README.old.md

Trees

Similar to https://github.com/rust-lang/rust-analyzer/blob/master/docs/dev/syntax.md#design-goals

• MathLayout: Green nodes, simply represent the formula's structure like { type: "frac", values: [top, bottom] }. Are immutable, and are built from the bottom up. Could be renamed to MathStructure.
  • Categories of nodes include: rows, containers, tables, symbols, text, errors
• MathLayoutZipper: Red nodes around it, a wrapper datastructure that keeps track of the parent nodes as you walk down the tree.
  • Also has editing utilities that create a new tree, which try to reuse as many of the green nodes as possible. As an implementation details, this is created lazily/on-demand. This means that they only incur an overhead when you actually use them.
• MathAst: An actually parsed representation of the formula, which tries to assign a meaning to each symbol. Like tagging digits as numbers, or taking |x| and deciding that it's the absolute value of x.

Sources:

• Eric Lippert explaining red-green trees https://ericlippert.com/2012/06/08/red-green-trees/ , also has a bit of info about "widths"/"ranges"/"absolute positions", just like this https://github.com/rust-lang/rust-analyzer/blob/master/docs/dev/syntax.md#greennode has
• Simple post about red-green trees https://blog.yaakov.online/red-green-trees/
• Roslyn archives https://github.com/KirillOsenkov/Bliki/wiki/Roslyn-Immutable-Trees
• Rust Analyzer https://github.com/rust-lang/rust-analyzer/blob/master/docs/dev/syntax.md

Structure

• Display: display on screen, keeps references to the layout ranges for editing
• Semantics: computed/parsed, keeps references to the layout ranges
• Layout: core, for editing, user-input
• Cosmetics: like colors or text annotations

Type Theory

• MathJson -> Typechecking -> Evaluation
• Catch errors before evaluating, like 1 + {1,2,3} would be "error: cannot add number and set"
• Figuring out the correct invisible operator, like
  • AB with A and B being vectors (vec from A to B)
  • ac with a and b being strings (concat)
  • (\x -> 3x)(x) with (\x -> 3x) being a function (apply)
  • 2x with x being a boring old value (multiply)
• Type inference for arbitrary expressions and functions
• https://en.wikipedia.org/wiki/Logical_framework
• https://en.wikipedia.org/wiki/Dependent_type#First_order_dependent_type_theory
• https://math.andrej.com/2012/11/08/how-to-implement-dependent-type-theory-i/

References

• Accessibility
• Canonicalize
• Test cases
  • cortex-js/compute-engine#11
  • cortex-js/compute-engine#10
  • cortex-js/compute-engine#13
• Examples
  • https://fred-wang.github.io/TeXZilla/
  • https://fred-wang.github.io/MathFonts/mozilla_mathml_test/
  • https://build-chromium.igalia.com/mathml/torture-test/mathml-torture-test.html
  • https://corpora.mathweb.org/corpus/arxmliv/tex%5Fto%5Fhtml/no_problem
  • https://fred-wang.github.io/TeXZilla/examples/customElement.html
  • https://fred-wang.github.io/MathFonts/
  • https://people.igalia.com/fwang/pell-bigint-mathml/
  • http://eyeasme.com/Joe/MathML/MathML_browser_test.html
• Mathml operator priority and this
• Mathml operators
• https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbols