, and associativity.
• Add deliberate rules for unequal-denominator fraction addition. Applied addition now uses a least common denominator while retaining Fraction.
• Add canonical flattening policies for nested Sum and Product forms.
• Add public inspection, rendering, collapse, and transformation methods on structural values.
• Add domain-aware cancellation with explicit nonzero assumptions.

Parser plugins and tooling

• Add a RiX-level helper for constructing registered parser objects without host JavaScript.
• Add CodeMirror mixed-language highlighting selected by the leading-dot parser header.
• Add structured source spans to every secondary-language node rather than retaining only errors relative to the backtick body.
• Remove the transitional uppercase LANG(context):body parser syntax after downstream uses have migrated to .Name:body.