math-ast

AST for symbolic math

Motivation

The goal of this project is to enable software that manipulates math expressions to interoperate.

There are a number of free symbolic math libraries for JavaScript. Each has its own syntax and more important its own AST.

Having a common AST is an ideal way to enable interoperability as evidenced by Mozilla's Parser API and all of the tools that sprung up around it.

For symbolic math, a common AST would allow for different parsers, renderers, solvers, and other tools to all interoperate with each other.

Scope

The hope is to cover K-12 and undergrad math and science.

Key Ideas

• AST is data only
• use similar node structure
• avoid one-off nodes
• any node type can be the root of the AST

Parser Notes

• An AST produced by a parser must only be syntatically valid although a parser may choose to enforce some level semantic correctness as well.
• In the absense of semantic information, parsers are encouraged to generate the most general nodes, but are free to make their own assumptions.
• Parsers are free to define their own syntax. One parser may decide to treat abc as a single identifier whereas another might treat it as implicit multiplication between a, b, and c. Software that manipulate ASTs should ensure that they can handle multi-character strings for identifiers because this is what's in the spec.

TODO

• A reference parser (wip) that produces a math AST according to the spec.
• A formatter that accepts a math AST object and outputs TeX code.
• A set of helper functions:
  • isExpression, isProduct, isFraction, etc.
  • hasCommonDenominators
  • findCommonTerms
• A function to manipulate math ASTs by replacing certain nodes.
• A set of useful transforms:
  • adding 0 is a no-op and can be revemoved
  • multiplication by 1 is a no-op and can be removed
  • intervals can't be closed when either end is +/- infinity
  • division by 0 is undefined or +infinity or -infinity depending on the exact situation.
  • raising 0 to the 0 power is undefined
• Semantic knowledge that can be used to determine whether a transform is valid:
  • addition/multiplication are commutative and associative for these operands
  • multplication does not commute for matrices