DesmosPlus

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Write less. Say more. DesmosPlus is a text-based language that compiles to Desmos graphs.

The main objective of the language is to make all code easier to use and remove repetitive actions.

Examples:

• If you want to recreate the physics formulae in https://www.desmos.com/calculator/uutnykxaiu, you don't need to copy-paste the gravitation equations many times; you can just declare a function that takes lists and returns the net force.
• If you want to make a 3D engine, you don't have to keep track of three lists of x, y, and z: you can just use a list of Point3D
• If you want to write a ton of polygon s like https://www.desmos.com/calculator/br3mu4hqxc, you can map a show polygon over a list (with compile-time length)

The language is in active development, and development is proceeding here at http://github.com/jared-hughes/DesmosPlus.

Design philosophy

• Everything possible in Desmos should be possible in DesmosPlus as well at similar or better convenience.
• It should be easy for a human to translate Desmos graphs to DesmosPlus; hence, DesmosPlus syntax should be as similar as possible to Desmos while still maintaining convenience
• DesmosPlus is not a strict superset of the Desmos syntax. DesmosPlus does not make an attempt to handle LaTeX expressions, but I think there's TeX to text converters if you want to paste expressions from existing graphs.
• Compiling DesmosPlus code may not always produce idiomatic Desmos code. The compiled output will, in most cases, be readable Desmos code, but this is not guaranteed.
• DesmosPlus is a functional language like normal web Desmos; variables are generally immutable, and the order of statements does not affect execution.

Reference

To see official, correct examples of DesmosPlus syntax, see the examples.

See ARCHITECTURE.md for an overview of the code.

To see a somewhat-complete guide of the language (also a language spec to some degree, evolving until initial release), read:

• Syntax
• Types
• Statements
• Standard Library

Progress Timeline

Current progress to 0.1 release (custom types and feature parity with Desmos):

• Language design: 80% (100% = includes all features of desktop Desmos)
• Lexing and Parsing: 80% (100% = can parse all of that)
• Visitor and Execution: 25% (100% = can reproduce any glitchless Desmos graph in DesmosPlus)

Comparison With Desmos

Advantages

• Split functions and expressions across multiple lines
• Use long variable names without subscripts
• Custom data types
• First-class booleans
• Recursive functions (limited)
• Lists can be passed into functions
• ... more!

Disadvantages

• Need to compile
• Not (fully) implemented (or designed)

Contributing

Contributions are welcome. Feel free to send pull requests or open issues!

Some quick notes for development:

For syntax development:

• I'm using language-antlr4 Atom package for syntax highlighting.
• https://github.com/antlr/Antlr4Formatter to format .g4 code

TODOs / Random ideas

Short-term

• Scope should be stored in construction of an Expr instead of passed down through the ENTIRE chain
• Use proper type inference and allow for Any type
• Allow for f(a)=2*a and a=f(1) to be compatible
• Reduce confusion between (FunctionExpression).args and (FunctionExpression).resolvedDefinition.args be renaming the latter to .argVariables
• Store local variables in a stack instead of localVars/globalVars
• typeclasses with increasing specificity to automatically define _add(Any, Any) (add similar) by adding corresponding terms, but can be overridden by defining _add(MyType, MyType)
• Enforce capital/lowercase conventions? Otherwise need some check to prevent collisions like def Fun(x)=x^2 and type Fun@{x:1}
• Some throws don't have line nums
• bugs, bugs, bugs
• Maybe make graph a synonym for show? May complicate things though
• Graphing polar functions: should these just be parametrics?
• Should Num be changed to Float? Maybe Num should be a synonym for Float?
• /* ... */ multiline comments desired?
  • would both be viable? ;)
• regression syntax (along with a way to get regression parameters and other generated values such as the R^2 value?).
  • Prefer to use ~ but could also use ==
  • The hard decision is how to capture the output. Maybe [$a, $b, $r2] ← Regress(y1==a*x1+b) or something
• Add absolute value with pipes |expr|
• Add factorial with bang !
• How to determine default colors?
• Add tuple type? Do we even need to have Point as a primitive?
• _get([Any], [Num])
• Reversal inferencing like __rmul__ in python. So you only need to define _mul(a:Num, z:Complex) to allow executing both 5*Complex(1,2) and Complex(1,2)*5

Medium-term

• unused variables warning
• clearer error messages
  • "Piecewise conditions must have type Bool" → specific condition that lacks type Bool
  • point to error in desp code. Should be simple with ctx.line and ctx.col
• Enum type? To represent e.g lineStyle∊["DASHED", "DOTTED", "SOLID"]
• Syntax for summations/products/integrals
• default fields in custom types (e.g. default step: 1 for Intervals)
• Provide a way to set the name of the graph or other graph metadata like axes, random seed, degrees/radians, etc.
  • choose a slider/simulation to start playing on initial graph load
• multiline strings (helpful for folder descriptions)
• map blocks over const arrays, at least to get a list of polygons
• allow statement types/other special tokens as field names? Javascript allows a = {function: 1}; a.function and it shouldn't be too hard to work into the parser?
• string interpolation syntax ... or maybe just show function and concat
• string escape sequences. Main ones being \n and \t for note formatting but also \"
• Vectorization syntax, e.g. [1,2]+[3,4]==_add([1,2], [3,4]) while [1,2]+/[3,4] == [_add(1,2), _add(3,4)] or maybe [1,2]+.[3,4] == [_add(1,2), _add(3,4)]
  • This could be handled with map + zip
• Operations on Intervals
• Need to make x, y, t, etc. reserved in some way?
  • Do not remove the ability to have x as a custom type field
  • Do not remove the ability to have x as a function argument
  • Do remove the ability to let x=... and const x=..., etc.
• Can't do arithmetic on VariableReferences and other types. Can these be taken up to a FullExpr rule?
• Unicode synonyms ≤≥≠×÷∨∧≡← maybe.
• Some general format to allowing casting Num to Complex?

Long-term

• Allow for DesmosPlus packages (e.g. 3D/complex libraries, root-finding libraries)
• show [Point] should have metadata option to enable bezier curve fitting;)
• 2D arrays??
• Option to embolden notes
• Make a slider of points to avoid needing several variables
• images lol
• Allow nested folders and prepend something to folder name on Desmos export
• errors for incorrect identifiers include fuzzy matching "Maybe you meant ____"

Random Notes

• If a list is defined in a table column, it need not be defined in its own let block