mathlang

A small language I'm writing to learn more about compilers/virtual machines/optimizers/type checkers/etc. without using dependencies.

Roadmap

• Playground plotting
• Playground backend
• Playground operator ligatures
• Language server (https://github.com/microsoft/vscode-extension-samples/tree/master/lsp-sample)
• Inline function optimizer
• Conditionals
• Units on numbers
• Better error messages
• Better type checking messages

Syntax

Basics

Each line is considered its own statement, and can be:

• a mathematical expression
• a function definition
• a local variable assignment

Expressions

Expressions looks like you would normally express math on paper. Here are some examples:

• 1 + 2 + 3
• 2 - 3 - 4
• 3 * 4 * 5
• 4 / 5 / 6
• 7^8
• (1 + 2) * 3

Implicit multiplication

Writing a number and then a variable will imply multiplication, as in:

x = 2
3x

Functions

Functions are local to whatever context you're currently in (top-level or another function). They become defined wherever you define them and are not hoisted (so you can only call them after you've declared them, there are no forward-declarations). They support implicit returns, so whatever the final expression in your function body will be what is returned. Here is an example:

f(x) = x * 3

You would then be able to call that function with:

f(x)

You can also define more complex functions using the multi-line layout, as in:

f(x) = {
  y = x * 2
  y + 1
}

Built-in

A couple of functions comes built-in to the runtime. Those include:

• add(x, y) - add two numbers
• div(x, y) - divide two numbers
• exp(x, p) - raise a number to a power
• ln(x) - get the natural log of a number
• log(x) - get the base10 log of a number
• mod(x, y) - get a number modulo a base
• mul(x, y) - multiply two numbers
• neg(x) - negate a number
• sqrt(x) - get the square root of a number
• sub(x, y) - subtract two numbers

Local

There is support for local variables either at the top-level or inside a function. Local variables are only scoped to their current context and are not inherited by inner functions. They are untyped, as the only type at the moment is a number. Here are examples of setting and using local variables:

a = 5
f(a * 5)

Running

For now you can run bin/math.ts [path/to/file] or you can pipe a script into it, as in echo "1 + 2" | bin/math.ts.