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This is a toy Wolfram/Mathematica language interpreter written in Typescript. You can find a writeup about it here.

The goal of the project is for me to develop a better understanding of exactly how Mathematica works. I first wrote a toy differentiator in Mathematica that's good enough to differentiate many simple functions from a standard single variable calculus textbook:

D[_?NumberQ, x_Symbol] = 0;
D[x_, x_Symbol] = 1;
D[Times[expr1_, expr2_], x_Symbol] =
  D[expr1, x] expr2 + D[expr2, x] expr1;
D[Plus[expr1_, expr2_], x_Symbol] = D[expr1, x] + D[expr2, x];
D[Sin[x_], x_Symbol] = Cos[x];
D[Cos[x_], x_Symbol] = -Sin[x];
D[f_Symbol[expr_], x_Symbol] :=
  (D[f[x], x] /. x -> expr) * D[expr, x];
D[Power[expr_, p_Integer], x_Symbol] := p expr^(p - 1) * D[expr, x];

The ts-wolfram project implements enough of the Wolfram Language to successfully (and correctly) evaluate D on the following examples:

D[1, x],
D[x, x],
D[x^5, x],
D[3 x^2, x],
D[(x + 1) (x + 2), x],
D[x^2 + x^3, x],
D[Cos[x], x],
D[x^3/(x^2 + 1), x],
D[Cos[Cos[x]], x],
D[Cos[Cos[Cos[x]]], x],
D[Cos[x^2 + 1], x],
D[(x + 1)^2, x]

This has been a really fun and instructive project. Supported features are:

  • Literals: parses integers, symbols, forms, arithmetic operators, and lists. Multiplication is parsed correctly (i.e. a*b and a b both parse as Times[a,b]).
  • Attributes: HoldFirst, HoldRest, HoldAll, Protected, Flat. Also the builtins Attributes, SetAttributes, ClearAttributes.
  • Number functions: Plus, Times, Minus, NumberQ.
  • Form manipulation: currently only Head.
  • Pattern matching: MatchQ, HoldPattern, Pattern, PatternTest, Blank.
  • Term rewriting: Replace, ReplaceAll, ReplaceRepeated, Rule, DelayedRule.
  • Values: OwnValues, DownValues, Clear.
  • Evaluation control: Hold, CompoundExpression.

To use, clone the project and run:

npm install
npm run build && node dist/index.js